LLM and Simulation as Bilevel Optimizers: A New Paradigm to Advance Physical Scientific Discovery

Authors: pingchuan  ma
tsun-hsuan  wang
minghao  guo
zhiqing  sun
joshua b tenenbaum
daniela  rus
chuang  gan
wojciech  matusik
mit  csail
cmu  lti
mit  bcs
  cbmm
umass  amherst
Venue: NeurIPS_cc_2024_Workshop_MATH-AI
Published: 2024-09-20 06:39:48

Abstract: Large Language Models have recently gained significant attention in scientific discovery for their extensive knowledge and advanced reasoning capabilities. However, they encounter challenges in effectively simulating observational feedback and grounding it with language to propel advancements in physical scientific discovery. Conversely, human scientists undertake scientific discovery by formulating hypotheses, conducting experiments, and revising theories through observational analysis. Inspired by this, we propose to enhance the knowledge-driven, abstract reasoning abilities of LLMs with the computational strength of simulations. We introduce Scientific Generative Agent (SGA), a bilevel optimization framework: LLMs act as knowledgeable and versatile thinkers, proposing scientific hypotheses and reason about discrete components, such as physics equations or molecule structures; meanwhile, simulations function as experimental platforms, providing observational feedback and optimizing via differentiability for continuous parts, such as physical parameters. We conduct extensive experiments to demonstrate our framework's efficacy in constitutive law discovery and molecular design, unveiling novel solutions that differ from conventional human expectations yet remain coherent upon analysis.

