Augmenting Molecular Graphs with Geometries via Machine Learning Interatomic Potentials
Authors: Cong Fu
Yuchao Lin
Zachary Krueger
Haiyang Yu
Maho Nakata
Jianwen Xie
Emine Kucukbenli
Xiaofeng Qian
Shuiwang Ji
Venue: Accepted by TMLR ()

Abstract: Accurate molecular property predictions require 3D geometries, which are typically obtained using expensive methods such as density functional theory (DFT). Here, we attempt to obtain molecular geometries by relying solely on machine learning interatomic potential (MLIP) models. To this end, we first curate a large-scale molecular relaxation dataset comprising 3.5 million molecules and 300 million snapshots. Then MLIP pre-trained models are trained with supervised learning to predict energy and forces given 3D molecular structures. Once trained, we show that the pre-trained models can be used in different ways to obtain geometries either explicitly or implicitly. First, it can be used to obtain approximate low-energy 3D geometries via geometry optimization. While these geometries do not consistently reach DFT-level chemical accuracy or convergence, they can still improve downstream performance compared to non-relaxed structures. To mitigate potential biases and enhance downstream predictions, we introduce geometry fine-tuning based on the relaxed 3D geometries. Second, the pre-trained models can be directly fine-tuned for property prediction when ground truth 3D geometries are available. Our results demonstrate that MLIP pre-trained models trained on relaxation data can learn transferable molecular representations to improve downstream molecular property prediction and can provide practically valuable but approximate molecular geometries that benefit property predictions. Our code is publicly available at: https://github.com/divelab/AIRS/.

Published in Transactions on Machine Learning Research (02/2026)
Augmenting Molecular Graphs with Geometries via Machine Learning Interatomic Potentials
Cong Fu" Deportment of Computer Science & Engineering Teaas ABM University
conguu@tamu.cki edu
Yuchao Lin"
kruskallón &tama, edu
Department of Computer Science & Engineering Texas ABM University
Zachary Krueger
zachargbrvager331180omee Stamau edu
Department of Computer Science & Engineering Texas A ABM University
Haiyang Yu
hasyong@tamuu edu
Deportment of Computer Science & Engineering Texas A6M Universily
Maho Nakata
maho Ariken.jjp
RIKEN Cluster for Pioneering Researeh, RIKEN
Jianwen Xie
jianuen.iie@llmmbal.com
Lambda, Inc.
Emine Kucukbenli NVIDIA
ckuccukeenliBmriddi.ccom com
Xiaofeng Qian
ftng edu
Department of Materials Science & Engineering Tezas A6M University
Shuiwang Ji
sji Sji edu
Department of Computer Science Engineering Texas ABM University
Reviewed OpenReview: https: openreview. net/ forum? id= JuchHTISJL
Abstract
Accurate molecular property predictions require 3D geometries, which are typically obtained using expensive methods such as density functional theory (DFT). Here, we attempt to obtain molecular geometries by relying solely on machine learning interatomic potential (MLIP) models. To this end, we first curate a largo-scale molccular relaxation dataset comprising 3.5 million molecules and 300 million snapshots. Then MLIP pre-trained models trained with supervised learning to predict energy and forces given 3D molecular structures. Once trained, we show that the pre-trained models can be used in different ways to obtain geometries either explicitly or implicitly. First, it can be used to obtain approximate low-energy 3D geometries via geometry oplimization. While these geometries do not consistently reach De'T-level chemical accuracy or convergence, they can still improve downstream performance compared to non-rclaxed structures. To mitigate potential biases
Equal contribution

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Published in Transactions on Machine Learning Research (02/2026)
and enhance downstream predictions, we introduce geometry fine-tuning based on the relaxed 3D geometries. Second, the pre-trained models can be directly fine-tuned for property prediction when ground truth 3D geometries are available. Our results demonstrate that MLIP pre-trained models trained on relaxation data can learn transferable molecular representations to improve downstream molecular property prediction and can provide practically valuable but approximate molccular geometries that benefit property predictions. Our code publicly available at: https: /tt
1
Introduction
Molecular property prediction is critical task in drug discovery, chemistry, and materials science (Zhang
et al. 2023 Liyagat et al. 2024). Many molecular properties are strongly influenced by the stable 3D structure of molccule, corresponding to its lowest potential energy configuration. For example, as shown
in Table 1 in predicting the HOMO-LUMO gap property, GIN (Hu et al., 2021 which uses only 2D molecular graphs as input- achieves notably worse performance compared to PaiNN (Schütt et al.] 2021). J which leverages stable 3D geometrics. With accurate 3D structures, 3D geometric neural networks (3DGNNs)
can siguificantly improve properly prediction accuracy. However, the current standard for obtaining stable molecular structures relies on computationally expensive methods such as density functional theory (DFT) for geometry optimization. Uni-Mol+ (Lu et al., 2023) attempts to bridge this gap by predicting stable 3D geometries during training, allowing only non-stable molecule structures to be used during testing; however, it outperforms GIN but still exhibits a significant, performance gap compared to 3DGNNs, highlighting that. obtaining useful 3D geometries for property prediction remains a major challenge.
To bridge the gap of obtaining 3D geometries for molecular prop- erty prediction, aim to train machine learning interatomic potential (MLIP) pro-trained model to assist geometry relaxation for downstream tasks where only non-stable molecular structures are available during testing. This approach enables the use of downstream 3DGNNs for property prediction using pre-trained model-relaxed geometries, referred to as Force2Geo in Table [ We emphasize that Force2Geo produces approximate geometries that may not always converge to the true DFTT-optimized structures, and its effectiveness depends the molecular system and down-
Table 1: Performance gap between 2D and 3D models for HOMO-LUMÖ gap prediction on Molecule3D dataset.
Model
Validation MAE (eV)
GIN
0.1249
Uni Mol+
0.1070
Forer2Gro PaINN
0.0794
DFT PaiNN
0,0562
stream lask. Additionally, the pre-trained model can be directly fine-tuned on downstream lasks when 3D
molecular structures are provided. pre-trained models have demonstrated remarkable success in computer vision [Bommasani et al. 2021 Liu et al. 2024h and natural language processing (Brown et al. 2020 Touvron et al. 2023), where pre-training yields transferable representations that significantly enhance downstream performance. However, the development of ML.IP pre-trained models for small molecules has been hindered by the lack of large-scale datasets with Devellevel accurate energy and force labels.
In this work, to address the challenge of efficiently obtaining accurate 3D molecular structures, curate large-scale molecular relaxation dataset comprising 3.5 million small molecules and 300 million snapshots with energy and force labels, including 105 million snapshots computed using DFT at the B3LYP B3LYP/6-31CH /6-31 level of theory. By leveraging this extensive dataset, we can train an MLIP pre-trained model that can be used in geometry optimization to obtain computationally efficient but approximate 3D geometries, referred to as Force2Gco, providing a cost-cffective alternative to conventional quantum methods such as DFT. The choice of backbone models for pre-training can be found in Section 4.1 Additionally, we introduce geometry fine- fine-tuning to enhance the downstream predictive accuracy of 3DGNNs using relaxed 3D structures. Furthermore, the MLIP pre-trained model can be directly fine-tuned for property prediction when ground truth 3D geometries are available, termed Force2Prop, extending its applicability to range of downstream tasks.
Our contributions are threefold:
We curate a large-scale molecular relaxation dataset with 3.5M molecules and 300M snapshots, including 105M Dev-leveel energy and force labels, enabling MLIP model pre-training.
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Large-Scale
Supervised Pre-Training
Evaluation
Relaxation Dataset
MLIP Pre-Trained Model
Atomic numbers
Atom forces
Energy MAE
Force RMSE
Atom positions
Energies
Downstream Tasks
Force Prediction
Fine-Tuning
Geometry
Molecular Property Prediction
3D Molecules
Property Predictor
Optimization
Figure 1: Overview of the MLIP pre-trained model training pipeline. The model is pre-trained using our curated large-scale relaxation dataset, which includes atomic numbers, forces, positions, and energies for each snapshot. The pre-trained MLIP model can either be fine-tuned for molecular property prediction when stable 3D geometries are available or employed for geometry optimization to obtain 3D geometries for downstream property prediction.
We show that the pre-trained MLIP model dataset efficiently produce low-energy 3D geometries via geometry optimization for downstream property prediction, and introduce geomelry fine-tuning to further improve 3D GNN performance.
