LLEMA: Evolutionary Search with LLMs for Multi-Objective Materials Discovery
Authors: Nikhil Abhyankar
Sanchit Kabra
Saaketh Desai
Chandan K. Reddy
Venue: ICLR 2026 Poster (2026)
Keywords: Large Language Models
Evolutionary Optimization
AI for Science
Materials Discovery
Primary area: foundation or frontier models, including LLMs
TL;DR: LLM-guided Evolution for Materials design (LLEMA) is a unified evolutionary framework that couples the scientific knowledge embedded in large language models with chemistry-informed evolutionary rules and memory-based refinement.

Abstract: Materials discovery requires navigating vast chemical and structural spaces while satisfying multiple, often conflicting, objectives. We present LLM-guided Evolution for MAterials discovery (**LLEMA**), a unified framework that couples the scientific knowledge embedded in large language models with chemistry-informed evolutionary rules and memory-based refinement. At each iteration, an LLM proposes crystallographically specified candidates under explicit property constraints; a surrogate-augmented oracle estimates physicochemical properties; and a multi-objective scorer updates success/failure memories to guide subsequent generations. Evaluated on **14 realistic tasks** that span electronics, energy, coatings, optics, and aerospace, LLEMA discovers candidates that are chemically plausible, thermodynamically stable, and property-aligned, achieving higher hit rates and improved Pareto front quality relative to generative and LLM-only baselines. Ablation studies confirm the importance of rule-guided generation, memory-based refinement, and surrogate prediction. By enforcing synthesizability and multi-objective trade-offs, LLEMA provides a principled approach to accelerating practical materials discovery. Project website: https://scientific-discovery.github.io/llema-project/

Published as a conference paper at ICLR 2026
LLEMA: EVOLUTIONARY SEARCH WITH LLMs FOR MULTI-OBJECTIVE MATERIALS DISCOVERY
Nikhil Abhyankar' Sanchit Kabra'
Saaketh Desai Chandan K. Reddy'
Department of Computer Science, Virginia Tech
2 Center of Integrated Nanotechnologies, Sandia National Laboratories
ABSTRACT
Materials discovery requires navigating vast chemical and structural spaces while satisfying multiple, often conflicting, objectives. We present LLM-guided Evolution for MAterials discovery (LLEMA), a unified framework that couples the scientific knowledge embedded in large language models with chemistry- informed evolutionary rules and memory- -bsed refinement. At each iteration, an LLM proposes crystallographically specified candidates under explicit property constraints; currogate-augmente oracle estimates physicochemical properties; and a multi-objective scorer updates success/failure memories to guide subsequent generations. Evaluated on 14 realistic tasks that span electronics, energy, coatings, optics, and aerospace, LLEMA discovers candidates that are chemically plausible, thermodynamically stable, and property-aligned, achieving higher hit rates and improved Pareto front quality relative to generative and LLM-only baselines. Ablation studies confirm the importance of rule-guided generation, memory- based refinement, and surrogate prediction. By enforcing synthesizability and multi-objeccivve trade-offs, LLEMA provides principled approach accelerating practical materials discovery.
Code http:://aagguunnee..oo//tttttttt
Dataset
INTRODUCTION
Materials discovery requires identifying or designing materials with properties tailored a specific task. However, the immense combinatorial space of chemical and structural compositions makes the traditional discovery process resource-intensive and slow (Hautier et al. 2012, Davies et al. 2016). While machine learning has significantly accelerated materials screening. its effectiveness is often constrained by the availability of large, high-quality labeled datasets, limiting performance in data- scarce regimes (Chang et al. 2022, Xu al. (023). Trained vast text corpora, including scientific literature, large language models (LLMs) offer a means to inject prior knowledge, making them promising tools for scientific discovery in data-scarce settings (White) 2023). Recently, LLMs have been leveraged to bridge natural language and material science, using textual knowledge to generate and refine hypotheses (Jia al., 2024 Sprueill et al., 2024 Ghafarollahi & Buehler 2025 Kumbhar eet al. 2025). However, most existing methods rely on prompt engineering or unguided material generation, often producing candidates that are theoretically plausible yet unstable or impractical to synthesize. Moreover, they typically formulate materials discovery as a single-objective task, optimizing for one property (e.g., bandgap, stability, or conductivity) in isolation, whereas real-world materials discovery is inherently multi-objective (Gopakumar et al. 2018), requiring trade-offs among competing targets such as electrical conductivity and thermal resistance in thermoelectric materials (Hao et al. 2019).
To address these challenges, we propose L.MM-gudded Evolution for MAterial discovery (LLEMA), novel agentic framework that integrates LLM scientifiic priors with evolutionary search and chemistry- informed design principles to autonomously generate, evaluate, and refine candidate materials under multiple task-specific property constraints. LLEMA introduces a set of chemistry- -inforree design
"qqual contribution. Correspondence: ni khi sa@vt.edu, sanchi t230vt.... edu.

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principles that act operators to guide the LLM to generate and refine candidates iteratively. These principles encode core knowledge across the entire materials discovery cycle, spanning compositional substitution, crystal structure manipulation, phase stability, and property-specific conditions. Unlike prior baselines, this chemically grounded generation integrates thermodynamic stability, enabling the systematic discovery of compounds that both novel and experimentally realizable. At each iteration, the LLM fuses pretrained chemical knowledge with domain rules to balance exploration of chemical space and exploitation promising leads. The candidates are then expressed as crystallographic information files (CIFs) for downstream property prediction (Figure IB). Surrogate-ae surrogate-assisted assisted oracle models then estimate task-relevant physicochemical properties (Figure IC). and candidates are scored against both performance objectives and design constraints. Successful and failed trajectories are fed back to the LLM (Figure ID), enabling evolutionary refinement of subsequent generations. Thus, LLEMA provides a principled framework for multi-objective discovery by explicitly enforcing stability and synthesizability to generate compounds that are not only novel but also physically realizable.
Table T compares LLEMA with traditional and LLM-based materials discovery methods. Traditional generative methods require task-specific retraining that limits their generalizability across materials design problems. Furthermore, they lack the extensive prior knowledge embedded in LLMs and feedback-drive refinement mechanisms. Methods like LLMatDesign employ sequential, single-step modifications with self-reflection to optimize candidates for single property. In contrast, LLEMA combines ceamistty-informeet evolutionary operators, surrogate-augmeened oracle, multi-objective scoring mechanisms, and memory-based evolution to achieve feedback-driven materials design.
Table 1: Existing materials discovery frameworks.
Medhed
Dimmale Knunledgs
Maltissjeriiee Oplimization
RuheGeatded Exuiiiinary
Generation
Relnnmmni
CIIAR Douna MIP
Manotti
11 MeMelne
LEBMI (Ohno
To evaluate I.LEMA, we introduce new benchmark suite of 14 diverse, industrially relevant discovery tasks. The benchmark focuses on application-critical settings, covering problems relevant to electronics, energy, coatings, optics, and aerospace (Appendix C Unlike existing benchmarks that focus optimizing a single material property, each task in our suite is formulated an explicit multi- objective discovery problem satisfying multiple properties. For example, discovering wide- bade-bandgap semiconductors, task critical for power and optoelectronic industries, requires simultaneously optimizing band gap and formation energy, rather than optimizing for a property in isolation. By capturing the complexity of real-world materials design, this benchmark provides rigorous testbed for data-efficient, multi-objective discovery under physical and chemical constraints. Combining chemistry-infe -nffrmeeed design with iterative LLM-guided evolution, LLEMA goes beyond proposing candidates that are good at a single metric. instead generating plausible, synthesizable materials that satisfy complex, world objectives. We evaluated LLEMA using GP 40 4--mn n (OpenAT 2023) and Mi Mistral-SSe 1 1 1-3 -B results demonstrate that LLEMA consistently discovers chemically valid and structurally accurate candidates, with faster convergence across test settings. Our analysis further highlights the crucial role rule-guided generation, memory-based feedback, and surrogate-assister property prediction in LLEMA's performance. The contributions of this work are summarized as:
(Mistral All (025) as LLM backbones. Our
A synthesizabillty-aware evolutionary framework, We introduce LLEMA, a framework that integrates LLMs' scientific knowledge with themistry-informer evolutionary operators, explicitly enforcing chemical validity and thermodynamic feasibility during the search process.
Memory-based evolution. We design a mechanism that leverages success and failure pools, together with multi-island sampling, iteratively steer LLMs toward high-performing regions while avoiding memorization.
Constrained multi-objective formulation for materials discovery. We cast materials design as a constrained multi-objective optimization problem, jointly optimizing competing property objectives.
Large-scale evaluation on realistic discovery tasks. We construct benchmark suite of 14 industrially motivated materials discovery tasks and demonstrate that LLEMA consistently achieves higher validity, stability, and Pareto efficiency than state-of-the-art baselines.
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Molecular Candidate
(B) Crystallographic Representation
Instruction
Taak:
"Tuak Deseritiions
Candidatex
Candidatex
Formeta:
Candidatex
A LLM 15
&
Formala:
Formala:
CC
enciecile formuaa
Properties:
Rutes fillowed: vismooing
Rutes filloedd:
LLM
sreacsing
Austiicatio:
Auctiiiation:
Chemistry
centecdal
Gosrdimati::
Chomionry
vecordiatopr
Ecamplec
Cenerita crystallogiaphic representation for each material
Example Hateriata
Design materials constraints
Sample
(D) Assessment Feedback
(C) Physicochemical Property Prediction
memory
Candidates
Candidates
Reward
Propery
Hamory
Bendgaas:
Lattice:
2.54 cf
Speries:
Error Memory
Propartie:: sul
Formation Energy 11 elitatom
Coardraaeer:
Island k
cora
Check predicted follow constraints and calculate the score store memory
Figure 1: LLEMA Framework, consisting of four main components: (A) Material Candidate Generation, where an LLM generates candidates based task descriptions and property constraints: (B) Crystallographic Representation. which converts generated materials into structured crystallographic information files (CIFs); (C) Physicochemical Property Prediction, to predict material properties such as formation energy and band gap, etc; and (D) Fitness Assessment and Feedback, which evaluates constraint satisfaction and provides iterative feedback through success/failure memory pools.
LLEMA METHOD
2.1 PROBLEM FORMULATION
We formulate the materials discovery task T as an optimization problem over the chemical space, where the goal is to identify the optimal material:
arg max (m),
(I)
meM
where m denotes material from the valid candidate set M representing the chemical space, and the function f M + R is a black-box objective that assigns each material a scalar value to the property of interest. However, in practice, materials discovery rarely involves optimizing a single property. Instead, materials must satisfy multiple property constraints C = {ei, c e2,,,.,.... ... ca. } while jointly optimizing competing objectives fI...., Jn. Each constraint 6, corresponds to a property function fi M + R and takes one of the following canonical forms: interval constraint, enforcing that the property lies within a feasible range; lower-bound constraint, enforcing a minimum acceptable value; upper-bound constraint, enforcing maximum allowable value. Formally.