Main paper: 
 introduction: 
 Physical science automation aims to accelerate discovery [55] . Key aspects of human scientific process include: iterative hypothesis testing [40] , discrete and continuous solution components [55] , knowledge exploitation with occasional exploration [58] , and universal principles with disciplinespecific nuances [44] . LLMs excel as generalist tools with vast knowledge [1] , aiding scientific discovery through reasoning and natural language interfaces. However, they lack computational capabilities crucial for physical sciences that requires specific domain knowledge.To this end, inspired by the overarching philosophy of human scientists, we introduce Scientific Generative Agent (SGA), a bilevel optimization approach wherein the outer-level engages LLMs as knowledgeable and versatile thinkers for generating and revising scientific hypothesis, while the inner-level involves simulations as experimental platforms for providing observational feedback. Overall, our contributions are concluded as:• We present a generic framework for physical scientific discovery that combines LLMs with physical simulations. • We propose a bilevel optimization with LLMs for discrete-space search-based optimization and differentiable simulations for continuous-space gradient-based optimization. • We conduct extensive experiments to demonstrate the effectiveness and generality of the proposed framework in physics law discovery and molecular design.38th Conference on Neural Information Processing Systems (NeurIPS 2024). The overall pipeline of Scientific Generative Agent (SGA). Taking the constitutive law searching problem as an example, the input is an initial guess (a purely elastic material), and the output is another constitutive law optimized towards the ground truth (weakly compressible fluid).ContinuousQuestion: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?Answer: [Yes] Justification: See Section 2 and Section 3.• The answer NA means that the abstract and introduction do not include the claims made in the paper. • The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers. • The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings. • It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper. 
scientific generative agent: 
 SGA is a bilevel optimization framework where the upper level features LLMs as proposers of scientific solutions, and the lower level utilizes simulations as experimental platforms for validation. We illustrate the overall pipeline in Fig. 1 .First, we describe the simulation as a process where a simulator takes in a scientific expression and continuous components as inputs and gives simulated physical phenomenon and additional observational feedback as outputs. Next, the LLM acts as a thinker to propose expressions based on past experimental results from simulation. This process involves the LLM taking in a set of past simulation results containing an evaluation of the scientific problem, other physical feedback, and past proposals, along with a prompt. The LLM then outputs proposed expressions and continuous parameterization for the decision variables. With these elements, we define a bilevel optimization problem: the objective is to minimize the evaluation of the simulated physical phenomenon, which depends on the proposed expression, continuous parameterization, and optimal continuous parameters.The optimization problem has two levels: (i) the outer optimization searches for an expression that defines what experiments to be conducted and continuous parameterization that defines the search space of the inner continuous optimization; (ii) the inner optimization, which depends on the outerlevel variables, searches for the optimal continuous parameters given the proposed expression via differentiable simulation. We detail the complete algorithm with a python-like pseudo-code in Alg. 1.LLM-driven Optimization LLMs are effective for generic optimization through prompting and context [60, 43] . Inspired by [31] , we use evolutionary search with multiple offspring per iteration.Our approach selects several high-performing candidates, enhancing hypothesis feasibility and facilitating crossover, with LLMs generating new hypotheses from past experiments [43] . Interfacing with Simulation Integrating LLMs with simulation requires efficient, structured communication. We use equation searching and entity searching for LLM-to-simulation communication, unified as an abstraction. Equation searching allows LLMs to propose equations and search spaces, while entity searching focuses on structural descriptions. For simulation-to-LLM communication, we use expert knowledge to extract relevant information as feedback, similar to a senior scientist guiding a junior colleague. The inner optimization results also serve as feedback from simulation to LLMs, detailed in the next section.We employ an exploit-and-explore strategy by adjusting LLMs' decoding temperature [60] , mimicking human scientists' approach to breakthroughs. When generating offspring, we divide them into two groups: cautious followers (exploit) and daring adventurers (explore). We observed that the exploit group often repeats previous solutions, while the explore group tends to yield overly random or invalid solutions. A 1:3 ratio between exploit and explore groups has proven effective emperically based our experiments.Inner optimization uses gradient-based methods to find optimal parameters within the search space defined by the outer level. Domain-specific knowledge is distilled through gradients from the simulation to intermediate optimization results. These results, along with the final output, are fed back to LLMs for solution refinement. The feedback may include loss curves and auxiliary recordings, providing information on various aspects of improvement.Question: Does the paper discuss the limitations of the work performed by the authors?Answer: [Yes]Justification: See Appendix E.Guidelines:• The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper. • The authors are encouraged to create a separate "Limitations" section in their paper.• The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be. • The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated. • The authors should reflect on the factors that influence the performance of the approach.For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon. • The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size. • If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness. • While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations. 
problem definitions: 