We demonstrate that the pre-trained model can be directly fine-tuned for molecular property prediction when ground-truth 3D geometries are available, highlighting the effectiveness of pre-trained MLIPs in supporting diverse downstream tasks.
2 Method
In Section 2.1 we present our curated large-scale relaxation dataset. In Section 2.2 we describe the MLIP pre-trained model. In Section 2.3 we outline the geometry optimization process using the pre-trained model. Finally, in Section 2.4 we discuss geometry fine-tuning for molecular property prediction on MLIP pre-trained model-relaxed structures.
2.1 Large-Scale DFT Relaxation Dataset
To train an MLIP pre-trained model, a large-scale relaxation datasot with energy and force labels is essential. However, such a dataset. for small molecules currently unavailable. To address this gap, we curated PubChemQCR (Fu et al., 2025), new dataset containing DFT-based geometry optimization trajectories for approximately 3.5 million molecules. Those molocules sourced from the PubChem Compound database. The raw trajectory data originale from the PubChemQC database (Nakata & Shimazaki 2017), and molecular relaxation is performed sequentially using PM3 semi-emperical method, Hartree-Food and DFT at the B3LYP 133YP//6311** G level. We extracted atomic numbers, energies, and atomic forces for each snapshot, resulting in 3,471,000 trajectories and 298,75 098,751,667 molecular snapshots, of which 105,494 095,494,71 snapshots are DFT-caleulated. On average, each molecule contains atoms, including 14 heavy atoms. Further dataset. details can be found in Appendix A and PubChemQCR (Fu et al. 2025
2.2 MLIP pre-trained Models for Small Molecules
Machine learning interatomic potentials (MLIPs) are designed approximate the potential energy surface (PES) of molecular systems, which is traditionally computed using quantum mechanical methods such density functional theory (DFT). These methods computationally intensive, motivating the use of MLIPs
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to learn the PES from DFTTcclluulaedd data. The total energy E is predicted based atomic coordinates {ar and atomic numbers [a)):= often decomposed as sum over atom-wise contributions, F = = Pa.. To ensure energy conservation, atomic forces are obtained as the negative gradient of the predicted energy with respect to atomic positions, fi = Vv, E. The pipeline of the training and usage of the MLIP pre-trained model is shown in Fig. T The MLIP pre-trained model enables efficient geometry optimization to oblain 3D geometries for downstream predictors requiring 3D molecular structures as inputs. Additionally, by capturing the underlying physics of atomic interactions during pre-training, the MLIP pre-trained model learns informative molecular representations that can be directly fine-tuned for varions downstream tasks.
To effectively serve an MLIP pre-trained model, suitable backbone architecture is required to encode molecular information and learn geometric relationships. For molecule representation, we usually represent molecules as graphs g = {V. A}, where V E Rx denotes node features, X E R=x3 represents the 3D coordinates of atoms, and A E {0, 1]mxx the adjacency matrix. In 3D molccular graphs, edges are often constructod using radius graph, where an edge is formed between two atoms if their Euclidean distance is within predefined cutoff. Molecules that share the same chemical graph but differ in their 3D coordinates X are referred to as conformers. For backbone models, geometric neural networks are well-suited as they are designed for learning on data with underlying spatial or gcometric structures, and are widely used for modeling molecular systems. In this work, we consider existing geometric neural networks as candidate backbones without developing new architectures, as architecture design is outside the scope of this study.
Formally, given a 3D molecular graph g = XV A}, where each node has a feature vector Us E R and position I2 E R3, and each edge has a feature ai E Rd a general message passing layer for molecular systems at layer 1 is defined as:
m = 6'm (o,), 2
(o.).e/) I..
(1)
(++1) = By (v.) AGG ((m)) ls i ()())) d
(2)
y READOUT (of
where 6m and du are neural networks, and AGG(-) denotes a permutation-invarian aggregation function such as mean, sum, or attention-based mechanisms. After the final message passing layer, a readout function is applied to aggregate the node embeddings into graph-level representation y for molecular property prediction. Alternatively, node embeddings can be used for node-level prediction such as predicting atom-wise energy. In molecular applications, geometric neural networks preserve equivariant or invariant representations to respect symmetries like rotation and translation, requiring Ωm and du to be equivariant functions and o!") to be geometric objects (e.g. vectors or tensors).
Since the dataset includes trajectories computed at varying levels of quantum accuracy, we use only the snapshots from the DFT substage to train the MLIP pre-trained model, leaving the exploration of training with mixed levels of accuracy for future work. Additionally, the DFT substage is the most computationally intensive, taking several hours per molecule, whereas the PM3 and Hartree-Fock stages require only a few minutes. The training objective for the MLIIP pre-trained model includes both energy and force prediction, formulated as:
L = XE LE + XF LFF
(4)
N
1
CE
E - Eilp
(5)
N
1=1
M
CF = M
Σ 1ff - fI1.,
(6)
3=1
where N denotes the number of molocules in a batch, M denotes the number of atoms in a batch, Ag and Af are weights to balance the energy and force loss terms, é, and e, are the predicted and ground truth energies, and fy and fj are the predicted and ground truth forces for each atom.
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Downstream Pre-Training
3D Molecule
Property Predictor
Property Prediction
Geometry Fine-Tuning
Pre-trained
Property Prediction
Initial 3D
Relaxation
Relaxed 3D Molecule
Property Predictor
Molecule
MLIP
Geometry
Alignment
Figure 3: Overview of geometry fine-tuning. In the pre-training stage, a properly predictor is trained on stable 3D molecules for property prediction. This pre-trained predictor is then fine-tuned on 3D molecular structures relaxed by the MLIP pre-trained model, with both property prediction and geometry alignment losses.
2.3 Geometry Optimization
After training the MLIP pre-trained model, it can be employed to perform geometry optimization to obtain stable 3D molecular structures. The objective of geometry optimization to adjust the atomic positions to minimize the potential energy of the system while adhering to predefined convergence criteria.
Initial Geometry
MLIP
DFT
Choose Functional and Basis Set
Neural Networks
Salve Self- Consistent Field
As shown in Fig. 2 the conventional DFT- relaxation Nakata & Shi- mazaki 2017) process begins by selecting an exchange-correlation energy functional and a basis set. The electronic structure then determined iteratively using the self-consistent field (SCF) method. Once the SCF loop converges, the energy of the molecule and the corresponding atomic gradients are calculated. These gradients then used to update atomic positions through optimization algorithms, such Newton's method. This process is repeated until the maximum force falls below the predefined convergence threshold. In the MLIP-based relaxation process, the neu- ral network predicts the forces directly, replacing the DFT calculation, while the remaining procedure, including the optimization loop, remains unchangod.
Energy and Gradlent
Update Geometry
No
No
Force Converge
Yes
Final Geometry and Energy
Figure 2: Comparison of geome- try optimization based on DFT and MLIP.
In this work, we utilize the Broyden Fletcher Goldfarb Shanno (BFGS) (Fletcher 2000) as the optimization algorithm for geometry op-
timization. BFGS is quasi-Newton method that approximates the Hessian matrix to efficiently update atomic coordinates and reduce the overall computational cost. The optimization process iteratively adjusts the atomic coordinates [x to minimize the potential energy E(x) predicted by the MLIP pre-trained model. each step, the atomic forces f. = V E are computed to guide the atomic displacements. The maximum force calculated as:
max force max (IIAI)),
where ft E 3 is the force vector for atom i and || denotes L.2 norm. The optimization process terminates when one the following stopping criteria is met:
The maximum force, as defined above, falls below a threshold of 0.05 eV /V/A.
The maxinum number of optimization steps is reached, set 500.

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2.4 Geometry Fine-Tume Tuning
As discussed in Section 1 when accurate 3D molecular structures are available in the lest set, 3DGNNs can predict molecular properties more effectively than Uni-Mol+. The MLIP pre-trained model can be used to obtain 3D geometrics through geometry optimization. However, using pre-trained model-relaxed conformers may introduce errors and biases due to imperfect force prediction. To address this, we introduce geometry fine-tuning to improve the accuracy of 3DGNN predictions based on these relaxed structures. The whole pipeline of geometry fine-tuning is shown in Fig. 3 Specifically, we first pre-train a downstream predictor the downstream dataset using ground-truth 3D geometries imput. We then relax the downstream training molecules pooleules-sttrrting from unstable conformers using the pre-trained ML.PP model, and fine-tune the downstream predictor on these relaxed structures. This allows the predictor to adapt to the geometric distribution produced by the pre-trained model. During testing, only the pre-trained model-relaxed geometries are provided to the downstream predictor.