(i( us) or C; fi(m)= 2 4 or f((m)
where 4, u, E R denote constraint-specio speciiff thresholds. The overall task thus reduces to identifying candidates m M that satisfy all constraints while achieving favorable trade-offs across objectives. A naive strategy for multi-objective optimization is to aggregate objectives via a weighted sum:
Σ wi Sc(m),
m = -arg max mEM
where w; denotes the weight of the i-th objective. This formulation captures the multi-objective nature of materials discovery, where competing property goals must be jointly optimized under domain-specific constraints. The task, therefore, consists of efficiently identifying candidate materials that meet all property requirements while maximizing overall performance across objectives.
2.2 HYPOTHESIS GENERATION
As illustrated in Figure I LLEMA begins with the generation of material candidates, followed by the prediction of physicochemical properties, the evaluation of candidates and the evolutionary refinement. This stage combines the generative capabilities of LLMs with domain- guided constraints to synthesize chemically plausible hypotheses aligned with quantitative property targets. At each iteration n, the
L.MM मe samples a batch candidate materials M from the prompt Pn- Appendix D.2 Figure details the construction of this prompt, composed of four components:
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The task description contains the natural language discovery objective T (e.g., Swide-bandger semiconductors") ensuring that candidate generation remains aligned with the overarching goals of the task, while also encoding the property constraints C (e.g., band gap 2 2.5 eV, formation energy I - 1.0 eV/atom) that distinguish valid from invalid designs.
Task Specification:
Chemistry-Informed Design Principles: After the initial generation (n 0), the prompt incorporates chemistry-infornet design rules (e.g., same-group elemental substitutions, petthhoommetr--eeerviin replacements). These rules act operators that encode domain knowledge, guiding the search toward chemically meaningful regions of the space while maintaining enough flexibility to allow for novel discoveries. Appendix Be.iii...44eedee details the evolution rules.
The population buffer Pn-1 maintains separate buffers to hold examples of successful (M++ and failed (M- candidates from prior iterations. Storing them in distinct buffers makes it possible to supply balanced demonstrations in Pa, providing the LLM with explicit in- context feedback. This organization helps the model infer decision boundaries between promising and invalid designs more effectively.
Demonstrations:
Crystallographic Representation: For each proposed candidate Mj. the LLM outputs a crystallographic configuration in structured JSON format, specifying the reduced chemical formula, lattice parameters, atomic species, and fractional coordinates (Figure [B). This standardized, machine-readable representation enables direct downstream evaluation with the groperty-predictee f. which predicts physicochemical properties and updates the population state.
2.3 PHYSICOCHEMICAL PROPERTY PREDICTION
Following candidate generation, LLEMA estimates the physicochemical properties of the CIF representation of each material using hierarchical prediction system. For given candidate Mj, the workflow first queries the reference model. which retrieves property values from curated experimental and computational databases like Materials Project (Jain et al. 2013) through exact or similarity- based matching. For out-of-distribution candidates, which lie outside the coverage of this reference model, LLEMA employs surrogate models such as CGCNN (Xie & Grossman 201 8) and ALIGNN Choudhary & DeCost 2021) to provide predictions. This yields a property vector f(m) E IRd, where each component corresponds to physicochemical attribute of interest. The vector is subsequently evaluated by a multi- nulti-obeecctiv scoring function against the design constraints C. Additional details on the implementation of these surrogate models are provided in Appendix B.I
2.4 FITNESS ASSESSMENT AND MEMORY MANAGEMENT
Candidates evaluated using multi-objective scoring function that measures the degree of alignment between their predicted properties and the target design constraints C. For each candidate material Mj generated in iteration n, the set of predicted properties is denoted by f(M The composite score is then computed as
S(T,C;,))= = Σ w. (.)f(())).)
(4)
where w, represents the relative importance of the i-th property, denotes the corresponding target constraint, and ()(..)) is normalized reward function that quantifies the satisfaction of the constraint by the predicted value fi(M)) (See Appendix B.2). Each candidate is then assigned to one two memory pools: the success pool MT, containing candidates that satisfy all hard constraints (i.c., S 2 0; 4 2 0 for all i), and the failure pool M containing candidates that violate one or more constraints. To progressively improve candidate quality and guide the search toward property regions, LLEMA employs memory based evolutionary refinement step inspired by island-moded strategies (Romera-Paredee et al.) 2024 Shojaee et al., 2025a Abhyankar et al. 2025). The candidate population is divided into m independent islands containing success (MT)) and failure memory (M-), each initialized with a copy of the initial exemplars. This structure supports parallel exploration, enabling different regions of the chemical space evolve independently and explore a range of candidates. At each iteration we first select one of the m (m = 5) islands using Boltzmann sampling (De La Maza Tidor 1992), with a score-based probability of choosing exp(s./T.) where s, denotes the mean score of the i-th cluster and To is the
a cluster i: P E3 exp(s,/T=)
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temperature parameter. Within the chosen island, candidates sampled from memory construct the next prompt Px+1- Specifically, top-k selection is applied to M and M to provide explicit demonstrations of high-scoring exemplars along with constraint violations. This mixture of successful and unsuccessful candidates, combined with domain-specific evolution rules R, forms the in-context examples that guide the L.LM in generating new candidates.
As described in Algorithm [ we initialize the population of materials Po and the candidate pool M that stores feasible solutions under the given design constraints C. Subsequently, we construct prompt by combining the task description with the associated physicochemical design constraints for generating candidate materials. At each iteration n, top-k entries from prior iterations (from one of the m islands), along with pre-defined evolution rules R (e.g., stoichiometry, oxidation state, substitution rules) provided by domain scientists, are injected to ensure chemical and structural validity while exploring the candidate space. The LLM uses the prompt to generate crystallographic information file (CIF)-based material representations. These candidates are then evaluated using an oracle predictor estimate their physicochemical properties. A scoring function assesses their performance relative to the target design objectives. partitioning candidates
Algorithm 1 LLEMA
Require: Task T, Design constraints C. Evolution rules R. Predictor f. LLM ne. iterations N
Ensure: Optimized material population M++
b Initialize population
1: Py t InitPop ()
b Initialize candidate pool
2: M <- InitCand ()
p BuildP -oiildPrompt((.c)) for 1 .V 1 do
P Add rules and population data
5:
P.. p P....topk () + R
b Crystallographic molecule generation MM f (P.)
6:
for = propert b Physicochemical property prediction
8:
x; = f(M}) ==
Evaluation and population update
if X, E then Mt + M3,
10:
11:
else
into success or failure pools based on whether
12:
M Mjidj end if
they satisfy the constraints. Memory is updated
13:
accordingly and a balanced sampling from both
14:
P. + UpdatePop(PA-I...k
15: end for
success and failure trajectories is used to provide
16: end for
feedback to the LLM,, ensuring both exploitation of geghpperorrmng regions and exploration of
17: Return: M
underexplored design spaces. This iterative loop continues for N rounds, after which the optimized candidate MI+ is returned.
2.5 IMPLEMENTATION DETAILS
To evaluate a new task, the user is only required to supply a CSV file specifying the task name and associated property constraints. From this input, the agentic framework automatically and iteratively constructs prompts to generate candidate materials, followed by their crystallographic structures in CIF format using an LLM. Next, for property evaluation, LLEMA adopts hierarchical oracle strategy where the candidates are first queried against curated materials databases, while pretrained ML surrogates (e.g.. CGCNN, ALIGNN) are invoked only for out-of-distribution compounds. These surrogates are used in inference mode with publicly available pretrained weights, which avoids retraining and significantly reduces computational overhead. For reproducibility, we report all surrogate model checkpoints and APIs in Table 5 (Appendix B.I. Candidates violating hard constraints are directly assigned low scores, ensuring efficient pruning before expensive evaluations. A detailed implementation of LLEMA is provided in Appendix D.2
EXPERIMENTS
3.1 DATASETS AND BENCHMARKS
We evaluate LLEMA on fourteen application-driven discovery tasks spanning electronics, energy. coatings, optics, and aerospace, to probe multi-objective reasoning under realistic constraints, and thermodynamic stability (Table Each task reflects industrially relevant challenge and is designed to probe multi-objective reasoning under realistic constraints. Our benchmark design follows three guiding principles: (i) Application relevance: the target properties align with pressing technological needs such as sustainable energy, advanced electronics, and structural resilience; (ii) Multi-constraint optimization: tasks involve simultaneous optimization of multiple, often competing, objectives (e.g..
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maximizing hardness and conductivity), mirroring real-world engineering specifications; and (iii) Thermodynamic stability: all tasks enforce stability requirements through energy-above-hun criteria (Enoy = 0) to ensure synthetic accessibility rather than purely theoretical feasibility. Appendix C contains additional details on all tasks, including property thresholds and predictive models.
Table Materials Discovery Benchmark. Each task is characterized by its application domain quantitative property constraints.
Task
Domain
Property Constraints
Wide Bandgap
Band gap
Electronics
Semiconductors
Formation energy S -1.0eVlatom
SAWBBWW Acoustic
Sheur modulus 2P-150GPs
Acoustics/ / Optics
Substrates
Dielectric constant 3.7-95
High-k Dielectrics
Dielectrics
Dielectric constant 10-90; Band 2.5
Formation energy S -looo/ Band gap 2.0eV Must contain Li, No, K, Mg, Ca, or Al
Solid-State Flectrolytes
Energy
Piezo Energy Harvesters
Energy
Piezoclectric coefficient 2 SpC/N; 10 K S 8000 ranking: use d /x:: higher better)
Transparent Conductors
Electronics
Band gap 3.0 50 & Electrical conductivity 5/cm Must he themoddynamicall stable;
Insulating Dielectries
Dielectrics
Band gap eV,.V, Dielectric constant 2 8.0
Band 0.7 2.0e;; Formation energy S e.Deevato
Photovoltaic Alsorbers
Energy
Earth-abundant and non-toxic elements only
Hard Coating Materials
Mechanical
Balk modulus 2 200 GPæ; Formation energy S -1.0eVatom: Bund gup 2 3.0eV
Hard, StifT Ceramics
Structural
Bulk modalus 100-300 GPs: Shear modulus G0-200GP:
Structural Materials
Density S glem" " Balk modulus 2 Shear modulus GPs; Energy above hull
Acrospace
Aerospace
Acousto Optic Hybrids
Acoustics/ Optics
Piezoelectric coefficient 9pC/N:
85
Density S 3.5 glcm 65 S Shear modulus S 195
Low-Density Structures
Acrospace
Toxic-Free
Electronics/ /
Band gap 2 2.0.V; 90 & Bulk modulus < 135 GPa Exclude Ph, Cd., Hg. TI, Be, As, Sh, Se, U, Th; Prefer stable ABOg oxides
Perovskite Oxides
Sustainahility
3.2 EXPERIMENTAL SETUP
We assessed LLEMA using complementary evaluation criteria designed to capture both the efficiency and the quality of material generation. Hit-Rate measures the percentage of generated candidates that simultaneously satisfy all property constraints, quantifying the efficiency of valid discovery. Stability evaluates the percentage of valid and thermodynamically stable, reflecting physical practicality beyond theoretical feasibility. Specifically, materials having an energy above the hull value less than 0.1 V/attom are considered stable. Finally, Pareto Front Analysis compares the quality of multi-objective trade-off's, with superior methods producing non-dominated solutions that span larger and more diverse regions of the design space. We benchmark LLEMA against generative models such CDVAE (Xie et al. 2022). G-SchNet (Gebauer et al.) 2019). DiffCSP (Jiao al., (023). and MatterGen (Zeni et al. 2025). as well as LLM-driven approaches including LeMatDesign (Jia al.] 2024) and direct prompting baselines. For comparison, all non-LLM baselines (e.g., CDVAE, G-SchNet. DiffCSP) were assigned ~ 10x candidate generations than LLM-based methods, generating 1500 samples, offset their lack of in-context feedback. Unlike the baselines, LLEMA refines its outputs by iteratively sampling candidates from its experience buffer through an in-context refinement process. Detailed implementation settings for baselines are provided in Appendix D
3.3 QUANTITATIVE RESULTS
Table 3 reports task-specific performance across fourteen benchmark domains, measured by hit-rate (H.R) and stability (Stab.) under varying physical and chemical constraints. Overall, LLEMA consistently outperforms all baselines, achieving higher hit-rates and markedly better stability across diverse material classes. Traditional generative models perform reasonably well on tasks like 'hard, stiff ceramics' or 'acousto-optic hybrids' but often produce valid yet unstable candidates. Even LLM-based baselines show limited robustness, performing well in some domains but failing in others, suggesting poor generalization across different physical regimes. In contrast, LLEMA consistently achieves higher hit-rates and markedly greater stability than the baselines. This elevated

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stability indicates that evolutionary refinement and chemistry-infomaa rules enable LLEMA not only to meet design constraints more reliably but also to generate thermodynamically consistent and physically meaningful structures. Overall, these results demonstrate that LLEMA generalizes robustly across material classes, combining exploration and constraint satisfaction more effectively than prior methods. A deeper discussion the qualitative aspects of LLEMA follows in the upcoming sections.