 Constitutive Law Discovery Identifying the constitutive law from motion observations stands as one of the most difficult challenges in fields such as physics, material science, and mechanical engineering. Here we follow the recent advances in physical simulation and formulate the constitutive law discovery task as an optimization problem [29] .Molecule Design We focus on a prevalent task in molecule design: discovering molecules with specific quantum mechanical properties. Our objective is to determine the optimal molecular structure and its 3D conformation to match a predefined target quantum mechanical property. The design process involves both the discrete expression -the molecular structure represented by SMILES strings [57] , and the continuous parameters -the 3D coordinates of each atom in the molecule.We design a diverse set of challenging tasks for evaluation. For constitutive law discovery, we propose 4 tasks including: (a) fitting the non-linear elastic material starting from a linear elastic material, (b) fitting the von Mises plastic material starting from a purely elastic material, (c) fitting the granular material starting from a purely elastic material, and (d) fitting the weakly compressible fluid starting from a purely elastic material. For molecular design task, we consider 4 popular tasks, centering on 3 commonly evaluated quantum mechanical properties [13, 65] : (e) HOMO (Highest Occupied Molecular Orbital) set to 0, (f) LUMO (Lowest Unoccupied Molecular Orbital) set to 0, (g) the HOMO-LUMO energy gap set to 0, and (h) the HOMO-LUMO energy gap set to -2.We consider 6 strong baselines for evaluation: (i) Chain-of-Thoughts (CoT) prompting [56] solves the problem by looking at step-by-step solutions from examples. We provide 5 examples with an explanation to CoT as the initial solution. (ii) FunSearch [43] utilizes evolutionary strategy to avoid local optimum. We adopt the given hyperparameters from the original implementation with 2 optimization histories and 4 explorers. We set the number of iterations to 20, yielding the same number of solutions evaluated, for a fair comparison to other methods. (iii) Eureka [31] generates multiple solutions in each iteration to improve the success rate of the generated code. We keep the hyperparameters from the original implementation. (iv) Optimization by PROmpting (OPRO) [60] highlights the advantages of involving a sorted optimization trajectory. We set the hyperparameters to be equal to Eureka except for the number of historical optimization steps. In all these works (i-iv), we notice the temperatures for LLM inference are all 1.0, which is equal to the exploring temperature in our method, so we denote them with 0 exploiter. We also consider 2 variants of our method: (v) Ours (no bilevel) removes the bilevel optimization by only searching with LLM. (vi) Ours (no exploit) removes the exploitation by setting the temperature to 1.0 all the time. We present our experiments against the 8 designed tasks and show the results in Table 1 . Compared to baselines (i-iv), our method is significantly better by a number of magnitudes. When the bilevel optimization is removed from our method, the performance drops dramatically, but still statistically better than baselines (i-iv), indicating the choice of hyperparameters and the integration of exploitation is helpful for the task. When we remove the exploitation but restore the bilevel optimization, we notice the performance grows back. It has comparable performance compared to our method in (d) or even better results in (h). However, in some tasks, especially hard ones (e.g., (b) and (f)) that we care more in reality, the performance gap is over 50%, indicating the effectiveness of our exploit-and-explore strategy. We also present the loss trend in task (a) in Figure 2a , our method outstands with a much lower loss and a converging trend. We present more experiments in Sec. C.Here we evaluate the importance of bilevel optimization in Figure 2b using the task (h). Comparing the blue triangle curve and the red dot curve, which represent the LLM-driven outer-level optimization and the simulation-driven inner-level optimization, it is easy to conclude that the loss performance with bilevel optimization is better. Nevertheless, we are also interested in how bilevel optimization works inside each optimization step and how much LLMs and simulations help respectively. As shown as a zigzag curve, we found that LLMs and simulations help each other over all optimization steps: the next proposal from LLMs will be better with simulation-optimized results, and vice versa. We argue that LLMs and simulations have different expertise: LLMs are generalist scientists who have cross-discipline knowledge, while simulations are domain experts who have specialized knowledge.A.1 Automated Scientific Discovery Automated scientific discovery, enhanced by machine learning methods, serves as a powerful accelerator for research, enabling scientists to generate hypotheses, design experiments, interpret vast datasets, and unearth insights that may elude traditional scientific methodologies [1, 22, 55] . This multifaceted process unfolds through two synergistically linked stages: hypothesis formation and the collection and analysis of experimental data. The integration of automated systems not only augments the scientific inquiry process but also streamlines the discovery pipeline, from conceptualization to empirical validation. This paper places a particular emphasis on, but is not limited to, constitutive # Generate M l solutions from LLM 8:(E,Θ)[:M l ] ← LLM(H.topk(K),T l ) 9:# Generate M h solutions from LLM 10:(E,Θ)[M l :M l +M h ] ← LLM(H.topk(K),T h ) 11: for m = 1, . . . , M l + M h do 12:# Continuous optimization 13:θ ← optim(E,θ ∈ Θ;Φ)H.append((E, θ)) 15:end for 16: end for Ensure: H.topk(1) # Return the best law discovery and molecular design. These areas exemplify the profound impact of automation in unraveling complex material behaviors and in the innovative design of molecules with tailored properties. Automatic identification of constitutive material models has been a long-standing problem and recent works utilizes differentiable simulation [12, 29, 30] to address it as a system identification problem. Leveraging machine learning and artificial intelligence, researchers are able to predict molecular behavior, optimize chemical structures for specific functions, and thus, rapidly accelerate the development of new drugs, materials, and chemicals [17, 66, 46] .The advancement of Large Language Models (LLMs) such as ChatGPT and GPT-4 has sparked considerable interest in their potential as autonomous agents [6, 35, 36] . Recent developments have shown that LLMs can be enhanced to solve complex problems by creating and utilizing their own tools, as demonstrated in the LATM framework [49] , and by acting as optimizers in the absence of gradients, as seen in the OPRO methodology [60] . These approaches signify a shift towards more independent and versatile LLM-based agents capable of generating solutions through self-crafted tools and optimization techniques [8, 62, 61] , showcasing their evolving problem-solving capabilities. In the realm of scientific discovery, LLMs have begun to make significant contributions, particularly in mathematics and computational problems. The FunSearch method [43] pairs LLMs with evaluators to exceed known results in extremal combinatorics and online bin packing, illustrating LLMs' ability to discover new solutions to established problems. Similarly, AlphaGeometry's success [50] in solving olympiad-level geometry problems without human demonstrations highlights the potential of LLMs in automating complex reasoning tasks. These examples underline the transformative impact of LLMs in pushing the boundaries of scientific inquiry and automated reasoning.Bilevel optimization