For geometry fine-tuning, we adopt a multi-task learning framework by introducing geometry alignment as an auxiliary task to support the primary objective of property prediction. This auxiliary task is motivated by two key intuitions: (1) learning to predict deviations from the ground-truth geometry encourages the model to attend to subtle 3D structural cues that are critical for accurate property estimation; and (2) during fine-tuning, the model is exposed to relaxed geometries generated by the pre-trained model, which inevitably differ from the ground-truth geometries seen during pre-training. This introduces a distribution shift, and the auxiliary geometry alignment task helps bridge this gap by encouraging the model to relate the relaxed geometries back to the original ground-truth domain.
To implement the auxiliary task, we adopt mixed conformer denoising strategy. During training, half of the input structures are ground-truth conformers with added coordinate noise, and the other half are randomly sampled from the relaxation trajectory produced by the MLIP pre-trained model. In addition to the main property prediction loss, we include a geometry aligmment loss based on cosine similarity, which encourages alignment between the predicted and target atomic displacements. Formally,
Liotal = Cpop A Lgeo+
where Cprop is the loss for molecular property prediction and Cgoo is the auxiliary geometry alignment loss, defined as:
N cos cos Ar:)),
Egoo
N Σ (1 -
(9)
where Af; is the predicted displacement vector for atom i, Ar; is the target displacement vector, and cos(:,) denotes cosine similarity. À is hyperparameter to weight the auxiliary loss.
3 Related Work
Molecular Representation Learning. Learning informative molecular representations is critical for accurately predicting molecular properties. Early efforts focused on pre- pre-training models on SMILES strings using language modeling techniques such as BERT (Devlin et al. 2019 exemplified by SMILES BERT (Wang
et al. 2019 Subsequently, attention shifted toward pre- training on 2D molecular graphs by designing self-supervise learning tasks (Hu et al.] 2019 Rong al. 2020). Other works further explored learning
shared representations between 2D and 3D molecular graphs through contrastive learning (Liu et al. 2021
Stärk et al. 2022). More recently, denoising pre-training (Zaidi et al. 2022 Feng et al., 2023 Ni et al. 2023
Liao et al. 2024 has emerged as highly effective approach for molecular representation learning. In this paradigm, 3D molccular structures are perturbed with specific noise, and the model is trained to predict the applied noise. Denoising pre-training has been shown to oulperform previous pre-training methods, as it mathematically equivalent to learning an underlying interatomic potential, leading to richer and more physically grounded representations. Another line of work focuses on 3D GNNs that learn informative representations of molecular geometries to predict molecular propertics. Representative methods include SchNet. (Schütt. et al., 2017). SphereNet (Liu et al. 2022
ComENet (Wang et al. 2022), NemeNet+++

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Gasteiger et al. 2020). TorchMD-Net (Thölke & De Fabritiis 2022. and PaiNN (Schütt et al. 2021 etc. A
key limitation of these methods is that they require access to ground-truth 3D geometries in order to achieve accurate predictions.
Molecular Foundation Models. Inspired by the remarkable success of pre- pre-trained models in computer
vision (Bommasani et al., 2021 Liu et al. 2024; Zhai et al.) 2022 Dehghani et al., 2023 and natural language
processing [Brown et al. 2020 Touvron et al. 2023 Achiam al. 2023: Bai et al. 2023). molecular pre-trained
models have also begun to attract significant attention. However, due to the lack of large-scale 3D molecule
data with energy and force labels, existing molecule pre-trained models primarily focus ID SMILES strings or 2D molccular graph representations. For example, ChemFM (Cai et al. 2024) adopts self-supervised causal language modeling on SMILES, while MolE (Méndez-Lucio et al. 2022 adapts DeBERTa (He et al.) 2020) for molecular graphs. MolFM (Luo et al., 2023) jointly learns molecular representations from graphs, biomedical texts, and knowledge graphs. Nevertheless, none of these models address the fundamental task of learning 3D molecular energies and forces, which limits their applicability to geometry coometty-doendent tasks such as 3D molecular property prediction, geomelry optimization, elc.
4 Experiments
In this section, we demonstrate the effectiveness of the MLIP pro-trained model across several downstream tasks. In Section 4.1 we benchmark several backbone model candidates on PubChenQCR-S. In Section 4.2 we present geometry optimization using the pre-trained model. In Section 4.3 we show that pre-trained model-relaxed geomctrics can improve molecular property prediction when stable 3D structures are unavailable in the test set. In Section
1.4
we fine-tune the pre-trained model for 3D molecular property prediction.
4.1 Backbone Models
To select the backbone architecture for the MLIP pre- pre-trained model, we benchmark several repre- sentative MLIP models on our curated dataset.
Table Performance of represcntative machine learn- ing interatomic potential (MLIP) models on the PubChemQCR-S validation set.
The methods include SchNet (Schütt et al. 2018).
Modill
Energ MAE (man)) /acom)
Force RMSE (m=))/A
Time (minn/ppohh)
FAENct (Duval et al.) 2023). NequlP (Batzner et al.
2022). : Equilormer (Liao & Smidi 2022).
PaiNN
5.13
46.31
28
Seven
et (Park et al. 2024), Allegro (Musaclian 2023), PaiNN (Schütt et al. 2021).
SevenNet
NegfP
8.77
7.57
54.78
47.65
150
130
et al.
10
FAENes
7.28
011.24
16
PACE
Xu et 2024). and MACE (Batatia et al.
MACE
7.54
51.48
120
PACE
6.34
140
2022
Equiformer
4.69
For training efficiency, we curated smaller subset for model benchmarking, named PubChemQCR-S, which contains 40,979 trajectories and 1,504,431 molecular snapshots from the DFT stage calculations. The benchmark results are summarized in Table 2 Tn selecting a pre-trained model backbone, we consider both predictive performance and computational efficiency. Among the candidates, PaiNN demonstrates relatively strong energy prediction accuracy and the second-best. force prediction performance on the benchmark while maintaining computational efficiency, making it a strong choice for large-scale pre-training. Detailed introduction and training of those benchmarked methods can be found in Appendices B and C
4.2 Geometry Optimization
Dataset. To evaluate geometry optimization performance, we select 1,000 molecules from the test set of PubChemQCR-S using MaxMin diversity sampling to ensure maximal structural diversity. Specifically, we compute the Morgan fingerprint for each molecule in the test set and randomly select an initial molecule. We then iteratively add the molecule that has the largest. Tanimoto distance from the currently selected set. We refer to the resulting geometry optimization test set as Dopt
Metrics. Since the pre-trained model is trained using data from the DFT relaxation stage, we evaluate its geometry optimization performance by relaxing molecules starting from the first snapshot of the DFT
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trajectory. The evaluation metrics adopt are partially based on those proposed in [Tsyinn et al. 2023 and include: (1) Average Energy Minimization Percentage, petr, quantifies how much energy is minimized by the MLLP-bbsed optimization relative to the DFT-based optimization; (2) Chemical Accuracy Success Rate, puccesssss measures the percentage of relaxed molecules whose residual energy is within chemical accuracy (commonly defined as 1 Bcol/mol);
(3) Divergence Rate, pel represents the percentage of relaxed molecules for which either the singlo-point DFT energy calculation failed or the relaxed DFT energy is higher than the initial energy; (4) Force Convergence Rate, potewT, measures the percentage of relaxed molecules whose maximum force is below threshold of 0.05 eV/A. More details can be found in Appendix D
The results are presented in Ta- ble 3 While the value of pelr indicates that the MLIP-relaxed geometries reduce a certain amount of energy compared to the initial structures, notable portion of con- formers remains outside the optimal region. Consequently, the values of success and pCt are relatively low. This highlights the inherent challenge of optimizing molecular geometries that are already near the energy minimum regime where achieving further relaxation requires extremely accurate modeling of the potential energy surface.
Results.
Table 3: Geometry optimization performance of the MLIP pre-trained model pre-trained on the curated PubChemQCR dataset.