Table 3: Comparison of Baselines Materials Discovery Benchmark. We implemented LLEMA with GPT-40-mi 4o-miiiiiii and Mi Mistral -attral-maalll across materials design tasks. We report hit-rate (H.R.) and stability (Stah.), where higher values indicate better performance.
-4 against state-of-the-art baselines
Widd-Bandeap Semicond.
SAW/BAW Acoustic Substrates
High- Dielectrics
Solid-Slate Electrolytes
Piezo Energy Harvesters
Transparent Conductors
Insulating Diclectries
Method
H.R
Stab.
H.R
Stals
HR
Stab
H.R
Stab.
H.R
Stah
H.R
Suhh
H.R
Stab.
COVAE
0.04
0.04
0.29
0.00
0.82
0.00
0.04
0.04
42.19
0.00
0.00
0.00
1.06
0.12
Net
0.00
0.00
0.00
0.00
0.01
2.49
0.00
0.01
0.00
DifCCSP
0.00
0.00
0.36
0.00
0.75
0.00
0.00
0.00
41.21
0.00
0.01
0.00
1.13
0.04
MatterGen
6.56
4.15
26.27
0.00
0.61
0.00
5.33
3.11
21.61
0.00
9.38
0.00
0.91
0.10
Ead2end
0.95
0.49
0.30
10.34
0.78
0.00
0.00
0.00
LLsMan
4,19
1.13
47.59
0.13
1.35
0.32
2.51
2.44
32.16
1.38
0.04
0.04
0.21
0.08
LLEMA (Mistral)
17.08
10.71
31,58
6.80
7.53
3.62
31.79
20.78
67.11
4.84
43.87
18.48
21.54
9.42
LLEMA (GPT)
33.62
22.42
59.88
10.74
19.96
12.68
46.17
25.37
63:46
3.22
39.11
14.85
17.61
4.60
Photovoltaies Absorbers
Hard Coating Materials
Hard, Stir
Aerospace Materials
Acousto-optic Hybrids
Low Deusity
Perosskite Oxides
Method
Ceramics
Structures
H.R
Slab.
H.R
Siab.
H.R
Stab.
H.R
Stab.
H.R
Stal.
H.R
Stab
H.R
Stub.
COVAE
1,07
0.00
0.00
0.00
15.25
0.11
1.18
0.00
21.85
0,00
0.00
13000
0.00
0.00
G-SchNet
0.00
0.00
0.06
0.00
0.01
0.17
0.00
0.04
0.00
DifCSP
1.11
0.00
0.00
0.00
14.75
0.00
0.09
0.00
21.53
0.01
0.00
0.00
0.04
0.00
MatterGenn
1.88
0.00
2.12
0.00
8.23
0.00
7.34
0.00
11.24
0.00
0.27
0.00
0.93
0.00
EndZend
24.59
10.72
0.00
8.57
1.99
0.40
0.00
0.00
LLMaDDeign
3,92
0.00
0.00
0.00
19.00
0.41
0.00
0.00
15.45
0.55
0.07
0.00
1,10
0.81
LLEMA (Mistral)
20.47
3.71
10.80
1.12
27.92
2.65
1.50
0.54
14.04
0.50
1.51
0,14
22.90
2.78
LLEMA (GPT)
22.90
4.76
17.78
4.61
30.99
5.73
0.97
0.26
26.26
0.82
0.47
0.14
19.37
2.79
3.4
QUALITATIVE RESULTS
We analyzed qualitative outcomes to understand LLEMA's 's behavior under realistic discovery settings, focusing on: (i) Convergence dynamics, which examines how iterative feedback progressively steers the LLM toward feasible design regions; (ii) Pareto trade-offs, which assess whether the method can balance competing objectives under strict property constraints; and (iii) Discovered candidates, which illustrate how novel yet chemically plausible compositions emerge and how they align with domain knowledge.
Convergence Toward Feasible Frontiers. First, we analyzed how solutions evolve over iterations. Early generations scatter broadly across the search space, often violating property constraints or collapsing into suboptimal regions. As the search progresses, the feedback from the oracle, evolutionary memory, and constraint-based selection gradually steers LLEMA toward more promising areas of chemical design space. The proportion of valid candidates increases from roughly 27% at the 250th iteration to about 33% near the 1000th iteration, indicating that the algorithm effectively exploits high-fitness regions while maintaining exploration across diverse chemical configurations. This gradual improvement reflects stronger selection pressure toward feasible trade-offs, resulting in a visible migration of candidate clusters into constraint- satisfying zones (e.g., band gaps above e with low formation energies). These convergence dynamics show how iterative feedhack-driven evolution
Ranaaios 250
Hanaatian 893
gat oe sog
Figure 2: Evolution of candidates for the Wide- Bandgap Semiconductor task at different stages of I.E.M.
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refines the LLM's proposal distribution, preserving diversity while increasingly focusing on candidates that balance multiple objectives in physically meaningful ways.
LLMatDesign
CDVAE
DifCCSP
SchNet -- Pareto Front
LLEMA
Baeedaa Semiconductors
Hard, Stiff Ceramics
Funmation e40ostoo
200
Shear Modulus (GPa)
Band Gap (eV)
150
100
Band Gapa2.5
50
Shaer Moduluss2000
100
200
250
Formation Energy (eViatom)
Bulk Modulus (GPa)
Figure 3: Pareto front analysis of candidate materials for two design tasks. (a) Vide-Bandgap Semiconductors: (b) Hard, Stiff Ceramics.
Pareto Tradeoff. We then examined the Pareto fronts for the Wide-Bandgap Semiconductor and Hard-Stiff Ceramic tasks, both of which impose stringent property requirements: semiconductors must exhibit band gaps 2 2.5eV with formation energies V e/atom to ensure functionality and stability, while ceramics require bulk moduli the range 100-300 GPa and shear moduli between 60-200 GPa. As shown in Figure 3 the optimal Pareto front is completely dominated by LLEMA, and all Pareto-optimal solutions originate from our method on both tasks. This shows that LLEMA not only generates a higher proportion of valid and thermodynamicall stable candidates, but also consistently identifies the globally optimal trade-offs between competing objectives. By enforcing explicit constraints and applying domain- Nomain-guided evolutionary refinement, LLEMA effectively filters infeasible solutions while converging toward the true Pareto-optimal frontier, surpassing all baseline methods that fail to reach this region of the design space.
Discovered Candidates. Finally, we evaluated the plausibility of discovered compositions in the real world. We find that the materials proposed by LLEMA align with families previously investigated by domain experts, underscoring their ability to generate realistic candidates. For example, in the High-k diclectric task, LLEMA suggests Zr and Hfo. 52,, which connect closely to Zr-Al and Hf-Zr oxides studied promising high-k materials (Hakala al., 2006 Das & Jeon 2020 Islam et al. (021). Similarly, LLEMA reflects expert strategies, such as substitution and doping. e.g., proposinn BaHfZr oxide, which is consistent with known dopant-driven improvements in HfZr oxides (Kim et al.) 2024). In photovoltaics, candidates such as CaZnSi and MgZnSi oxides emerge, which, although not directly reported, are chemically related to established ZnO-based systems (Esgin et al. (2022). These examples demonstrate that LLEMA not only respects constraints, but also uncovers novel yet chemically plausible families, validating its utility guide real-world discovery.
ANALYSIS
4.1 IMPACT OF DOMAIN-GUIDED EVOLUTIONARY REFINEMENT
We evaluate the benefits of evolutionary refinement with domain-guided generation rules by benchmarking LLEMA against two baselines: (i) an LLM with iterative feedback (LLM w/ Memory), and (ii an unguided mutation-crossoverr search implemented within multi-island evolutionary framework followingRRomer- Romera- Cainera-Paredess et al. (2024).
Table 4: Comparison of hit-rate (H.R), stability
(Stab.). and Memorization Rate (Mem.) across
generation methods aggregated over four tasks.
Method
H.R
Stab.
Mem.l
LLM
4.4
1.8
95.3
Memory w/ Mutation & Crussover
20.1
58.3
29.8
21.5
25.3
All methods were run for 250 iterations across
LLEMA
30.2
27.6
16.6
four benchmark datasets, with property constraints
relaxed by 20% allow broader exploration while preserving task relevance. The results of Table
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show that LLMs with iterative feedback yield limited improvement, as the model tends to recall known materials and overfit to training patterns, However, the introduction of multi-island evolution substantially improves hit-rate and stability by promoting parallel exploration and mitigating premature convergence, though the absence of chemical constraints results in memorization. Incorporating chemistry-informed generation rules in LLEMA achieves the best overall balance (H.R = 30.2, Stab. = 27.6, Mem. = 16.6), constraining the search to thermodynamically and compositionally plausible regions while maintaining diversity. This staged refinement from the use of memory to the evolutionary search and domain
samain-guided guided evolution demonstrates how each component progressively enhances exploration, stability, and chemical realism in generative materials design.