involves a hierarchical structure with two levels of optimization problems, where the solution to the upper-level problem is contingent upon the outcome of the lower-level problem [11] . Bilevel optimization problems are inherently more complex than their single-level counterparts due to the nested nature of the optimization tasks and the intricate interdependencies between them. Recent advancements have focused on developing efficient algorithms, including evolutionary algorithms [48] , gradient-based approaches [28] , and approximation techniques [47] , to tackle the computational challenges presented by the non-convex and non-differentiable characteristics of many bilevel problems. Among a wide span of application domains of bilevel optimization, neural architecture search (NAS) [27, 4, 7, 59 ] is prominent and close to the problem setting in this paper: the upper level optimizes the discrete neural network architecture while the lower level optimizes We run all our experiments 5 times with different random seeds following previous practices [31] .Due to the complexity of the task, we provide a simple bootstrapping example of a valid design to ensure the success rate. We use warp [32] for the differentiable MPM simulation, and we develop our inner-level optimization upon PyTorch [38] . In all our experiments, we use mean square error as the criteria and Adam optimizer [20] . We choose gpt-4-turbo-preview as the backbone model for LLM and tentatively set the exploiting temperature T l = 0.5 and exploring temperature T h = 1.0.For the generation of 3D conformations, we utilize the ETKGD algorithm [42] followed by optimization using the Merck Molecular Force Field (MMFF) [14] , both implemented within the RDKit [25] . To get the quantum mechanical property values, we employ UniMol [65] , a pre-trained transformer-based large model, which has been fine-tuned on the QM9 dataset [41] .We attach the full python-like pseudo-code of Scientific Generative Agent pipeline in Alg. 1.The full input to LLM has 3 main parts: (i) system prompt, (ii) iteration information, and (iii) format prompt. For the system prompt, we insert it into the LLM at the beginning or input it as a special instruction depending on the type of LLM. For the iteration information, we first concatenate the code and its feedback and then simply stack the top K solutions. Finally, we append the format prompt at the end of the prompt to regularize the expected output. From our experiments, it is important to keep the order of prompts to ensure the performance and the successful parsing. More precisely, we show this process in the following python-like code: • Our problem focuses on loss-guided general scientific discovery, which is a super-set of regular regression problems. In the constitutive law search tasks, we do not directly feed the input/output pair to our method. Instead, we consider a much more challenging task: apply the generated constitutive law recursively and use the overall loss as the performance metric. Concretely, a classic SR methods solve arg min f ∥f (X) -y∥ given < X, y > pairs, whereas our method solves arg min f ∥g(f (X))∥ given < X, g(f (X)) > pairs and g is a complex function like physical simulation. It is easy to construct g to cover the former case using the later formulation, proving the generality of our problem setup. We formulate our problem as such to reflect a more realistic scenario in scientific discovery, where direct supervision is extremely sparse. • Our method supports arbitrary number of input variables and output features, where most of SR methods [52] have limitation on the number of input and output. The input limitation strongly caps the complexity of tasks they can solve, and the output limitation forces them ignore the structural correlation between each output dimension. In a comparison, our method supports arbitrary problem settings thanks to the code-based representation, which enables multi-dimensional arrays and tensor operations. • Our model adapts to multi-discipline application easily, while traditional SR methods typically incorporate with domain-experts' priors via hard-coded constraints and heuristic [51] , which is limited, domain-specific, and difficult to customize. Our method is built upon LLMs pre-trained on internet-level data that contains multi-discipline natural languages, mathematical expressions, and codes. As a result, it is easy for users to customize it and adapt to their own diverse applications via natural language guidance.We also compare our method with traditional methods in each specific area to demonstrate the generalizability of our method. First, we reformulate our constitutive law search task (a) into a symbolic regression task by (i) capture the ground-truth output (the stress tensors) as the supervision, and (ii) separate the 9 output dimension into 9 independent problems and ensemble them for evaluation. Note that these modifications dramatically simplified the original task: we removed back-propagation through time (BPTT) and directly discover the constitutive law without surrogate loss. We evaluate For molecule design tasks, we also compare our method with GhemGE [63] , which employs a population-based molecule design algorithm. As shown in Table 3 , our method presents a much lower loss, demonstrating the general effectiveness of our method.In order to figure out if the improvement introduced by our method is merely because the LLM saw the solutions in its training phase, we design an experiment ablating it by making it invent an imaginary constitutive law that does not exist on the earth. We mix the constitutive law of von Mises plasticity, granular material, and weakly compressible fluid by 50%, 30%, and 20%, so that the new constitutive law represents an imaginary material whose behavior is extremely complex. We repeat our experiment setup as in Figure 1 . We compare our method against the baselines and report the performances in Table 4 . As shown in the table, our method can still discover the constitutive law with a low quantitative loss. From our observation, there is very little visual difference between the ground-truth material and the optimized constitutive law.In addition to GPT-4 [36] , we repeat the experiments in Table 1 using 3 additional LLM backbones: (i) GPT-3.5 [37] , (ii) Claude-3-Sonnet [2] , and (iii) Mixtral-8x7B [16] , and report the rank of them in Figure 3 . Indicated by the largest area, GPT-4, as our choice, statistically outperforms the other methods. Interestingly, we found Claude-3-Sonnet is the second top method on most of constitutive law search task, while Mixtral-8x7B even tops on 2 molecule design tasks. As a result, our workflow also works for other LLMs, however, our suggestion for practitioners is to try GPT-4 as the first choice but also consider open-source model (e.g., Mixtral-8x7B) for budget or customizability.We visualize the statistics of the simulation execution status in Figure 4 (a) using the task (b), which is one of the most challenging tasks in our experiments. When the exploitation is removed, the error rate dramatically increases, as shown by a decrease in green bars. It leads to a degeneration in the performance of the methods with exploitation