Model
(ct
pet success (%)
potaie (%)
potpwr (%)
Force2Geo
57.37
10.29
8.1
4.2
Discussions. We observe that the performance of geometry optimization is not yet ideal, indicating substantial room for improvement. The challenge of achieving high-quality geometry optimization using near-optimal training data can be attributed to several factors. First, the training data predominantly resides in low-force regimes, which provide weak learning signals. In these regions, even though the model has seen similar configurations, the small forces make it difficult for the model to learn very accurate gradients. Second, MLIP-based relaxation bocomes highly sensitive to small doviations in force direction when truc gradients are small. Near energy minima, the model is required to predict very small force vectors with high precision an inherently difficult task. Third, in low-gradient regions, the predicted forces often contain noise that can be significant relative to the magnitude of the true forces, further increasing the difficulty of accurate force prediction.
4.3 Molecular Property Prediction with MLIP Pre- Trained Model Relaxed Geometries
Task. As discussed in Section 1 obtaining accurate 3D geometries is crucial for achieving strong performance in quantum property prediction. However, acquiring ground-state geometries typically requires time-consuming DFT-based relaxation. To address this limitation, it is highly desirable to leverage machine learning interatomic polentials (MLIPs) to generate approximate stable geometries that can support downstream property prediction. Tn this task, we focus on a practical setting where ground-truth 3D geometries are available during training, but only non-stable geometries are available test time consistent with the setup used in Uni-Mol+.
Dataset. We use the Molecule3D dataset and predict the HOMO-LUMO gap, key quantum property of molecular electronic structure. We use a subset of the dataset containing 600,000 molecules for random and scoffold splits. More details about the dataset can be found in Appendix
Results. We compare geometry fine-tuning using input structures with varying levels of geometric accuracy. Specifically, we evaluate downstream performance using: (1) RDKit-generated geometries, (2) geometries after the PM3 and HF optimization, i.e. geometries before the DFT relaxation, and (3) MLIP pre-trained model- relaxed geometries. We include (2) because the pre- pre-trained model is trained on DFT substage trajectories and the relaxation begins from the first snapshot of the DFT substage. For fair comparison with Uni-Mol+,, we also evaluate Uni-Mol+ using both RDKit-generated geometries and geometries after the PM3 and HF optimization. The results of geometry fine-tuning on the random and scaffold splits are shown in Table 4 These results demonstrate that using pre-trained model-relaxed geometrics consistently improves downstream property prediction. Furthermore, compared to Uni-Mol+, our paproach-combineg MLIP-basse relaxation with downstream 3D achieves superior performance, suggesting that this modular pipeline is more
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Table Results of geometry fine-tuning with different kinds of conformers for the downstream PaiNN model on the Molecule3D dataset. In this setting, ground-trun geometries are available during training, while only non-stable geometries are provided at test time.
Random Split
Scaffold Split
Conformer + Model
Validation MAE (cV)
Test MAE (cV)
Validation MAE (cV)
Test MAE (cV)
RDKit 3D + Uni-Mol+
0,1070
0,1090
0.1688
0.2245
PM3 & HF 3D + Uni-Mol+
0,1052
0,1080
0.1660
0,2211
RDKit 3D + PaiNN
0.1576
0,1598
0,2089
0.2741
PM8 & HF 3D + PaiNN
0.0889
0.0916
0.1400
0.1880
Force2Geo PaiNN
0.0794
0.0822
0.1281
0.1832
DFT 3D + PaiNN (Ground truth)
0.0562
0.0575
0.1083
0.1548
effective than architectures specifically designed to bridge the gap between non-stable and ground truth molecular structures.
4.4 Fine- Tone-Tnnnn MLIP Tre-Trained Model for Molecular Property Prediction
Task. To demonstrate the effectiveness of the MLIP pre-trained model for 3D molecular property prediction, we fine-tune the pre-trained pre-trained model on downstream tasks where the goal is to predict molccular propertics given 3D molccular structures. In this setting, ground-truth geometries are used input. We evaluate the performance two benchmark datasets, described below.
Table 5: Results of HOMO-LUMO gap prediction on the 22DFT dataset. Best results are shown in bold, and second- best results are underlined.
Model
Validation MAE (eV)
Test MAE (eV)
SchNet
0.1216
0.1461
SphereNet
0.0625
0.0819
ComENet
0,0831
0.1135
DimeNet
0,05445
0.0786
Datasets. We use Molecule3D subset created in Section 4.3 and DFT Khrabrov et al. 2024 datasets. The details of the datasets can found
TorchMD-Net
0,0815
0,1029
PaiNN
0.0589
0.0857
Force2Prop w/ PaINN
0.0483
0.0683
in Appendix E In this task, we predict the HOMO-LUMO gap, and ground truth 3D geometries are provided.
Additional results the full Molecule3D dataset provided in Appendix G.1
Baselines. We select a set of representative models baselines, including GIN-virtual (Hu et al. 2021), SchNet (Schütt et al.] 2017), SphereNet (Liu et al.] (0022), ComENet (Wang et al.] 2022). N (Gasteiger et al., 2020), TDrchMD-Net (Thölke & De Fabritiis 2022), Uni-Mol+ {Lu et al.. 2021.. For the Molccule3D dataset, we include 2D models, 3D models, and 2023 and PaiNN (Schütt et al.
hybrid approaches like Uni-Mol+. For the D2DFT dataset, we focus exclusively on 3D models.
Results. The results for the Molecule3D random split and scaffold split are reported in Table 0 The fine-tuned pre-trained model achieves the best performance in both settings. The scaffold split is a more challenging evalua- tion setup, as it requires models to generalize to out-of- distribution molecular scaffolds. As expected, all meth-
0.6
Randem feature & train head
Pre-trained model & frieune head
Validation MAE (eV0
MM
0.4
0.3
ods perform worse on the scaffold split compared to the random split, and the gap between validation and test accuracy is also larger in the scaffold setting. GIN-virtual performs the worst among all methods, it only uses the 2D molccular graph as input, while the HOMO-LUMO gap is highly sensitive to 3D molecular geometry. Uni-Mol+ outperforms GIN-virtual by incorporating ground-trun truth 3D geometries during training and learning to predict stable 3D structures from RDKit-initiaiie conformers. However, it still lags behind 3D GNN models, which
0.1
400000
Training steps
Figure 4: Compare fine-tuming the full pre- pre-trained model versus training only the prediction head using pre-trained or random features.
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Table 6: Results HOMO-LUMO gap prediction on two splits of the Molecule3D dataset. Force2Prop w PaiNN denotes the MLIP model pre-trained on our PubChemQCR dataset. Best results are shown in bold, and second-best results are underlined.
Random Split
Scaffold Split
Model
Validation MAE (eV)
Test MAE (eV)
Validation MAB (eV)
Test MAE (eV)
GIN-virtual
0.1249
0.1272
0.1920
0.2421
Uni-Mol+
0.1070
0.1090
0.1688
0.2245
SchNet.
0.0718
0.0731
0.1253
0.1837
ComENet
0.0675
0.0693
0.1258
0.1876
DimeNet+
0.0550
0.0569
0.1106
0.1729
TorchMD-Net
0.0507
0.0525
0.1037
0.1454
PaiNN
0.0562
0.0575
0.1083
0.1548
Force2Prop w/ PaiNN
0.0471
0.0486
0.0911
0.1298
Downstream training different (random)
Downstream training different (scaffold)
0.12
0.12
scratch
Pro Pre-trained model finetune
Pre traitrannd medel finetune
0.10
0.10
Validation MAE (eV)
Validation MAE (eV)
0.06
0.06
0.04
0.04
0.00
0.00
0.75
1.00
1.25
1.50
1.75
2.00
2.25
0.75
1.00
1.25
1.50
1755
2.00
2.25
Training data size (M)
Training data size (M)
(b)
Figure 6: Results of fine-tuning the MLIP gre-trained model on Molecule3D with different sizes of downstream data for (a) random and (b) scaffold split.
accurate 3D geometries during both training and inference. The results the DFFFT dalaset are presenled in Table 5 Again, the fine-tuned pre-trained model achieves the best performance among the 3D baselines, further demonstrating its offectiveness in downstream molocular quantum property prediction tasks.
A Analysis. Inspired by Zaidi et al. (2022). we conduct an experiment to evaluate the usefulness of pre-trained features. Specifically, freeze the backbone and finc-tune only the prediction head, and compare it to baseline where the backbone is randomly initialized and only the prediction head is trained. The training curves are shown
Pre erettrining with different data size
0.12
Random splt
Scaffold split
Validation MAE (eV)
in Fig. 1 As expected, fine-tuning only the prediction head performs worse than fine-tuning the entire model, but
0.04
still significantly outperforms training the head on top of random features. This indicates that pre-trained features provide meaningful representation for the downstream task. However, to fully adapt the model and achieve optimal performance, it is necessary to fine-tune the entire network.