4.2 MEMORIZATION VS. GUIDED EXPLORATION
A central challenge in leveraging large language models (LLMs) for scientific discovery is their tendency to memorize training data and regenerate during generation, rather than exploring novel solutions. Prior work has shown that LLMs frequently reproduce examples from their training al.
Simple LLM call
LLM with Memory
LLEMA
100
%6 From Materials Project APr
96.2
190.
96.7
BB.
75
corpus (Carlini et al. 2021; Hartmann 2023). In materials discovery, this manifests as repeated suggestions of compounds already present in databases such as the Materials Project, leading to high duplication rates and limited novelty. We compare three approaches: a direct LLM call, an
50
10:1
19.
Wide band GaD semicondaactrss didlectrics
High-k
SAWWBAW acoustics
Hard stiff
LLM augmented with a memory buffer and iterative feedback, and LLEMA. The direct LLM call exhibits the highest duplication and near-total reliance on the Materials Project (e.g.. High-k dielectrics show almost 100% overlap). Although adding a memory buffer helps the model explore diverse leads, it still shows a high rate of memorization, thus implying that simply storing past candidates does not guide the search toward new or diverse regions of chemical space. In contrast, incorporating multi-island evolutionary framework enables the model to avoid local optima and repeated patterns. When further combined with chemically informed rules such oxidation-state consistency, stoichiometry preservation, and prototype substitution, LLEMA effectively reduces redundancy and expands exploration into novel, chemically plausible regions of the design space. Together, these components push the model beyond memorization toward genuine discovery.
Figure 4: Percentage of generated candidates from the Materials Project four domains different baselines. Lower values indicate less memorization.
4.3 IMPACT OF SURROGATE MODELS
Figure quaatiffees the effect surrogate model-based property prediction on I.LEMA's performance. All experiments were run for 250 iterations with task constraints relaxed to encourage exploration, similar to Section
surrogate madels
30
27.6
Percentage
20
To isolate the contribution of ML- removed surrogate ML models like CGCNN and ALIGNN, and restricted the workflow using only the Materials Project database for property annotations. Furthermore, we experimented with fewer iterations while relaxing task constraints for the wide- bandgap semiconductors dataset. Even in this setting, both hit-rate and stability collapse to near-zero (< 5%), as the evolutionary process cannot assign meaningful rewards without surrogate models to candidates for missing property annotations in the Materials Project API. The search then drifts toward trivial or repeated compounds instead of progressing toward novel solutions. By contrast, reintroducing surrogate predictors produces more than sixfold improvement, increasing hit-rate and stability into the 25-30% range. The surrogate estimates for the -ntto--distribution candidates provide the evaluation signals needed to sustain exploration beyond the sparse coverage of existing datasets.
based surrogates,
15
10
4.8
Hit rate
Stability
Figure 5: Hit-Rate and Stability performance of LLEMA with and without surrogate model- based property prediction.

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These results demonstrate that surrogate models are indispensable for providing informative fitness signals under sparse supervision, preventing collapse, and enabling effective discovery.
5 RELATED WORK
Material Discovery. Materials discovery has progressed from trial-and-error (Nagamatsu et al.
2001) to ab initio modeling (Jain et al.] 2011: Hautier et al.) 2012 Pyzer- Knapp et al. 2013)). with
DFT and high-throughput screening as standard tools. Machine learning further accelerates discovery via rapid property prediction (Xie & Grossman| 2018 Chen et al.]
2019 Choudhary & DeCost
202T) and generative design (Gebauer et al., 2019 Xie et al. 2022 Jiao et al. 2023), including
multi-ojeective optimization (Gopakumar et al. [0088] JaJJlnka et al. (202]). Yet, these methods
remain limited by data scareity and poor transferability across domains. contrast, LLMs have broad
scientific knowledge that enables reasoning in data-poor regimes, making them natural foundation for knowledge- guided materials design frameworks.
LLMs and Evolutionary Algorithms. Recent advances in generative models have shown their ability generalize across diverse tasks using pre-trained knowledge and simple prompting strategies (Brown et al. (2020) Reddy & Shojace, 2025 Wei et al. (202)). However, their outputs
are often unreliable or inconsistent (Madaan et al., [2024] Zhu et al.] (023). motivating the use of
evolutionary optimization frameworks where LLMs act as generators and external evaluators guide
selection and refinement (Lange et al. 2024] Lehman et al. 2023: Liu et al. 20244 Zheng et al. 2023).
Such frameworks have been successfully applied in areas including code and prompi generation (Guo) ct al. 2.24p. scientific discovery (Shojace et al.] 2025a b). mathematical optimization (Yang et al. 2024b), program synthesis (Romera- Pareedss- et al. 2024). robotics reward design (Ma et al.) 2024).
feature engineering (Abhyankar et al., (002)), and chemical discovery (Wang et al., 2025). We extend this line of work to real-world materials science challenges by incorporating themistry-informed informed LLM evolution that enforces structural validity and physical plausibility, enabling principled discovery under multi-objective constraints.
LLMs in Material Science. Early work applied L.M-- frameworks to literature mining, named-entity recognition, and property extraction (Gupta et al. 2022 2024 Niyongabo Rubungo
ctt al. 2025). Beyond text extraction, more recent methods use LLMs for hypothesis generation (Miret
& Krishnan 2024). synthesis route planning, and reasoning engines in multi-agent systems (Zhang
et al.; 2024, Kang & Kim 2024 Kumbhar et al.) 2025). Systems such as MatAgent (Bazgir
al. 2025) and LLMatDesign (Jia et al.) (024)) combine LLM reasoning with property predictors
and optimization loops, but often emphasize narrow objectives and weak constraint enforcement, leading to an unguided or infeasible search. Closely related efforts, such MMtarh (Gan let al. 2025), use LLM proposals in an evolutionary refinement loop for crystal discovery, and MatterGen Zeni al. 2025) uses a diffusion-basee model with conditional sampling for the inverse design. Although effective, these approaches rely on either learned generative priors or limited objective formulations. LLEMA instead frames the design of materials as a objeetobeeeetive search problem with synthesizability, integrating LLMM reasoning with surrogate predictors, domain constraints, and memory-ban based refinement to balance novelty, feasibility and property alignment.
6 CONCLUSION
In this work, we present LLEMA, a unified framework that integrates the evolutionary paradigm, domain-guided rules, and the scientific knowledge of LLMs to enable multi-objective and synthesizabiltt-aaaar materials discovery. To rigorously evaluate generality, we curate a benchmark suite of 14 diverse, real-world discovery tasks spanning electronics, energy, coatings, optics, and acrospace. Our experiments demonstrate three key findings: (i) LLEMA achieves higher hit rates and stronger Pareto fronts than generative and LLMM-nll baselines, showing improved ability to balance competing design objectives. (ii) LLEMA produces larger fraction of thermodynamically stable and chemically plausible compounds, validating its emphasis on synthesizability. (iii) LLEMA significantly reduces duplication and corpus recall, mitigating the memorization tendency of vanilla LLM generation and enabling genuine exploration of novel chemical space. While these results highlight the potential of LLEMA, validation, and the cost of iterative LLM queries suggest opportunities for future work paving the way toward scalable and reliable automated materials discovery.
reliance surrogate predictors, limited experimental
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ACKNOWLEDGEMENTS
This research was partially supported by the U.S. National Science Foundation (NSF) under Grant No. 2416728 and Autodesk Research. The authors thank Modal for providing computational resources that supported the hosting and implementation of the models used in this study. Saaketh Desai is supported in part by the Center for Integrated Nanotechnologies, an Office of Science user facility operated for the U.S. Department of Energy. This article has been authored by an employee of Engineering Solutions of Sandia, LLC under Contract No. DE-NA0003525 with the U.S. Department of Energy (DOE). The employee owns all rights, title, and interest in and to the article and is solely responsible for its contents. The United States Government retains, and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this article allow others to do so, for United States Government purposes. The DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan.
National Technology
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A AUTONOMOUS MATERIALS DISCOVERY
The discovery of novel materials with tailored properties is fundamental technological progress, contributing to a global materials industry generating approximately $ 8 trillion in revenue in 2023 (McKinsey] [024). The impact of tailored materials is particularly significant in critical domains such as energy storage Ling (2022), photovoltaics Solak & Irmak (2023), and microclectronics
Refai-Ahhed et al. 2024), where advanced materials can enhance efficiency, reduce energy footprint, and improve sustainability. The grand challenge in materials discovery lies in navigating enormous design space encompassing a vast number of material compositions and manufacturing techniques while achieving the target material structures and properties across multiple length and time scales (Oganov et al. 2019). Human intuition-basee methods, along with traditional design of experiments and computational investigations, are slow and ineffective at screening this vast space possible materials and synthesis conditions. Consequently, the field has witnessed a rapid emergence of data-driven discovery paradigms Agrawal & Choudhary (2016) and autonomous self-driving laboratories Abollhasaa & Kumacheva (2023). integrating artificial intelligence, robotics, and high- throughput computation. Data-centric platforms such as the Materials Project (Jain et al., 2013) exemplify this shift, offering open high-throughput DFT databases that enable large-scale screening of candidate materials (Horton et al. 2025). Agent-basee based frameworks further advance this paradigm by autonomously navigating complex chemical spaces and identifying novel stable compounds (Montoyal ctt al. 2020). Together, these systems mark a paradigm shift, transforming materials discovery from a process of numan-guided trial and error one of algorithmic intuition and autonomous exploration.
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B ADDITIONAL DETAILS
B.I SURROGATE MODEL
The oracle in LLEMA is designed to provide scalable and reliable property estimation by combining external databases with pretrained surrogates, After generating crystallographic representations (CIFs) for each candidate, we first query the Materials Project AP to retrieve available properties. However, the API has limited coverage: many target properties, such as electrical conductivity and dielectric constants, are either missing for several materials or absent altogether, and the database itself, though large, cannot cover all generated candidates. To overcome this limitation, we conducted preliminary experiments with several pretrained models and identified ALIGNN (Choudhary & DeCost (021) and CGCNN (Xie & Grossman 2018) as the most reliable surrogates across key properties. We use ALIGNN checkpoints trained on the JARVIS-DFT datase via their official implementation and the official CGCNN release") This design ensures a clear mapping: when properties are available in the Materials Project, we use them directly; when they are not, the most appropriate surrogate model selected based on our prior experimentation. By integrating database queries with pretrained ML predictors, the oracle balances accuracy, scalability, and coverage, enabling consistent evaluation across all discovery tasks. Table J provides mapping between the surrogate models and the source pretrained files used to predict the corresponding physicochemical properties.
2
Table 5: Mapping between target properties and oracle sources. Flectrical conductivity does not have dedicated pretrained model and is computed from the Seeheck coefficient and power factor. Density computed directly from the structure (CIF/POSCAR).