as shown in Figure 4 (b). However, even though the success rate remains high, when exploration is removed, the optimization result is still worse than keeping them both. We argue that exploration is significant when the optimization problem is challenging, especially in our case, where the search space is highly non-linear and unstructured and resulting in numerous local optimum. In order to further investigate the potential of our method and ablate the hyper-parameters for practitioners, we add a new study in terms of the number of iterations (question-answering cycles). We repeat our experiment in Table 1 with a prolonged number of iterations to 20 and report the performance in Table 5 .As shown in the table, the number of iterations turns out to be a determining hyper-parameter with significant impart on the performance. While it has little affect on relatively easier tasks, it dramatically improves the performance of the most challenging tasks including (b) and (c). For practitioners, the number of iteration should be first considered as the most important hyper-parameter when adapting our method to their own tasks.We provide a trimmed snippet of our searched constitutive law in Figure 5 (a) for task (a) where a highly non-linear material is provided as the trajectory to fit. We reformat the code slightly to fit into the text. Starting from a linear material, our method is able to automatically generate the constitutive law with a quadratic deviatoric term. Note that our method also provides a concrete implementation of __init__ function that defines the continuous parameters in the computational graph for later inner-level optimization.When comparing the two molecules with respect to their HOMO-LUMO energy gap based on optimized results from the LLM as shown in Figure 5 (b), we observe distinct characteristics in each: (i) Molecule A (gap-0) includes sulfur and chlorine atoms attached to a ring, coupled with a trifluoromethyl group, introducing electron-withdrawing effects, and (ii) Molecule B (gap-2) includes oxygen (notably in ethers) and sulfur within the ring structures introducing localized non-bonding electron pairs. Furthermore, the overall structure of Molecule B is more complex than that of Molecule A, containing multiple rings. An intriguing aspect of Molecule B, which might initially defy expectations, is the presence of a single fluorine atom. The high electronegativity of fluorine typically leads to electron density withdrawal, influencing the gap value. However, due to the complexity of Molecule B's structure, the impact of the fluorine atom is somewhat localized, thereby not significantly altering the gap value. We consider a few limitations and future directions. (i) Although we prompt the LLM to generate pseudo-code plans and comments, it is generally hard to ensure the interpretability of LLM-generated solutions. (ii) Since the LLM-generated codes are executed directly without any filtering in our application, there exists potential AI safety risk that hazards the operating system. (iii) Our method only utilizes the internal knowledge of LLMs as the prior, where in reality people design manual constraints and rule to regularize and improve the optimization [51] . We leave these domainspecific applications and human feedback-based regularization methods as our future work. (iv) The performance our method highly depends on the differentiablity of the generated code. However, Zero-order optimizers [15] should also shine since the number of continuous parameters is relatively limited. (v) LLM inference requires large computational resources and thus increases expense. For example, it spends around $10 for our method to complete one task using GPT-4, which will be increasingly inacceptable when the number of iteration grows. (vi) Due to the reuse of previously generated solutions in our proposed top-k heap, the KV cache in LLM will be highly similar between neighbor iterations. It opens a gate for recent KV cache optimization methods [64] to speedup our method by KV cache reusing.In conclution, we present Scientific Generative Agent, a bi-level optimization framework: LLMs serve as knowledgeable and adaptable thinkers, formulating scientific solutions like physics equations or molecule structures; concurrently, simulations operate as platforms for experimentation, offering observational feedback and optimizing continuous components like physical parameters. We focused on two scientific problems: constitutive law search and molecular design. Our approach outperforms other LLM-based benchmark methods, delivering consistent, robust, and nearly monotonic improvement. Furthermore, it shows exceptional ability in identifying unknown, true constitutive laws and molecular structures. Remarkably, our system generates innovative solutions that, despite being unconventional, are deemed reasonable after being thoroughly analyzed by experts in their respective domains. We view our process as a trailblazer, establishing a new paradigm for utilizing LLMs and simulations as bilevel optimization to further advancements in physical scientific discoveries.Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?Answer Guidelines:• The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.• If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics. • The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction). 
broader impacts: 
 Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?Answer: [Yes] Justification: See Section E.Guidelines:• The answer NA means that there is no societal impact of the work performed.• If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact. • Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.• The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster. • The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology. • If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML). 
safeguards: 
 Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?Answer: [Yes] Justification: See Section E.Guidelines:• The answer NA means that the paper poses no such risks.• Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters. • Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images. • We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort.12. Licenses for existing assets Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?Answer: [Yes] Justification: See Section 3.Guidelines:• The answer NA means that the paper does not use existing assets.• The authors should cite the original paper that produced the code package or dataset.• The authors should state which version of the asset is used and, if possible, include a URL. • The name of the license (e.g., CC-BY 4.0) should be included for each asset.• For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided. • If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset. • For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.traditional baselines in SRBench[24] and 3 data-driven pre-trained baselines. As shown in Table2, our method topped on this task even with a much more challenging setting. Also, since our method depends on the in-context learning ability of LLMs, it has little constraint in the number of variables than the data-driven pre-trained baselines. 
 