0.62
0.00
Pre-training data size (M)
Figure 5: Fine-tuning performance of the pre- trained model pre-trained with different sizes of data.
We also conduct experiments to investigate how the sizes of the pre-training and downstream datasets affect performance on downstream tasks. As case study, we use HOMO-LUMO gap prediction on the Molecule3D dataset. First, evaluate the effect of downstream dataset.
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size by fine-tuning the same pre-trained model varying amounts of downstream data. The results, shown in Fig- 6 demonstrate that increasing the amount of downstream data consistently improves performance for both the random and scaffold splits. More importantly, the performance gain from fine-tuning the MLIP pre-trained model over training from scratch especially pronounced when the downstream data is limited. This suggests that the pre-trained models is particularly beneficial low-data regimes for downstream tasks.
Second, we assess how pre-training dataset size impacts downstream performance by fine-tuning the MLIP pre- trained model pre-trained with different amounts of data while keeping the downstream data fixed. As shown in Fig. 5] rownstream accuracy improves steadily as the size the pre-training dataset increases. These results highlight the dual importance of both pre-training scale and downstream data availability, and underscore the value of pre-trained models in resource-constrainnell set- tings. Additionally, we pre-train different model architecture to demonstrate that the benefits of pre- pre-training generalize across architectures. Spocifically, we pre-train SchNet as the pre-trained model and observe that it also outperforms training from scratch, as shown in Table 7 which further validates the effectiveness of the MLIP pre-training.
Table 7: Comparison between fine-tuning the pre-trained model and training from scratch us- ing SchNet the backbone the Molecule3D dataset.
Model
Validation MAE (eV)
SchNet
0.0718
Force2Prop w/ SchNet
0.0572
5
Summary
In this work, we train machine learning interatomic potential (MLIP) pre-trained model using large-scale molecule relaxation data. By curating dataset comprising 3.5 million small molecules and 300 million snapshots with energy and force labels computed at multiple levels of quantum accuracy, we enable the development of MLIP pre-trained models that can be used to efficiently obtain low-energy 3D structures through geometry optimization for downstream property predictions. Additionally, we introduce geometry fine-tuning as a stralegy to mitigale errors and biases introduced during structure relaxation, enhancing the downstream property prediction performance using relaxed 3D geometries. Furthermore, we demonstrate that the MLIP pre-trained model can be directly fine-tuned for molccular property prediction tasks, further extending its applicability.
6 Broader Impact Statement
DFT-based geometry optimization can produce highly accurate molecular structures for property prediction, but it is computationally expensive. Our MLIP model, trained on the curated relaxation dataset, demonstrates strong potential for efficiently generating approximate geometries and can improve downstream property prediction to a certain extent. However, we emphasize that the geometries produced by the MLIP model are not yet. comparable to those obtained via DFT, and caution should be exercised when applying them critical or high-stakes scenarios. To support further research, we will release both the curated dataset and the trained model to facilitate continued development of MLIP methods.
Acknowledgments
SJ acknowledges support from SES AI Corporation, ARPA-H under grant 1AY1AX000053, National Institutes of Health under grant U01 AO070112 12, and National Science Foundation under grant IIS-2243850. XFQ acknowledges support from SES AI Corporation, the Center for Reconfigurable Electronic Materials Inspired by Nonlinear Dynamics (reMIND), an Energy Frontier Rescarch Center funded by the U.S. Department of Energy, Basic Energy Sciences, under Award Number DE-SC0023353. We acknowledge the support of Lambda, Inc. and NVIDIA for providing the computational resources for this project
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A More Details about the Parge-Scale DFT Relaxation Dataset
In this section, we introduce more details about curated PubChemQCR, dataset, covering data generation, curation process, and data statistics. Data are publicly available at: http:://auginngaacc../oottttttt divelab/PubChem(CR
A.1 Dataset Generation
The raw trajectory data are sourced from the PubChemQC database (Nakata & Shimazaki 2017). The geometry optimization of cach molccule follows a structured protocol. First, initial 3D molccular structures are generated from the InChI representation using OpenBabel, providing the starting point for subsequent quantum calculations. The first optimization is performed using the PM3 semi-empirical method. Next, the relaxed structures undergo further refinement using the Hartrco-Fock method with the STO-6G basis set. Finally, the 3D structures are fully optimized using the B3LYP functional with the 6-31 basis set. PM3 and Hartree-Fock optimizations are performed using the GAMESS software. The DFT optimization consists of three substeps: first, Firefly or SMASH is used for faster but slightly less accurate optimization. Then, GAMESS is employed for more precise geometry optimization, followed by final validation step to ensure molecules are indeed optimized.
A.2 Dataset Curation
The raw trajectory data is 7TB in size and not immediately suitable for machine learning. To make it more accessible, we parsed all raw log files to extract the energies and forces at each snapshot, along with the atomic numbers and coordinates of each alom.
We save the parsed trajectories six Lightning Memory-Mappeet Database (LMDB) files, leveraging its efficient kcy-value storage and fast data retrioval. Each trajectory is saved as a kcy-value pair, where the key is the PubChem CID, unique identifier for chemical compounds in the PubChem database, and the value is dictionary containing the parsed trajectory, with keys corresponding to the names of each optimization stage, f.e. pm3, hf, pFt_ and DFT 2nd. By storing snapshots from each optimization stage separately, we provide more flexibility in selecting specific trajectory segments for training. The curated dataset is 400GB in size, significantly smaller than the raw data. This size reduction, along with the structured data format, enhances accessibility and usability for the research community, making easier to develop models using the dataset.
A.3 Dataset Statistics
The full datasel contains 3,471,000 Irajectories and a total of 298,751, 667 molecular snapshots, including 163,015,359 snapshots from PM3, 19,274,130 snapshots from Hartree- Fock, 105,494,671 snapshots from the first substage of DFT calculations and 10,967,501 snapshots from the second substage of DFT calculations. On average, each molecule consists of 29 atoms, including 14 heavy atoms, and each molecular trajectory contains approximately 47 PM3 snapshots, 6 Hartree-Fock snapshots, 31 DFT first substage snapshots, and 3 DFT second substage snapshots. This dataset covers 25 chemical elements.
For training efficiency, we also curated smaller subset for model benchmarking, named PubChemQCR. S, which contains 40,979 trajectories and 1,504,431 molecular snapshots from the first substage of DFT calculations.
B Benchmarked Methods on PubChemQCR-S
SchNet (Schütt et al. 2018) is a continuous-Hf filter convolutional network that models local alomic correlations using learned filter teter-generating networks. FAENet (Duval et al., 2023 introduces frame averaging to enforce symmetry compliance molccular systems, allowing geometric information to be processod without explicit commetry-preservine architectural constraints. NequIP (Batzner et al. 2022p and Equiformer (Liao & Smidt 2022 are equivariant neural networks that model interatomic interactions while preserving geometric
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Table 8: Model configurations including the number of layers, hidden dimensions (or maximum irreducible representation channels), and batch sizes-are provided for all baseline models trained on the PubChemQCR-S dataset. These models include SchNet (Schütt al. 2018), PaiNN
(Schütt et al., 2021p. MACE (Batatia et al. 2022|, Equiformer (Liao & Smidt, 2022], PACE [Xu et al. 2024), FAENet (Duval et al. 2023
NequlP [Batzner et al. 2022). SevenNet (Park et al.
2024 and Allegro (Musaelian et al. 2023).
Models
Layers
Hidden Dimension
Batch Size
SchNet
128
128
PaiNN
4
128
32
FAENel
128
64
NequIP
64
16
SevenNet
128
16
MACE
128
8
PACE
128
8
Allegro
2
128
8
Equiformer
128
32
symmetries. They maintain varions types of geometric features during message passing and capture feature interactions using the Clebsch Gordan tensor product. Equiformer further incorporates attention mechanisms into the equivariant message passing process. SevenNet (Park et al. 2024) an equivariant model that builds upon the NequlP architecture by introducing scalable parallelization scheme designed for spatial decomposition in large-scale molecular dynamics (MD) simulations. Allegro (Musaclian et al. 2023 is highly efficient, local equivariant model lailored for scalable, high-accuracy sinulations. It models many-body interactions through series of tensor products of learned equivariant representations. PaiNN (Shüit et al. 2021 extends SchNet by introducing equivariant representations, enabling the model to capture directional dependencics while maintaining computational efficiency. MACE (Batatia et al. 2022) and PACE (Xu et al. 2024) are other equivariant frameworks that capture many-body interactions using symmelry-aware neural architectures.