Property
Surrogate Model
Source
Band gap
CGCNN
jv ganddggappth.tar
Formation energy
ALIGNN
_prrttoy
Bulk modulus
ALIGNN
jv sis_mooduuuss_
Shear modulus
ALIGNN
jv shear mocuurumouluu___
Dielectric constant
ALIGNN
jv_epsx
Piezoelectric constant
ALIGNN
jv d__dfft_piezz jv_ehull
Energy above hull
ALIGNN
Density, volume
ALIGNN / CGCNN
Seebeck coefficient
ALIGNN
jv iv_n-Seebeck
Power factor
ALIGNN
jv jy_n-powerfact__al
Electrical conductivity
ALIGNN
B.2 FITNESS ASSESSMENT
LLEMA uses multi-objective scoring function to evaluate candidate materials and guide the evolutionary search process. The scoring function defined as:
* S(T. C:M, = Σ wi (M)))M))).),
where s(())) denotes the predicted value of the i-th property for candidate Mj, G; is the corresponding design constraint, and w; 2 importance of property i. The function (...,.) measures the degree of satisfaction between predicted property value and its associated constraint, and maps to bounded reward space. A candidate is considered feasible if and only if 4; 2 0 for all constraints i. Each constraint c; is assumed to be one of three types: (a) a lower-bound constraint (Ji(M)) 2 4). (b) an upper-hound constraint (fr(M)) < u4), or (c) an interval constraint (f((M)) E [4. ull. The normalized reward 4; is
weighting coefficient that encodes the relative
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defined as signed, clipped feasibility margin that depends only on the constraint limits. Specifically, for a lower- bound constraint,
f((M)) -4
0 = clip
c
max 141.1) -1,1) -1,1)
for upper-bound constraint,
U4 - [:(M;) -
-1,1) -1.1)
Φ clip
1max((us))
and for an interval constraint,
P clip min(f:(M,) - 4, f:MM))) -1,,
max(|u, - 11,
where clip(z, 11 = max min(1, For example, in wide-handgap semiconductors. band gap is supposed to be higher than e. whereas for formation energy, it better have lower values Le. less than - e/atom and scores are calculated accordingly. The weighting coefficients w; encode the task-specific importance of each property, allowing LLEMA balance competing objectives during optimization. These weights act as hyperparameters. curated in consultation with domain heuristies: performance--ritical properties are emphasized, while feasibility constraints (stability- related) act as secondary filters after scoring the candidates to prevent chemically implausible candidates. However, for simplicity, we assign equal weights to all the properties associated with task. For example, in the wide hide-bandgap semiconductor task, band gap and formation energy given equal priorities, while energy-above-t principled scoring, along with stability check, ensures that the discovery process reflects the physical and industrial priorities of each benchmark task, rather than being tuned arbitrarily.
is used to ensure stability and synthesizability. This
B.3 MULTI-ISLAND EXPLORATION
LLEMA utilizes the multi- framework to evolve its candidate population. At initialization, the global population is partitioned into independent islands by evenly splitting the candidate set into A subpopulations. Each island maintains its own success and failure buffers and evolves independently of the others. Given a total evolutionary budget of iterations, each island receives approximately T/k iterations. Therefore, the choice of k determines the balance between exploration and exploitation. A smaller & allows deeper refinement per island (greater exploitation), and larger k enables more independent trajectories with shallower refinement (greater exploration). Because all islands run in parallel with distinct memory states, & primarily determines how the total computational budget is distributed across parallel search paths. We evaluate three representative settings: k 1 (single trajectory), = 5 (moderate multi-trajectory), and k: = 10 (highly parallel) for 250 iterations with relaxed constraints. Results for four representative tasks are shown Table 6 Moderate island counts (for example, & = 5) consistently provide the best balance: they allow broad exploration while still giving each island enough iterations to refine promising regions. very small restricts exploration, and a very large l reduces the per-island refinement depth. As each island maintains its own success and failure memories and adapts independently, the trajectories diverge early and explore different portions of the design space. As long as k is chosen in proportion to the available compute budget (for example, using more islands only when T sufficiently large), overall performance remains stable across tasks.
Table 6: Effect
of island count on representative tasks.
Islands
Wide-Bandgap Semicond.
High-k Dielectrics
SAW/BAW Acoustics
Hard, Stiff Ceramics
1
18.62
5.59
22,00
5.65
33.62
19.96
59.88
30.99
10
24.46
20.34
26.78
16.19
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B.4 EVOLUTIONARY GENERATION RULES
To constrain exploration and ensure chemical validity, LLEMA incorporates set of domain-informed rules that guide the modification of candidate materials during evolutionary refinement. These rules encode chemical heuristics such as group-wise substitutions, prototype preservation, and functional analog discovery. At each iteration, they are injected into the prompt as part of the evolutionary context, ensuring that candidate modifications follow chemically plausible pathways while maintaining diversity. Below, we enumerate the rules used this work. Each rule presented in monospaced format to emphasize its role design heuristic.
1. Same group elemental substitution: Replace each element with another from the same periodic group.
AgB3
C2D3, C Group(A), D E Group (B)
2. Stoichiometrry-preervvin substitution: Keep the formula ratios but replace with chemically similar elements.
A2 44
D D E F
3. Oxidation state substitution: Replace elements with others having the same oxidation state.
A +
C²+D
4. Functional group substitution: Swap one functional group with another similar chemical behavior.
R-X
R-Y,
X~Y
5. Crystal prototype substitution: Maintain the structural prototype (e.g., perovskite ABX3) and replace elements.
ABX3
CDY3
6. Coordination geometry mutation: Change the ligand coordination number around central atom.
(L)
+
A
7. Oxidation/redductoon variant: Adjust stoichiometry for different redox configurations.
A2B3
Az
8. Surface functionalization: Add functional groups to known material surface.
ABC
ABC-X
9. Template-guided combinatorics: Fill in a known formula structure with compatible elements.
ABX3
C-D-E3
10. Inverse property conditioning: Generate candidates with properties conditioned on a specified target.
Target:
High Hardness
+
A2B
11. Retrosynthesis-based forward design: Suggest plausible products from precursors.
A B
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12. Functional analog discovery: Replace with another compound serving the same role.
Bg (insulator)
C4Dg (insulator)
13. folerance-factor guided substitution: Replace atoms while preserving structural stability rules.
ABX3 - A' BX3, (A)) & (A)
14. Periodicity-presenve analog search: Replace atoms while maintaining periodic trends.
A2
C2D3, C~A
C DATASETS AND BENCHMARK
To evaluate multi-objective material discovery, curate diverse benchmark spanning 14 representative design tasks across various domains (see Table 2). Each task defines a distinct combination of physicochemical constraints that reflect practical design objectives in real-world materials engineering. Together, the benchmark captures the breadth challenges faced in materials design, from optimizing cefformance-staaille trade-offs balancing mechanical, dielectric, and sustainability objectives. The resulting dataset assesses how well models can reason over complex, interdependent physical properties and generate synthesizable candidates under realistic constraints.
Wide-Ban BadeeBandgap Semiconductors. Wide-bandgap semiconductors underpin high-power and high- frequency electronics, as well as optoelectronic applications like UV LEDs. Candidate materials must achieve a band gap 2 eV while maintaining formation energies < e and low energy- mergy-above--uut (< o/aem/a to ensure both performance and stability. This task challenges models to jointly balance wide electronic gaps with realistic thermodynamic feasibility, a combination critical for next-generation power electronics and photonics.
SAW/BAW Acoustic Substrates. Acoustic substrates are critical for wireless communication devices, including filters and resonators. Target materials must combine shear moduli between 25-150 with dielectric constants between 7-95, ensuring mechanical resonance with stable dielectric response. This task probes the ability to navigate trade-offs in mechanical and dielectric behavior to identify candidates for next-generation 5G/6G communication technologies.
High-k Dielectrics. High-permittiiity dielectrics enable miniaturization in capacitors and gate oxides for semiconductor technology. Desired materials exhibit dielectric constants between 10-90 and band gaps in the range 2.5-6.5 VV, ensuring both capacitance density and insulation. The task forces models to balance polarizability against leakage resistance, reflecting practical design needs in integrated circuits.
Solid-State Electrolytes. Solid electrolytes promise safe, high-energy batteries by replacing flammable liquid electrolytes. Candidates must be thermodynamically stable (formation energy - -attom, electronically insulating (band gap > 2.0eV), and contain mobile species such as Li, Na, K, Mg, Ca, or Al. This task reflects the fundamental trade-off between chemical stability and ionic conductivity, which is central enabling next-generation solid-state batteries.
Piezo Energy Harvesters. Energy-harvesting applications demand strong electromechanical coupling and dielectric robustness. Candidates must have piezoelectric coefficients d:j > 8 PC/N and dielectric constants in the range 10 < κ < 8000. Performance is often ranked by the figure of merit d² /K, which rewards high piezoelectric activity while penalizing excessive dielectric loading. This task reflects the practical requirement of optimizing efficiency under electrical and mechanical constraints in self-powered devices.
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Transparent Conductors. Transparent conducting oxides balance optical transparency with electronic conductivity for use in displays and photovoltaics. Candidates must exhibit band gaps Eg V. and conductivities 50 I 5000 S/em while remaining thermodynamically stable. This dual optimization captures the key trade-off between light transmission and carrier mobility.
Electrically Insulating Dielectries. Insulating dielectrics are critical for high-voltage applications requiring minimal current leakage. Materials must have band gaps Eg 2 e. and dielectric constants 8.0, ensuring high breakdown strength and stable polarization response. These constraints emphasize materials with strong insulation behavior and mechanical integrity under electric fields.
Photovoltaic Absorbers. Photovoltaic materials must absorb sunlight efficiently while remaining stable, earth-abundant, and non-toxic. Target absorbers have optimal band gaps (0.7-2.0eV for solar conversion, formation energies < 0.0 e.OeV/atom, and must exclude rare or hazardous elements. This task reflects real-world sustainability constraints, foreing models to move beyond theoretical optima and identify candidates suitable for large-scale, affordable solar deployment.
Hard Coating Materials. Coatings protect industrial components from wear, corrosion, and high temperatures. Desired materials exhibit high bulk modulus (2 200 GPa), wide band gaps (2 e.0,V), and strong thermodynamic stability (formation energy < -1.oe//ttmm). This task probes the ability of models to discover coatings that simultaneously resist deformation, provide electrical insulation, and remain synthesizable which key for aerospace, tooling, and cutting-edge manufacturing.
Hard, Stiff Ceramics. Ceramics used in extreme environments require resistance to deformation while maintaining stiffness across broad ranges. Candidates must exhibit bulk moduli between 100-300 GPa and shear moduli between 60-200 GPa. This task emphasizes the discovery of brittle but strong materials, essential for armor, cutting tools, and temperrtmper structural applications.
Structural Materials for Aerospace. Aerospace materials must balance light weight with mechanical resilience. This task enforces minimum stiffness (bulk modulus 100 shear modulus 2 40 GPa), low density (< 5.0 5.0g//m²), and sufficient thermodynamic stability (energy above hull S 5.0e V/atom). It challenges models identify materials that achieve high soongghtttowwighhe ratios while remaining manufacturable, crucial for aviation and spaceflight.