 Appendix:  



Reviews: review: title: title: Interesting Paper on the Integration of LLMs and Simulations
main_review: main_review: This paper introduces a bilevel optimization framework that combines LLMs with physical simulations to advance scientific discovery.  In their framework, LLMs are used to propose scientific hypotheses and reason about discrete components, while simulations are used to provide observational feedback and optimize continuous parameters. The authors demonstrate effectiveness in two scientific tasks. 

**Strengths:**
- I really enjoyed reading this paper. The direction of combining hypothesis generation capabilities of LLMs with Verifiability from scientific simulations sounds interesting for scientific discovery. 
- The authors conduct extensive experiments, including ablation studies and comparisons with methods in specific domains.

**Comments and Questions**
- How does the computational time of SGA compare to traditional methods in each domain? This information would help readers better understand the practical tradeoffs of using this approach.
- Have the authors considered ways to evaluate the interpretability and novelty of the LLM-generated hypotheses compared to the knowledge from the literature? This could be crucial for adoption in scientific communities and future research.
- I'm wondering how this framework deal with situations where simulation results contradict its proposed hypotheses? Is there a mechanism for analyzing such conflicts or these solutions are simply ignored?
title: title: Review of LLM and Simulation as Bilevel Optimizers: A New Paradigm to Advance Physical Scientific Discovery
main_review: main_review: This paper introduces a scientific generative agent framework for advancing scientific discovery---this framework builds on a bilevel optimization framework, which simultaneously optimizes the machine learning model for generating hypothesis as well as the evaluation of past experimental results from simulation. This framework is tested on new applications, namely molecular design and constitutive law discovery.