C Training Details of Benchmarked Methods
On the PubChemQCR-S subset, Equiformer uses a separate prediction head to directly predict atomic forces, whereas other methods compute forces as the gradient of the predicted energy. Note that to eliminate the influence of molecular size, we predict the energy per atom rather than the total energy. Additionally, we normalize the energy by subtracting the mean energy during training. To remove the effect of translation, also center the coordinates by shifting them to have a zero centroid.
Table summarizes the model configurations used for all baseline methods. For FAENet, we adopt the "simple" message- message-passing variant, while for MACE, we include the residual interaction block to enhance expressiveness. Initial attempts to train Equiformer using its original OC20 settings (6 layers with hidden irreps of either 256 Oc + 256x1c or 25 128 x1) failed converge; thus, we employ a reduced configuration consisting models including NequlP (Batzner et al. 2022 MACE [Batatia et al. 2022 PACE (Xu al. 2024h, Allegro (Musaelian et al. 2023 SevenNet (Park
of 4 layers with irreps 128x0e + 64 le. For all lensor-produut--esse
et al.
2024). and Equiformer [Lioo & Smidt, 2022 only even-parity irreducible representations are used
and
maa 2 except for Equilormer.
All experiments on the PubChem@CRRS benchmarks employ a cutoff radius of 4.5 the Adam opti- mizer (Kingma & Ba 2014) with an initial learning rate of 5 10-4, and a REDUCELRONPLLATEA learning rate scheduler with a patience of 2 epochs. Models are trained for up 100 epochs on the PubChemQCR-S subset. using NVIDIA A100-80GB GPUs.
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D Metrics for Geometry Optimization
Average Energy Minimization Percentage. This metric quantifies how much energy is minimized by the MLIP-relaxed conformer relative to the DFT-relaxed conformer:
petr =
Σ
pet(er),
(10)
(Popt
cEDops
where pet(er) is defined as:
EDFT EDFT EDFT EDFT Px
pet(er) 100%
(11)
Here, co, er; and Cgg denote the initial conformer, the MLIP-rolaxed conformer, and the DFT-relaxed conformer, respectively. E refers to the single-point DFT energy evaluated at the given conformer.
Chemical Accuracy Success Rate. This metric measures the percentage of relaxed conformers whose residual energy is within chemical accuracy (commonly defined as kcal/mol):
potsuccees
Σ cEDapt
([E < <]];
(12)
iDopt
with the residual energy defined as:
E = DFF EDFT
(13)
Divergence Rate. This metric, denoted as pel represents the percentage of relaxed molecules for which either the single-point DFT energy calculation failed or the relaxed DFT energy is higher than the initial energy.
Force Convergence Rate. This metric measures the percentage relaxed molecules whose maximum force below a threshold of 0.05 ev/A:
FoT
Σ
[max((((er) < 0.05)
(14)
[Dopt]
cEDapt
E Downstream Datasets Details
Molecule3D. The Molecule3D dataset (Xu et al., 2021 is curated from the PubChemQC dataset, which contains nearly 4 million organic small molecules. Each molecule is associated with ground-state 3D geometry derived from DFT calculations, along with corresponding quantum properties. In our experiments, we focus on predicting the HOMO-LUMO gap, a key quantum property of molecular electronic structure. Molecule3D provides two standard data splits: a random split, where training, validation, and test sets are sampled from the same distribution, and a scaffold split, which introduces a distribution shift between training and test sets to evaluate model gencralization. Since Molecule3D and our curated dataset are derived from the source, we remove any overlapping molecules from the Molecule3D test. set prevent data leakage.
D'D DDFT [Kraabovv et al. 2024 is recently introduced large-scale benchmark that includes DeT-level N-BB97--Ddeef-S71
calculations of energies, forces, molecular properties, and Hamiltonian matrices. For training, we use the large split comprising 99,018 molecules and 500,552 conformations. The structure test split includes 176,001 molecules.
F MLIP Pre- Trained Model and Training Details
For the MLIP pro-trained model, we use PaiNN with hidden dimension of 128, 128 Gaussian components in the radial basis function, layers, and cutoff distance of 4.5A. We adopt the PaiNN implementation from the Open Catalyst Project GitHub repository (Chanussot et al. 2021
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Published in Transactions on Machine Learning Research (02/2026)
Table 9: Results of HOMO-LUMO gap prediction on two splits the Molecule3D full dataset. Force2Prop w/ PaiNN denotes the MLIP pre-trained model pre-trained on the PubChemQCR dataset. Best results are shown in bold, and second- best results are underlined.
Random split
Scaffold split
Model
Validation MAE (eV)
Test MAE (eV)
Validation MAE (eV)
Test MAE (eV)
GIN-virtual
0.1038
0.1053
0.1875
0.2492
Uni-Mol+
0.0849
0.0850
0.1477
0.2044
SchNet.
0.0423
0.0438
0.0996
0.1619
ComENet
0.0432
0.0438
0.1048
0.1805
DimeNet+
0.0398
0.0418
0.0869
0.1451
TorchMD-Net
0,0348
0.0364
0.0895
0.1403
PaiNN
0.0338
0.0356
0.0901
0.1378
Force2Prop w/ PaiNN
0.0308
0.0324
0.0771
0.1204
For pre-training the MLIP pre-trained model on PubChemQCR, we use a learning rate of 1c-3 and batch size of 64. Optimization is performed using Adam (Kingma & Ba 2014) with 81 0.9, 82 = 0.999, and learning rate scheduling via RecnccLROnPllteau with patience of 2 epochs. Training is conducted for 9 epochs on four NVIDIA H100 GPUs.
For fine-tuning on downstream tasks, we use batch size of 256 and learning rate of 5e-4, with Adam optimizer (81 = 0.9, B2 = 0.999). We apply a StepLR scheduler with a step size of 40 and ạ = 0.5, and train on a single NVIDIA A100 GPU.
G Additional Results
G.1 Experimental Results of Molecule3D Full Dataset
Table presents the fine-tuning results the full Molecule3D dataset. With more training data, all methods show improved performance, and the MLIP pre-trained model continues to achieve the best results, demonstrrating the effectiveness of the pre-trained pre-trained model.
G.2 Different Pre- Training Strategies
In this work, we adopt supervised pre-training train the pre-trained model for explicit energy and force prediction. Previously, due to the lack of large-scale relaxation datasets with both energy and force labels, prior methods relied self-supervised pre-training. Among them, denoising pre-training has been the most effective, and we compare our approach against this strategy. Specifically, we consider two denoising methods: coordinate denoising (Zaidi et al. 2022) and the more recent DeNS method (Liao et al. 2024), which is designed to generalize to non-equilibrium structures. We then fine-tune the pre-trained models on the Molecule3D dataset for molecular property prediction. Results in Table I0 show that supervised pre-training outperforms denoising-based methods on downstream tasks, as enables the model to explicitly learn atomic interactions.
Table 10: Performance of fine-tuning PaiNN pre-trained with different strategies for HOMO-LUMO gap prediction Molecule3D subsct random split.
Model
Validation MAE (eV)
DeNS w/ PaiNN
0.0560
Denoising w/ PaiNN
0.0533
Force2Prop w/ PaiNN
0.0471
18

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Published in Transactions on Machine Learning Research (02/2026)
G.3 Different Training Hyperparameters in Geometry Fine- Tuning
As described in Section 2.4 we perform geometry line-tuning using multi-task learning by incorporating an additional geometry alignment task. During training, noise is added to the ground truth conformers to improve generalization. We evaluate the impact different noise scales, with results shown in Table [1]] The results indicate that performance is sensitive to the noise level-both overly small and overly large noise can degrade performance. We also investigate the effect of varying the loss weight for the geometry alignment. task. As shown in Table [2] the performance is relatively robust to the choice of loss weight.
Table 11: Performance comparison of different noise scales in multi-task learning for geometry fine-tuning.