A Acousto-Optic Hybrids. Materials for acousto-optic devices must balance piezoelectric and dielectric properties to minimize loading while enabling efficient coupling. Candidates are required to exhibit piezoelectric coefficients in the range 3 S dij S 9pC/N and dielectric constants in the range 8 < K I 85, with preference for narrow band to reduce dielectric loading. Ranking emphasizes proximity to target dl-ands and mid-range & values, highlighting the trade-off between acoustic response and dielectric stability.
Low-Density Structural Materials. Aerospace-gun -rade materials must combine low density with high stiffness-to-weits ratios. Candidates are constrained to density S 3.5 3/em/ and shear modulus 65 < G < 195 GPa, with optimization targeting the ratio G/p. The task favors lightweight systems that maintain strength and creep resistance under thermal stress.
Environmentally safe perovskite oxides aim to eliminate toxic elements while preserving desirable optoelectronic properties. Candidates must have band gaps E, 2 2.0eV and bulk moduli 90 < K 135 GPa, while excluding Pb, Cd, Hg, TI, Be, As, Sb, Se, U. and Th. The search prioritizes thermodynamically stable ABO, structures that retain mechanical durability without compromising sustainability.
Toxic-Free Perovskite Oxides.
D IMPLEMENTATION DETAILS
D.1 BASELINES
We compare LLEMA against several state-of-the-aa materials discovery baselines, encompassing a diverse range of methodologies from traditional deep learning-based techniques M-bM-based
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methods. For all baselines, generate candidate materials using their respective official implementations, applying minimal benchmark-specinn modifications when necessary. Property values for all generated candidates computed using the same property prediction pipeline as employed in LLEMA, ensuring a consistent and fair comparison. Specifically, we implement:
CDVAE. CDVAE (Xie et al. 2022) is a conditional variational autoencoder tailored for crystal structure generation. It learns latent representations of crystals conditioned on composition, enabling the generation of valid and diverse candidate structures. We implement CDVAE using the official open-source repository with default parameters, outputting the generated structures in CIF (Crystallographic Information File) format, along with latent embeddings stored as NumPy arrays for downstream analysis.
G-SchNet. G-SchNet (Gebauer et al. 2019) is a graph-based deep generative model for molecular and crystal structures, built on the SchNet architecture. incrementally generates atom types and positions conditioned the partially built structure, allowing it to capture geometric and chemical validity. We implement G-SchNet using the open-source codebase
wode with default hyperparameters for 15000 iterations. The generated samples are stored in database, which is subsequently converted into candidate-specific CIF files.
DifCCSP. DiffCsP (Jiao et al., 2023) introduces diffusion models for crystal structure prediction (CSP). It models the distribution over atomic positions and lattice parameters via denoising diffusion probabilistic model, enabling efficient sampling of realistic crystal structures. We implement DiffCSP using the official code release CIF files.
Sireassewwwaa with default settings and store the generated candidates in
We use the official mat mattergen release and checkpoints. For candidate generation, we sample batches from the released base checkpoint. Generated candidates are then evaluated using surrogate predictors and the Materials Project API to determine the candidate quality.
MatterGen.
End2end. We implemented pipeline with base LLM as GPT-4o-mini to generate candidates conditioned on the design task and its corresponding property constraints. The LLM operated with sampling temperature of = 0.8 to promote diversity while preserving structural coherence. was explicitly instructed to output candidates in Crystallographic Information File (CIF) format, ensuring standardized structural representations suitable for subsequent validation and property evaluation using the surrogate- assisted oracle prediction.
LLMatDesign. LLMatDesigg ign (Jia et al. 2024 leverages LLMs for material design by prompting LLMs to iteratively improve the provided material to return the material with the single target property. As A.LMaDDegign is primarily designed for single-objective optimization, we adapt its released implementation for our multi-objective materials discovery benchmarks and add surrogate- augmented oracle from pipeline for feedback. For candidate generation, we adopt their original prompt template, which provides a material's chemical formula and task-specific properties and asks the model propose modification that satisfies the constraints. The model selects one of four modification types among 'exchange', 'substitute', 'remove', or 'add', and outputs both the modification and natural-language hypothesis justifying the change.
D.2 LLEMA
Material Design. Figure 6 Figusteill illustrates task. The prompt begins with general instructions specifying the LLM's role and objective, followed by task-specific details such the description of the design problem, property constraints (e.g.. required band gap and formation energy), and set of previously explored candidates with their
example prompt for the Wide-Bandgap Semiconductor
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associated property values sampled from the experience buffer. We then sample b = 2 candidate outputs at a temperature of 7 0.8, chosen to balance creativity with adherence to constraints while exploiting promising directions in the search space. To further ensure physical plausibility, we introduce rule-based constraints during the evolutionary phase (after the initial generation step, 0), which guide the L.M through the material discovery cycle and promote chemically valid candidates. We randomly sample a subset of rules from the set of rules and provide it to the LLM guide the candidate generation. By providing task descriptions, prior evaluations, and rule-based constraints in the prompt, we effectively steer the LLM toward feasible, property- apppett--liinnd material candidates.
Crystallographic Representation. For each sampled compound, we generate crystallographic representation in the form of a CIF (Crystallographie Information File) (see Figure 6 A CIF encodes the lattice parameters, symmetry, and atomic positions of material, which directly determine key properties such as band gap, formation energy, and stability. Oracle models require this structure- aware representation to correctly predict thermodynamic and electronic properties, making CIF generation essential for evaluating whether candidates are both physically plausible and functionally relevant. By mapping each candidate to valid erystallographic structure, LLEMA enables property prediction and aligns with standard materials discovery workflows.
Data-Driven Evaluation. We rely on oracle-assisted surrogate models to return key property values such as band gap and formation energy, which serve as the basis for evaluating each candidate. The predictions are used to assess whether generated materials satisfy the task-specific constraints. Candidates that fully meet the constraints are scored highest, while those that partially satisfy them are ranked above those that fail entirely. This data-driven evaluation ensures that generation quality grounded in quantitative property predictions rather than heuristic filtering, making it critical component of the discovery pipeline.
Specification
an expert naterials discovery assistant with deep knouledgo of crystal cheristry and saterials design.
Your task is to generste mnterials for Mide-Band Gap Seniconductors
Using the design rules and peior outcones, propose candidate raterials that likely satisfy the constraints.
CIF Generation
Evolution Constraints
following corpound,
crystal lographie configunstion for it: Corpound Ng
Here are feu design rules for genensting new compounds:
Sane-group elemental substitution: Replace fron the same periodic
denenate a candicate crystallographie configuration and return it as 250h object with the following fields: "forsula"; string, reduced cherical forula species count).
Stoichlonetry preeeryyneeeeeiingggg substitution: Use chenically similar
cospound (must only).
array shape
angstrous (flosts
Deronstratioos
"species"s list of elesent systols is the unit cell. "coords": 1ist of fractional coordinates.
The following are the design constraints for this task: sand dap 2.5ek; Foreation energy per atos -1.8eV/stor
aau OUTPUT FORMAT ase
Example valid structure: (f
Top successful candidates (where constraints were sattiflle)::
"forsula": string, "lattice";
has band gape2.dev formation
stom:-1. Mbee//toos
flost],
[flost, flost, flost], [flast, flast, float]],
Top failled candidates (where
satisffied):
"species": [string, ...]s
Ago band gap=2. BeV and forsation energy pan atom- 2.20//aton
"coards": " [[float, float, float], ...]
enn OUTPUT FORMAT e*n Return 350N 1ist of new candidates, each with 'cospound', "rules used', and jjstiFication.
Figure 6: Example of input prompts for the wide-bandgap semiconductors task. (a) Candidate Generation Step including task specification, evolution constraints, in-context demonstrations, and (b) Crystallographic File (CIF) Representation Step containing the CIF generation prompt.
Experience Management. We adopt islend-based evolutionary strategy Coomera-Paredaee et al. 2024] Shojace et al., 2202aa] Abhyankar et al., 2025) to manage the experience buffer, where generated material candidates and their evaluation scores are distributed across 5 independently evolving
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islands. Each island is initialized with small set of seed candidates sampled from the Materials Project API and refined using the LLM. Within each island, the buffer is divided into two components: reward buffer, which stores candidates that fully satisfy all task task-specific constraints (e.g., band gap and formation energy), and an error buffer, which stores candidates that only partially satisfy or completely violate the constraints. This separation enables the framework to reinforce high-quality generations while also retaining failure cases, which serve as negative examples to guide exploration. The experience buffer is further leveraged to construct prompts for subsequent LLM calls. After the prompt template is updated with task-specifi information, one of the islands is selected, and & = 2 candidates are sampled from its buffers to serve as mn-context demonstrations. Candidate selection follows Boltzmann strategy (De La Maza & Tidor 1992) that assigns higher probability to clusters with stronger evaluation scores. Specifically, if denotes the score of the i-th cluster, the probability P. of selecting it is given by:
exp(s:/Te) P Σ, exp(s:/T.)*
To = To (1 (1- u mod M
M
where is the temperature parameter, u is the current number of candidates on the island, and To = 0.1 and M 10,000 are hyperparameters. Once cluster selected, we sample candidates from it for inclusion in the next generation. This mechanism integrates information from both successful and failed generations while preserving diversity across islands, thereby guiding the LLM toward more effective material discovery.
E
QUALITATIVE ANALYSIS
E.
CASE STUDY
To better understand how LLEMA's evolutionary mechanism balances exploration and exploitation, we analyze the temporal dynamics of the search process across iterations. This case study focuses on three aspects of the evolutionary trajectory: (i) memorization rate: the proportion of generated compounds retrieved directly from known databases such as the Materials Project; (ii) chemical diversity: the spread clemental coverage across the periodic table; and (iii) validity progression: the fraction of syntactically and physically valid compounds discovered over successive generations.
From Memorization to Exploration. In the early stages of optimization, LLEMA's search behavior is dominated by memorization, with substantial portion of generated candidates overlapping with known entries from the Materials Project (Figure [ As the search evolves, the proportion externally sourced structures rapidly declines. From about 83% initially, the overlap with Materials Project drops to 10% by 250 iterations, eventually dropping to about 3% by the end of the evolution. This steady decrease highlights clear transition from memorization of existing chemical knowledge exploration of novel compositions. By later iterations, the candidate pool is largely composed of previously unseen structures, indicating that the model has shifted from recall-driven synthesis toward genuine materials discovery. Figure 8 further highlights how the evolution process guides the exploration toward a more diverse set of elements.
83.3
From Matertuls Project (%)
60-
20-
10.0
3.0
3/0
100
250
300
700
1050
Iteration
The percentage of candidate structures sourced from Materials Project across iterations by LLEMA for SAW/BAW Acoustic Substrates.