This is a strong submission---the arguments are convincing, and the framework is very promising. I particularly enjoyed reading the related work and the thoughtfulness in writing, including discussing recent trends in agent-based learning. I recommend accepting this paper as an oral presentation if space permits.

More detailed notes:
- In Table 4, the presented results are orders better than the baselines---perhaps worth explaining this discrepancy in the text.

- This framework reminds me of GAN, since the LLM is essentially treated as a generator, so it may be worth discussing that literature in the related work.
title: title: Strong Methodology in Physical Scientific Discovery
main_review: main_review: **Summary**

The paper presents the Scientific Generative Agent (SGA), a bilevel optimization framework that combines the abstract reasoning capabilities of Large Language Models (LLMs) with the computational strength of simulations to enhance physical scientific discovery. In this framework, LLMs are used to propose hypotheses in a discrete optimization setting, while simulations perform continuous optimization through experimental feedback. The authors conduct extensive experiments demonstrating the efficacy of the proposed method in the domains of constitutive law discovery and molecular design, which reveals novel solutions that challenge conventional approaches.

**Strengths**
1. The proposed SGA framework is innovative. It combines LLM-based hypothesis generation with simulations in a bilevel optimization framework. 
2. The paper demonstrates that the framework is applicable to multiple challenging domains like molecular design and constitutive law discovery.
3. The experiments are well-executed, and the results demonstrate significant improvements over several strong baseline methods. 


**Weaknesses**
1. The caption for Figure 2 is missing. Also, it will be helpful to expand the descriptions for Figures 3-5 to clarify the specific tasks they illustrate and the motivations behind them.

2. There is limited discussion regarding the interpretability of the solutions generated by the LLM. 

3. The paper briefly mentions the computational requirements, but more detailed information on the computational costs associated with using LLMs and simulations together would be helpful, especially for practitioners considering practical deployment.

**Questions**

How well does the proposed bi-level framework scale with increased problem complexity, especially considering larger simulation environments or more complex LLM hypotheses?