Noise Std
Validation MAE (eV)
0.0
0.0876
0.02
0.0817
0.05
0.0807
0.1
0.0794
0.2
0.0825
0.3
0.0867
0.4
0.0907
Table 12: Performance comparison of different geometry loss weights in multi-task learning for geometry
fino-tuning.
Geometry Loss Weights
Validation MAE (cV)
0.01
0.0799
0.05
0.0802
0.1
0.0794
0.2
0.0801
0.3
0.0808
G.4 Dataset with Only 2D Graphs
In Section 2.4, the task assumes access to ground-truth 3D conformers during training but not at test time. A more challenging setting arises when neither the training nor the test set includes ground truth 3D goometrics-one
2D molccular graphs are available. For this experiment, we prodict the HOMO- LUMO gap on the QM9 dataset. using only 2D graphs. Initial 3D conformers are generated via RDKit and relaxed using pre-trained model; the downstream predictor is then trained from scratch these relaxed geometries. As shown in Table 13 a significant performance gap remains between using ground-truth versus relaxed conformers. This is partly because the pre-trained model was trained only on geometries near the energy minimum, making relaxation from RDKit conformers an out-of-distribution task. Also, the geometry optimization capability needs further improvement when is used to generate stable conformers for downstream property prediction tasks. If the optimized geometries are imperfect, correcting the relaxation bias becomes highly challenging without ground-truth geometries available during training. Although our current pre-trained model does not perform well in this setting, we highlight this scenario an important. future direction, aiming to eliminate reliance DFT-derived geometries entirely.
19

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Published in Transactions on Machine Learning Research (02/2026)
Table 13: Performance comparison of downstream predictors trained from scratch on MLIP-relaxed geometries versus ground-truth geometries for the QM9 HOMO-LUMO gap prediction task. In this setting, only 2D molecular graphs are provided for the MLIP to perform relaxation.
Conformers
Validation MAE (eV)
Relaxed 3D)
0.4846
Ground truth 3D
0.1137
20


Reviews:
[{"review_id": "aN9xIODt6u", "reviewer": "Reviewer_kKwo", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper demonstrates an ambitious workflow combining ML-based geometry optimization of molecules with ML-based molecular property prediction. MLIP models are trained on a large molecular relaxation dataset and are then applied to geometry optimization and fine-tuned for molecular property prediction tasks. The geometry fine-tuning step introduced in the paper is an interesting contribution to improve the overall performance of the proposed workflow. If the dataset could be made available, it would also be a major contribution and a valuable resource for the community.\n\nApplying graph neural network models (called 3DGNNs in the paper) trained to predict total energy and atomic forces for geometry optimization (or molecular dynamics) or to predict molecular properties directly is not new, but it is interesting to see these tasks combined in a workflow. However, the results presented in the paper are not entirely convincing and important information required to assess the results is either missing or needs clarification before the paper is ready for publication (see detailed comments below).", "claims_and_evidence_yn": "No", "claims_explanation": "There is not enough information about the training and evaluation procedures of all the different models to fully assess or reproduce the results presented in the paper (see detailed comments below).", "audience_yn": "Yes", "audience_explanation": "Many related works describe how ML-based techniques can accelerate drug or material discovery by replacing computationally expensive methods, but they often focus on a single task without considering the effect on downstream tasks. The application of MLIP-based geometry optimization followed by ML-based property prediction proposed in this paper is ambitious and interesting.", "requested_changes": "In the introduction, please clarify what is seen as the main contributions of the paper, i.e. what is novel and what is not. This will help the reader navigate the paper and strengthen the work.\n\nThe MLIP model presented in this paper is described as a “foundation model”. Without showing generalization to a wide range of tasks, I don’t think there is sufficient support for this claim. Using the term “foundation model” should be justified or changed.\n\nAs a reader, I am wondering what model architectures are applied in the work, but these are not introduced before section 4. This information could be mentioned in the introduction, directly or by adding a reference to a subsequent section.\n\nIn section 2.2, the notation E is used both as the total energy and as the adjacency matrix. Please consider using different notation. \n\nThe training objective for the MLIP model, defined in section 2.2, combines absolute error on energy and squared error on forces. What is the reasoning for combining absolute and squared error? Is this objective used for all the MLIP models evaluated in the paper? If this decision is based on any previous work, please add a reference.\n\nSection 3 on related work briefly covers models based on 1D SMILES strings and 2D molecular graphs but does not mention important work about models based on 3D structures, which are arguably more directly related to the present work. Please mention some of the more directly related work in this section or point to a section where this information can be found.\n\nIn section 4, it is difficult to follow exactly what models were used when and how they were trained. For example, the capacity of a NequIP or MACE model varies significantly with the node size and the L-order. Please clarify and make sure training details are presented in the paper or in a referenced appendix. Specifically, it is not completely clear from the main text what exact model architectures are referred to as “Force2Geo” and “Force2Prop” and how they were trained.\n\nIn section 4.2 it is noted that the performance of the geometry optimization is not ideal and the training data primarily has low forces. How does the distribution of forces in the training data compare to the distribution of forces in the test data, specifically the initial structures for the relaxation? Perhaps the training data is not sufficient for the task and more data with higher forces (for example from molecular dynamics simulations) is needed?\n\nIn section 4.3 it is not entirely clear if and how the geometry fine-tuning approach introduced in section 2.4 is applied and how it affects performance. It would be interesting to see results of a property prediction from MLIP relaxed geometries using a property prediction model trained with and without the geometry fine-tuning step to assess the effect of geometry fine-tuning.\n\nThe suite of models that are evaluated in section 4.1 and section 4.4 are not the same. Please clarify how and why were these models selected for each task?\n\nIn figure 4, how do the fine-tuning results compare to training a model from scratch?\n\nIn figures 5 and 6, please consider fixing the lower limit on the y-axis to zero to make the presentation of the results clearer. Showing such a narrow range on the y-axis can make the relative differences look more dramatic than they really are and thus be misleading. Using the same limits in all three plots would also make the results easier to compare and interpret.", "broader_impact_concerns": "None.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "f9hkVX1nY5", "reviewer": "Reviewer_Pk1o", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper addresses the challenge of obtaining accurate three-dimensional molecular geometries for molecular property prediction when density functional theory based geometries are unavailable or prohibitively expensive. The main contribution is the curation and use of PubChemQCR, a large-scale molecular relaxation dataset derived from PubChemQC, containing approximately 3.5 million molecules and nearly 300 million molecular snapshots with energy and force labels, including over 100 million snapshots computed at the DFT B3LYP/6-31G* level.\n\nUsing this dataset, the authors train a supervised machine learning interatomic potential foundation model, primarily based on a PaiNN backbone, to predict molecular energies and forces. The pretrained model is then used in three distinct but related ways. First, it is employed as a surrogate potential for geometry optimization, producing relaxed molecular conformers that can be fed into downstream three-dimensional graph neural networks for property prediction (Force2Geo). Second, the authors introduce a geometry fine-tuning strategy that adapts downstream predictors to the distribution shift induced by MLIP-relaxed geometries via a multi-task objective that includes a geometry alignment loss. Third, the pretrained MLIP model itself is fine-tuned directly for molecular property prediction when ground-truth geometries are available (Force2Prop).\n\nThe key strengths of the work are the scale and engineering effort involved in dataset construction, the modular framing that separates geometry generation from downstream prediction, and the comprehensive experimental evaluation across geometry optimization and property prediction benchmarks. The strongest empirical results are in the Force2Prop setting, where consistent improvements over strong baselines are reported. The main weakness is that the geometry optimization performance remains weak in absolute terms, and the current results do not convincingly demonstrate that MLIP-based relaxation can serve as a reliable replacement for DFT when no ground-truth geometries are available.", "claims_and_evidence_yn": "No", "claims_explanation": "The claim that large-scale supervised pretraining on relaxation trajectories yields transferable MLIP representations is well supported. The Force2Prop results on Molecule3D and ∇2DFT consistently outperform strong three-dimensional baselines such as SchNet, DimeNet++, TorchMD-Net, and PaiNN. The ablation studies on pretraining data size, downstream data size, and fine-tuning method convincingly show that pretraining is beneficial, especially in low-data regimes. Comparisons against denoising-based pretraining further support the argument that explicit energy and force supervision leads to stronger representations.