Figure 7:
Convergence Toward Feasible Frontiers. Tracking candidates in property space reveals how LLEMA's population progressively migrates toward feasible and optimal regions time. As shown in Figure at early stages (Iteration 250), only about 30% of SAW/BAW acoustic substrates satisfy physical validity constraints, with most scattering across thermodynamically unstable or
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Iteration
Iteration 500
1B
PO
(501))
Nd
Ad riwe for 15.
hp
Fu
28
Am
Iberation 750
Iteration 1000
H
Ma
P6
RC
T2
by
11
Tn
Rd
G4
Figure 8: Evolution of periodic table coverage during SAW/BAW acoustic substrate optimization. Each panel shows the clement-wise usage ratio across itcrations (250, 500, 750, 1000) the cvolutionary search process.
suboptimal zones. As the evolution proceeds, this fraction increases to nearly 46% by iteration 1000, reflecting the growing influence of rule-based chemical filters and adaptive feedback mechanisms. Concurrently, the Pareto front advances steadily, expanding the achievable trade-off frontier and uncovering materials that balance multiple performance criteria. This improvement stems from LLEMA's evolutionary refinmment process, where chemically guided mutations, crossover between promising candidates, and memory-based selection pressure iteratively prune the search space. The result is a guided transition from memorized priors to data-driven innovation, leading to denser clusters thermodynamically stable, property-aligned materials and a measurable improvement in both diversity and discovery quality across generations.
*
Iteration
Iteration 500
Iteratton 750
Iteration 1000
144
160
140
Dielecteic Constant
80
120
120
120
100
102
100
80
80
6-3
60)
20
4.
60
20
20
25
55
120
25
30
200
25
50
75
1000
255
50
75
300
Shear Modulus (GPs)
Shear Modulkss IGPPa!
Shear Modulus (GPs)
Shear Modullus (GPa)
Figure 9: Evolution of the Pareto front during multi-objective optimization for SAW/BAW Acoustics substrates.
Increasing Validity and Structural Fidelity. As memorization declines, the fraction of valid and physically plausible candidates rises steadily. Early populations contain roughly 30% valid materials, many of which are simple substitutions of known prototypes, while later generations surpass 80% validity. This improvement results from the combined effect of oracle-guided scoring and constraint- aware feedback that prunes chemically inconsistent structures while reinforcing successful design patterns. The process simultaneously expands the search's 's coverage of the periodic table: early iterations are dominated by light elements and common oxides, whereas later generations incorporate diverse transition metals, alkaline earths, and rare-earth substitutions, reflecting a richer exploration of the underlying chemical landscape.
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E.2 ROBUSTNESS TO PROMPT VARIATIONS
LLM-based generation can be sensitive to how prompts are phrased, so we assess whether LLEMA remains stable under changes in prompt structure. Starting from the base LLEMA prompt, we manually created three alternative versions by rephrasing instructions, reorganizing constraint descriptions, and varying the emphasis on key design objectives. These variants preserve the same semantics while altering the surface form of the prompt. We then evaluate whether LLEMA continues to produce consistent and chemically plausible candidates across these prompt variations. To assess robustness, we performed focused study on two representative tasks: Wide-Bandgap Semiconductors and Hard, Stiff Ceramics. For each task, we executed the design iterations while varying the prompt formulations used during generation. Across these controlled experiments, we observed only modest variation in the number of valid candidates produced, indicating that the method is reasonably stable under moderate prompt modifications. Results are summarized in Table 7
Table 7: Effect of different prompt formulations on valid candidate generation (hit-rate).
Wide-bandgap Semiconductors
Hard, stiff Ceramics
Prompt Version
Version Version
24.0
41.3
22.8
42.8
Version 3
26.8
44.5
E.3 EFFECT OF MODEL SCALE AND DOMAIN KNOWLEDGE
Our primary experiments GPT-4o-mini and Mi ratsal-Smaalll 11-3.21 both of which (Yang) mid-scale models. We further evaluate open-sourced models like Qwen2. ..een.55772 55-7B/14////
al. 2024a) to function within the pipeline. However, generating valid CIF files and proposing plausible materials is not a simple rule-based task, as LLMs must encode enough materials-science domain knowledge to respect crystallographic constraints, chemical compatibility, and physically realistic structures. This explains why performance improves from 7B to 14B/32B with the model size primarily acting as a proxy for embedded scientific priors (see Table Dp. This also underscores central point: rale-based evolution alone is not enough. Without domain knowledge, search trajectories drift toward non-physical or chemically invalid structures even if the output format correct. Larger models succeed not because of scale, but because they carry richer implicit understanding of stability, bonding, and symmetry. Thus, the framework leverages the domain knowledge encoded in the LLM, not the rules alone.
Table 8: Hit rates (%) across tasks for different model sizes.
Task
Qwen2.5-7B Qwen2.5-14B
Qwen2.5-32B
High-k Dielectrics
4.46
10.20
13.27
SAW/BAW Acoustic Substrates
1.30
20.83
23.81
Wide-Bandr Badd-Ba Semiconductors
9.80
22.55
20.00
E.4 RELIABILITY OF SURROGATE MODELS
Density Functional Theory (DFT) remains the gold standard for evaluating stability and functional properties; however, its high computational cost (tens of minutes hours per structure) makes impractical to incorporate directly into an evolutionary loop. To maintain fast iteration, LLEMA employs surrogate models as lightweight proxies, enabling rapid property estimation while guiding the search toward promising regions of the design space. To assess how well surrogate gurrogate-guided guided discoveries translate to high-fidelity physics, we sample 150 valid candidates across four tasks: Wide- Bandgap Semiconductors, Photovoltaic Absorbers, Piezo Energy Harvesters, and Acousto-optic Hybrids, and evaluate them using Quantum ESPRESSO (Giannozzi et al. (209) using default parameters. Among these candidates, 144 out of 150 (96 % satisfy the task constraints under DFT, indicating strong agreement between surrogate predictions and figh-iidelity outcomes. As shown in Table 9 the fraction of LLEMA--eeerattd candidate materials whose predicted properties are
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physically consistent with DFT reference calculations is provided. High DFT validity across all five evaluated properties indicates that the surrogate models used within LLEMA reliably approximate true quantum- mechaniccl behavior, supporting the robustness of property predictions across diverse materials design tasks.
Table 9: DFT Validity of predicted material properties across different tasks.
Property
DFT Validity
hand_gat gap formation energy
97%
99%
aul_abbo__uuu _uull
96%
beezo_ma___te piezo max dielectric
97%
98%
E.5 ROBUSTNESS NOISE
Since LLEMA 's evolutionary loop depends on surrogate model predictions to guide the search, it important to assess whether small perturbations these predictions alter the trajectory of the algorithm. To test robustness, we constructed noisy surrogate models by injecting additive Gaussian noise = 0, o = 0.05) into every predicted property at every evaluation step. The rest of the pipeline, including mutation, selection, and validity checks, was kept identical to the standard LLEMA setup. We then re-ran LLEMA with these noisy surrogates across all tasks and compared the resulting candidate sets with those obtained using the original models. While the overall validity rate decreases, LLEMA consistently identifies chemically similar regions of the design space: we observe 100% elemental overlap for Wide- Bide-Baaddgap Semiconductors and High-k Dielectrics, 96% for SAW/BAW Acoustics, and 84% for Hard, Stiff Ceramics. This high overlap indicates that LLEMA does not simply follow surrogate feedback. but leverages its domain knowledge and evolutionary reasoning to steer the search toward plausible solutions even when the guidance signal is perturbed. To further assess high-fidelity correctness under noisy guidance, we performed DFT calculations on set of 150 candidates generated with noisy surrogates. 141 out of 150 (94% satisfy the task constraints under DFT, closely matching the noiseless evaluation. Together, these results show that LLEMA maintains coherent, physically meaningful trajectories even under uncertain predictions, reinforcing the robustness and reliability of the method.
E.6 EFFICIENCY ANALYSIS
To evaluate computational efficiency, we compare LLEMA with LLMaiDesign and simple base LLM baseline using prompt token lengths, number of API calls, and per-iteration runtime. Table TO summarizes these results. Although LLEMA requires roughly 1.5x more tokens per iteration than the base LLM, it achieves an 8-10x improvement in discovery quality, yielding substantially more favorable performance-compurr tradeoff. The base LLM exhibits shorter runtimes primarily because it does not invoke surrogate prediction modules and often defaults to memorized priors or direct database lookups. For LLEMA and LLMaiDesign, the reported runtime includes loading pretrained surrogate models and performing property predictions. These overheads can be further reduced via model caching, parallelization across islands, and improved hardware utilization. Overall, I.LEMA delivers markedly higher scientific performance while requiring only modest additional compute, making it practical for real-world materials discovery pipelines.
Table 10: Efficiency comparison across methods.
Method
Input Tokens/Call Output Tokens/Call Time/Iter. (8) API Calls/Iter.
LLEMA L.MMatDesign
563
176
15.84
3
509
185
13.23
3
Base LLM
457
118
4.12
2
E.7 DIVERSITY OF IDENTIFIED MATERIALS
To assess the chemical diversity introduced by LLEMA, we compared the elemental distributions of generated materials against those proposed by the baseline HPT--0-m- n across four representative
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discovery tasks: photovoltaic absorbers, hard stiff ceramics, high-k dielectries, and wide-bandgap semiconductors (Figures TO 13). Each heatmap illustrates the normalized ratio of element occurennces aggregated over 250 LLM-guides iterations. Across all tasks, LLEMA consistently expands the explored chemical space, incorporating broader range of metallic, semiconducting, and nonmetallic elements compared to the baseline. For instance, in the hard ceramic and high-k dielectric tasks (Figures 12. LLEMA identifies richer combinations of transition metals and oxygen-rich compositions key building blocks for mechanically and electronically robust materials. Similarly, for wide-bandgay semiconductors (Figure 13), LLEMA diversifies the generated candidates beyond conventional group III-V and II-VI chemistries. These results highlight how the integration of memory-based refinement and themistry-informee evolutionary rules enables LLEMA to navigate and exploit underexplored regions of chemical space, thereby enhancing both diversity and relevance in LLM-driven materials discovery.
Photovoltaic Absorbers
GPT-4o-mini
LLEMA (GPT-4o-mini)
Te
0.75
2x
Agg
Rn
Nt
Gd
Dy
Hb
No
Am 3m
Ex
No
Figure Elemental distributions predicted photovoltaic absorbers 250 iterations for GPT-4o-mis and LLEMA (GPT-4o-mind The heatmap represents the normalized ratio of element occurrence in identified absorber materials.
Hard Stiff Ceramics
GPT-4o-mini
LLEMA (GPT-4o-mini)
G3
Ge
Se
2d
Ra
Pd
5n
3c
Frt
Pb
Po
An
N1h
-.26
5m
0d
1b
Ho
Pu
Am
6x
Cr
Es
Figure 11: Elemental distributions of predicted hard stiff ceramics after 250 iterations for GPT-4o-ming and LLEMA (GPT-4o-mini). The heatmap shows the normalized ratio of element occurrence in identified ceramic materials.