\n\nHowever, the claim that the foundation model can provide valuable molecular geometries via geometry optimization is only partially supported. The geometry optimization metrics in Table 3 show that only 10.29 percent of molecules reach chemical accuracy and only 4.2 percent satisfy the force convergence criterion. The gap between Force2Geo-relaxed geometries and DFT-relaxed geometries remains large, with downstream property prediction errors roughly 40 percent higher than when using DFT geometries. While the authors are transparent about these limitations and provide a qualitative discussion of why near-equilibrium force prediction is difficult, the evidence does not yet justify strong claims about the practical reliability of MLIP-based relaxation in this setting.\n\nOverall, the experimental evidence is accurate and extensive, but it fully supports the Force2Prop and representation learning claims more convincingly than the geometry optimization claims that motivate the Force2Geo pipeline.\n\n**Note** - My assessment of the claims is mixed rather than strictly negative. Several claims, especially those related to representation learning and the Force2Prop setting, are well supported by the experiments. However, claims about geometry optimization are less convincingly supported by the current results. Because the form allows only a Yes or No response, I selected No to reflect this imbalance, and I am open to discussion with the authors.", "audience_yn": "Yes", "audience_explanation": "This work addresses a problem of central importance to machine learning for chemistry, drug discovery, and geometric deep learning. The lack of large-scale, force-labeled datasets for small molecules is a well-known bottleneck, and the PubChemQCR dataset alone is likely to be of significant interest to the TMLR audience.\n\nBeyond the dataset, the paper contributes to ongoing discussions about molecular foundation models and the relative merits of supervised, physics-grounded pretraining versus self-supervised denoising approaches. The modular framing of Force2Geo and Force2Prop provides a useful conceptual lens for thinking about how MLIP models can be integrated into downstream pipelines. Even the negative and mixed results for geometry optimization are informative, as they highlight fundamental challenges in learning near-equilibrium force fields and generalizing beyond the training distribution.\n\nI believe people interested in AI for science, molecular representation learning, and scalable pretraining strategies will likely find both the successes and limitations of this work valuable.", "requested_changes": "## Critical Changes\n\n### 1. More Careful Framing of Geometry Optimization Claims\nThe abstract and introduction should more clearly reflect the limitations of the Force2Geo results. Statements suggesting that the model provides generally reliable geometries should be softened to align with the reported chemical accuracy and convergence rates.\n\n### 2. Computational Cost Analysis\nThe paper claims that MLIP-based relaxation is a cost-effective alternative to DFT, but no quantitative comparison is provided. A concrete analysis of wall-clock time and computational cost for MLIP-based relaxation versus standard DFT relaxation is required to justify this claim.\n\n### 3. Baseline Comparisons for Geometry Optimization\nThe geometry optimization results should be contextualized by comparison with simpler baselines such as classical force fields (e.g., UFF or MMFF). Without this, it is difficult to assess whether MLIP-based relaxation offers a meaningful advantage.\n\n### 4. Dataset Splitting and Leakage Details\nThe paper should more clearly describe how the foundation model training, validation, and test splits were constructed, and how overlap with downstream benchmarks was detected and removed.\n\n---\n\n## Changes That Would Strengthen the Work\n\n### 1. Failure Analysis for Geometry Optimization\nMore detailed empirical analysis of failed optimization cases would be valuable. This could include visualizations of relaxation trajectories, breakdowns by molecular size or functional group, or analysis of force prediction errors across different force regimes.\n\n### 2. Use of Multi-Fidelity Data\nSince PubChemQCR includes PM3, HF, and DFT stages, exploring multi-fidelity or curriculum-based training strategies could potentially improve Force2Geo performance and would strengthen the methodological contribution.\n\n### 3. Justification of Backbone Choice\nEquiformer achieves stronger force prediction accuracy than PaiNN in Table 2. A brief discussion or experiment quantifying performance versus computational cost would better justify the architectural choice.\n\n### 4. Visualization of Geometry Fine-Tuning Effects\nQualitative examples comparing RDKit, MLIP-relaxed, and DFT geometries for both success and failure cases would provide intuition for why geometry fine-tuning improves downstream performance.", "broader_impact_concerns": "The work does not raise major ethical concerns beyond those typical for computational chemistry research. However, a brief Broader Impact Statement would strengthen the paper by addressing the computational cost of large-scale DFT computation and model training, as well as the risks of over-reliance on approximate geometries in safety-critical applications such as drug discovery. Discussion of the dataset and model release plans would also support transparency and reproducibility.", "additional_comments": "I personally believe this is an ambitious and technically substantial paper that makes a meaningful contribution through dataset curation and careful experimental evaluation. The Force2Prop results are strong and convincingly demonstrate the value of supervised MLIP pretraining for molecular property prediction. The Force2Geo results are more exploratory and currently fall short of supporting the broader motivation of replacing DFT-based geometry optimization.\n\nIf the paper is reframed to emphasize representation learning and property prediction more strongly, while presenting geometry optimization as an important but unresolved challenge, it would be a solid and informative contribution to TMLR.\n\nI want to note that my background in quantum chemistry and interatomic potentials is limited, and I had to rely on careful reading of the related work to form this assessment. It is possible that I have missed or misunderstood some aspects of the work, and I remain open to engaging with the authors to clarify these points.", "extra_scores": {}, "extra_text": {}}, {"review_id": "HaIMjfr1Rf", "reviewer": "Reviewer_1nMr", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper suggests pretraining a MLIP foundation model in order to improve molecular property prediction. First, the authors curated a molecular relaxation dataset and then they trained a MLIP foundation model to predict energy and forces from these structures. Then, the pretrained model can be used in two ways in order to improve property prediction. \n1) In case no stable structures are available, the authors relax these structures using the foundation model and then they train the property predictor on the relaxed structures.\n2) When ground-truth geometries are available, they directly finetune the foundation model on the downstream task.\n\nStrengths:\n1) The authors provide a large-scale relaxation dataset at DFT accuracy that can be proved useful in training molecular foundation models.\n2) The authors showcase a consistent improvement of their proposed methods on test datasets and enough ablations to illustrate the improvements introduced by different components.\n\nWeaknesses:\n1) The results in Table 3 on geometry optimization of molecules are relatively low suggesting that Force2Geo optimization is far from DFT-level relaxation. While the authors explain the reasons behind the poor results, it would be nice to have some more analysis on this. Perhaps, they can do a similar ablation to Figure 5 but for geometry optimization in order to check the effect of train data size on the accuracy of the relaxation.\n2) It is not clearly stated that the dataset will be released in case of publication. I guess this should be the case.\n3) I am a bit skeptical about potential data leakage when using Molecule3D dataset. While the authors state that 'Since Molecule3D and our curated dataset are derived from the same source, we remove any overlapping molecules from the Molecule3D test set to prevent data leakage.' very similar molecules may still be present in pretraining and especially when testing on the scaffold split this may revert the distribution shift inserted by scaffold split making the task simpler than it looks.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The answer is yes. The authors showcase that their proposed methods (Force2Geo+PaiNN and Force2Prop+PaiNN) improve the performance of the downstream tasks giving enough ablations. Also, the scaling experiments in Figures 4-6 convincingly back up claims that pretraining helps when downstream data is limited and that larger pretraining datasets improve transferability.", "audience_yn": "Yes", "audience_explanation": "Yes.The paper is relevant to the TMLR audience and the authors provide a large-scale relaxation dataset along with a proposed methodology on using a foundation model for property prediction. Many researchers in the area of machine learning would be interested in both the proposed methodology and most importantly the dataset. It is important that this dataset will be released upon publication to promote research on MLIP foundation models. The authors also acknowledge the limitations of the paper in respect of relaxation accuracy and propose ways to improve the performance for future research.", "requested_changes": "1) It would be useful to include in Table 2 the training time of each MLIP models in order to justify the selection of PaiNN (instead of Equiformer  that achieves better performance).\n2) It would be useful to clarify how the overlap between PubChemQCR and Molecule3D was removed. If it was just removing overlaping structures, the authors should check on how they can remove overlaps but also keep the scaffold split robust with a important distribution shift between the train (+pretraining dataset) and test set.\n3) Minor typo on equations (1) and (2). I think $φ_{m}$ and $φ_{u}$ need a superscript $l$ since the mappings are different per layer.\n4) I don't understand exactly what is M and what is N in equations 5 and 6. Are these the number of atoms or the number of molecules? The authors should clarify that.\n\nI believe that all of the above recommendations are important for acceptance.", "broader_impact_concerns": "Nothing specific.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)