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Published as a conference paper at ICLR 2026
High-k dielectric
GPT-4o-mini
LLEMA (GPT-4o-mini)
H+
No
No
AT
No
AI
51
Ar
Sc
Cr
Fe
Co
NI
CU
2m
Ga
Se
A5
Se
Br
Kr
SC
Cr
Mn
Fe
Co
N1
CU
2n
Ga
Ge
Ad
Se
Kr
Rb
2x
Ru
Rm
Pr
Ag
Co
5m
50
Rb
S7
Ma
Ra
Rm
Pd
Ag
In
5m
700
Dv
11
Au
Pb
D1
A1
Run
0%
F1g
Pb
Po
mm
111
D6
14g
N0
0g
11
Kmh
Lv
0g
14
Pm
5m
5u
Gd
To
Dy
H0
Tm
Yb
Pm
5m
Tb
Dy
Ho
Tm
Adteva
Pu
Am
No
No
Cm
Es
10
Figure 12: Elemental distributions of predicted high-k dielectrics after 250 iterations for GPT-4o-mini and LLEMA (GPT-4o-mini) The heatmap shows the normalized ratio of clement occurrence in identified diclectries.
Wide-Bandgap Semiconductors
GPT-4o-mini
LLEMA (GPT-4o-mini)
He
Hu
N
No
Bc
No
No
i1g
AE
S1
No
14g
A1
51
Ar
14
Co
2m
Ga
Ge
AS
Se
Dr
Kr
Sc
Cr
Mm
Tw
Co
11
214
7m
Gx
Ge
Ag
Sm
1h
Agg
5m
501
16
M4
Rh
Pr
Ag
C3
Im
5m
Rodio
11
Av.
14g
PO
A4
1un
Ba
Au
Po
1m
11
Mt
R4
1hh
0g
15
Ra
Cn
Nth
MC
NN
5m
Bu
Gd
Te
Dy
40
1m
5m
Eu
Tb
Dy
Ho
7m
Am
Figure 13: Elemental distributions of predicted wide-bande badegaanggap semiconductors after 250 iterations for GFT-4o-mini and LLEMA (GPT-4o-mini). The heatmap shows the normalized ratio of element occurrence in identified semiconductors.
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Reviews:
[{"review_id": "Jf6Au0i6qv", "reviewer": "Reviewer_EVF3", "summary": "The proposed framework LLEMA is designed for efficient materials discovery, which includes an LLM-driven candidate generator with chemistry-aware evolutionary rules, memory pools of successful or failed candidates, and ML-based property predicting oracles. The authors designed ten materials design tasks with multi-constraint targets and stability screening. The effectiveness of the framework is demonstrated through the high valid hit rates and Pareto fronts than both generative models and LLM-only baselines. The key contribution of the work is its demonstration of materials discovery through constraining the LLM’s search with domain rules and iterative feedback, while grounding candidates with a surrogate oracle and enforcing stability.", "questions": "1. It is mentioned in A.2 that equal weights are assigned to each property in multi-objective scoring, but the section also suggests prioritized weighting. What are the specific weighting strategy used in each of the tasks? \n2. In the same section, it is also stated that  'performance-critical properties' prioritized over 'feasibility constraints' like formation energy, density, and hull stability. Is this the case for all tasks? Can you justify the design? An unstable crystal is still invalid with optimal shear modulus. How likely will the design sacrifice stability for certain performance metrics? \n3. How does the distribution of formation energy evolve over iterations in the tasks, e.g. stable wide-bandgap semiconductor task?\n4. Have you examined the failure pool for failure modes? The oracles can mislabel novel candidates as failures due to OOD, e.g. novel composition missing from the patched phase diagram or absent from the Materials Project API. Will this error being cumulated over iterations and lead to a conservative search bias toward known chemistries?\n5. How do you measure novelty and diversity beyond Materials Project, to ensure that the generated designs are not near-duplicates of known phases?\n6. What are the average prompt token lengths, number of LLM calls, API calls and pool sizes when executing each task? How does LLEMA compare to baselines in terms of efficiency and resources required, e.g. inference time and cost.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The work is a good demonstration of employing LLMs while injecting chemistry heuristics for 'multi-objective and synthesizability-aware materials design'.\n2. The diverse benchmarking tasks are well designed which align with realistic multi-constraint targets", "weaknesses": "1. No DFT validation provided on the top novel successful candidates for higher-fidelity stability evaluation.\n2. The quality of the accepted or rejected designs of the pool is highly dependent on the reliability of surrogate models. Exploration is potentially limited due to the unintentional error cumulated, which the system would favor correct known designs.\n3. The efficiency of the proposed framework is not fully explained.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "61JiGsHboF", "reviewer": "Reviewer_BxZr", "summary": "The paper proposes an LLM-guided evolutionary framework for generating candidate materials under explicit structural and property constraints. In each iteration, an LLM is prompted to produce crystallographically specified or composition-level candidates; chemistry-informed evolutionary rules and a success/failure memory then filter and refine these candidates; finally, a surrogate (learned) oracle estimates multiple target properties and a multi-objective scorer selects promising samples to feed back into the next round.", "questions": "1. Can you provide quantitative comparisons to the most similar recent frameworks that also do “LLM proposal + evolutionary/active search” for materials (e.g., [1])? Right now, the difference to those systems is mostly described at a high level.\n\n\n2. What happens if you (1) use a smaller/general-purpose model; (2) use a materials-tuned LLM; or (3) replace the LLM with a rule/template generator? This is important to justify that the gain comes from LLM knowledge, not only from the evolutionary loop.\n\n\n3. The current version seems to rely solely on surrogate-augmented oracles for property evaluation. I did not find evidence of a higher-fidelity (e.g., DFT) re-evaluation of the top candidates. Could you provide such validation or at least report surrogate error for late-stage candidates?\n\n\n4. Since every generation invokes an LLM under constraints, what is the total token/runtime cost across the 14 tasks? Are there caching or retrieval-augmentation tricks to keep the loop affordable?\n\n[1] Gan J, Zhong P, Du Y, et al. Large language models are innate crystal structure generators[C]//AI for Accelerated Materials Design-ICLR 2025. 2025.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. The proposed method puts the LLM inside an iterative optimization loop (LLM $\\rightarrow$ screen $\\rightarrow$ refine $\\rightarrow$ re-prompt). That aligns with current best practices in LLM-for-science/LLM-as-optimizer work and makes the contribution intelligible from an ML perspective.\n\n2. The framework explicitly tries to stay inside chemically plausible regions via rule-based evolution and feasibility checks, rather than treating materials generation as free-text generation. That’s an important realism step for this domain.\n\n3. The paper shows improvements on several tasks and on Pareto fronts (not just single-property top-1), making the method look more generally useful.", "weaknesses": "1. Several recent works also use pretrained LLMs to propose materials/structures and then improve them using an external scorer (e.g., [1]). The paper needs to spell out what is actually new here. Right now, the novelty can look like “a solid engineering combination” rather than a clearly new algorithmic design.\n\n2. The paper claims to “leverage scientific knowledge embedded in LLMs,” but it does not show: (1) performance when replacing the LLM with a lighter template-based (or rule-based) generator; (2) performance across LLM scales or domain specialization; or (3) how often the LLM actually proposes candidates that could not be reached by rules alone. Without that, it’s hard to justify the LLM cost.\n\n3. Surrogate reliability in out-of-distribution regions is not fully addressed. Evolutionary loops guided by learned oracles can be misled by over-optimistic predictions. The paper mentions memory-based refinement, but does not clearly report surrogate error over iterations or how many top candidates were re-evaluated with higher-fidelity methods. This weakens the “accelerating materials discovery” claim.\n\n4. Evaluation realism is partly unclear. Many of the reported constraints (stability, synthesizability, plausibility) can be enforced by heuristics or low-cost predictors. It is not obvious how many of the “hits” would remain if checked with higher-fidelity simulation or expert curation.\n\n5. The framework seems to rely on hand-crafted chemistry-informed rules. It is not clear how much effort is needed to move from the materials considered here to, say, MOFs, polymers, or battery electrolytes.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "YPlpRa9Kzn", "reviewer": "Reviewer_zEFw", "summary": "This paper presents LLEMA, which employs chemistry-informed evolutionary rules and memory-based refinement to guide large language models (LLM) in multi-objective materials discovery. Its performance is evaluated on 10 different tasks, showing higher hit rates and chemical plausibility (characterized by thermodynamic stability) than baselines including generative models and vanilla LLMs. The importance of components of the proposed method is assessed via ablation tests.", "questions": "## Technical \n1. Would statistically more principled design optimization methods, such as Bayesian optimization, work for the problem setting? How would they compare to the proposed method and other LLM-based or generative methods?\n2. In Table 2, the hit rate of generative models such as CDVAE are surprisingly low. What might be the reason? Is the tested task too different from what the methods are designed for?\n3. Following up on Q2, more recent generative models, such as MatterGen, are not covered in the benchmark. Would they perform better than the old ones?\n\n## Clarity\n4. In Sec. 2.4, how are the islands determined? This should be briefly explained in the main text. Besides, how much would the method choice or randomness in island partitioning affect the method’s performance?\n5. Minor issues\n    - in Line 33, “materials discovery remains a formidable challenge…” is an overstatement.\n    - Line 183, what format does the LLM output, CIF or JSON?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The proposed method combines LLM’s advantage of utilizing unstructured data sources with principled chemical knowledge guidance.\n- The ablation studies are comprehensive, in particular, the analysis of memorization vs guided exploration investigates a key question that LLM4Sci should answer.", "weaknesses": "- The application scenarios are oversimplifications of materials design. For example, thermodynamic stability is the minimum requirement of chemical plausibility.\n- Some common methods for constrained multi-objective optimization are not included in the benchmark tests (see Q1).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "bfVGRNLZMx", "reviewer": "Reviewer_Hxv1", "summary": "The paper introduce a unified framework called LLEMA to intergrates LLM-knowledge and domain knowledge to generate high-quality sample through iterative search and refinement. The authors test the framwork on 10 diverse tasks and achieve significant performance gain on some of the tasks.", "questions": "Please address my concerns in the weakness part. Also please check the accessibility of the code link in the abstract. I'm willing to raise the score if they're properly addressed.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. The framework provides good insight of combining LLM as search engine and modules that provides domain knowledge feedback.\n2. Significant improvements are made on some tasks.", "weaknesses": "1. The originality of the method is somewhat limited as its high-level framework is similar to LLMatDesign except for some module design like stage b and multi-objective optimization. For example, the implementation of surrogate predictor comes from previous work but provides major improvements according to figure 7.\n2. The experimental results are somewhat suspicious. LLEMA achieves very good results on tasks which LLMatDesign has nearly trivial values and has only comparable and slightly worse results on the tasks which LLMatDesign has non-trivial values. Although it's unreasonable to require SOTA result on every task, but more analysis should be made to explain this observation. For example, the author could demonstrate that the performance gain from trivial values to large values is not caused by some invalid setup of baseline methods but the design of some modules through ablation study.\n3. Different prompts are used to in candidate generation stage. It is neccessary to clarify how prompt engineering affects the results to illustrates the robustness of the method.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)