Pith. sign in

REVIEW 3 major objections 8 minor 57 references

MACS: Multi-Agent Reinforcement Learning for Optimization of Crystal Structures

T0 review · 3 major / 8 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Each atom is an agent: MACS learns to relax periodic crystal structures, cutting optimization time by 34% and energy calculations by 28% versus the strongest baseline.

desk verdict A well-executed first application of MARL to periodic crystal structure optimization, with real speedups under CHGNet and honest limitations; the main overreach is the unqualified abstract claim and the 'universal' language. read the letter →

arxiv 2506.04195 v1 pith:B3BW6WTY submitted 2025-06-04 cs.LG cs.AI

Elena Zamaraeva , Christopher M. Collins , George R. Darling , Matthew S. Dyer , Bei Peng , Rahul Savani , Dmytro Antypov , Vladimir V. Gusev
show 3 more authors
Judith Clymo Paul G. Spirakis Matthew J. Rosseinsky
This is my paper
classification cs.LGcs.AI
keywords multi-agentreinforcementlearningcrystalstructureoptimizationgeometrytooptimizeCHGNetzero-shottransferabilitysoftactor-criticmaterialsdiscovery
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper introduces MACS, a multi-agent reinforcement learning method for local geometry optimization of periodic crystals. It treats each atom as an agent that moves based on local observations to collectively reduce atomic forces, using the CHGNet machine-learned potential for energy and force estimates. The authors claim that on average across all test sets, MACS optimizes structures 34% faster and with 28% fewer energy calculations than the strongest baseline, BFGSLS, while maintaining the lowest failure rate. They also report zero-shot transfer to unseen compositions and larger structures. If correct, MACS offers a practical speedup for crystal structure prediction workflows that require thousands of local relaxations.

What carries the argument

The central object is the multi-agent reinforcement learning formulation itself: each atom is an agent in a partially observable Markov game, with a shared policy network trained by independent SAC. The load-bearing components are the local observation vector (per-atom covalent radius, scaled gradient and its log-norm, previous displacement and gradient change, plus the feature vectors and relative positions of the 12 nearest neighbors), the gradient-norm action scaling factor $c_i^t = \min(|g_i^t|, c_{\max})$ that sets the step size, and the reward $R_i^t = \log(|g_i^t|) - \log(|g_i^{t+1}|)$ that directly rewards force reduction. CHGNet supplies the energy and atomic forces that drive observations, rewards, and the termination condition of all compared methods.

What would settle it

Run MACS and BFGSLS on the same set of test structures with density functional theory forces in place of CHGNet; if MACS no longer requires fewer energy calculations or if its optimized structures have DFT forces above the 0.05 eV/Å threshold, the claimed efficiency advantage does not transfer beyond the machine-learned potential.

Watch

Extended reading notes

Core claim

The paper's central claim is that crystal structure geometry optimization can be reformulated as a partially observable Markov game in which each atom is an independent agent, and that a policy trained with independent Soft Actor-Critic on this game outperforms standard optimizers. Each agent observes its own covalent radius, scaled gradient history, and the features and relative positions of its twelve nearest neighbors; it outputs a displacement scaled by the gradient norm, and receives a reward equal to the reduction in log force magnitude. Trained across six diverse compositions and evaluated on those plus three unseen compositions, MACS achieves lower mean optimization time, fewer energy calculations, and lower failure rate than BFGS, BFGSLS, FIRE, FIRE+BFGSLS, MDMin, and conjugate gradient baselines. The optimized structures sample the same distribution of local minima as the baselines, and the policy scales to larger structures and new compositions without retraining.

Load-bearing premise

The entire comparison assumes that CHGNet's energy and force predictions are accurate enough that a structure relaxed under CHGNet corresponds to the same physical minimum that a density functional theory calculation would find, so the measured speedups transfer to real materials calculations.

Editorial extensions

If this is right

  • MACS can serve as a drop-in local optimizer inside crystal structure prediction loops, cutting the number of expensive energy evaluations per relaxation.
  • The trained policy transfers zero-shot to unit cells roughly twice the training size and to compositions not seen during training, so it can be applied to new materials without retraining.
  • The low failure rate (0.36% across all test sets) means fewer wasted optimization runs in high-throughput screening pipelines.
  • Because MACS outperforms baselines on both wall-clock time and energy-call count, it directly addresses the bottleneck of local relaxation in CSP workflows.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If CHGNet's accuracy transfers to DFT, the train-on-CHGNet-run-on-DFT workflow the authors suggest could replace standard relaxers in production materials discovery, but this transfer is not demonstrated in the paper.
  • The per-atom agent structure may extend naturally to optimizing unit-cell vectors as additional agents, which the authors list as future work and would broaden the method to variable-cell relaxation.
  • The exception seen for Ca3Al2Si3O12, where MACS trails BFGS, suggests a composition-targeted retraining strategy (which the paper tests successfully) as a practical refinement for difficult chemistries.
  • Combining MACS with a global search method such as basin hopping or random structure generation could reduce the total cost of finding stable crystal structures, not just the local relaxation step.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 8 minor

Summary. The paper proposes MACS, a multi-agent reinforcement learning method for local geometry optimization of periodic crystal structures. Atoms in a fixed unit cell act as agents with local observations of their k nearest neighbors, and all agents share a policy trained with independent Soft Actor-Critic. The reward is the per-atom decrease in log force norm, and atomic displacements are scaled by a force-norm-dependent factor. All energy and force evaluations use the CHGNet machine-learned potential. The authors train on six compositions and evaluate on 24 test sets that include the training compositions at three sizes and three Sr-Ti-O Ruddlesden-Popper compositions at two sizes, comparing against BFGS, BFGSLS, FIRE, FIRE+BFGSLS, MDMin, and CG. The reported results show that, on average, MACS is 34% faster and uses 28% fewer energy calculations than BFGSLS, with a failure rate of 0.36%.

Significance. If the results are taken as valid for optimization under the CHGNet potential, this is a novel and potentially useful contribution: it is, to my knowledge, the first multi-agent RL formulation for periodic crystal structure optimization, and the evaluation is extensive, with per-test-set failure rates, standard errors, final-energy distributions, and ablations covering observation features, reward designs, action scaling, hyperparameters, and transfer to larger sizes. The paper also provides transparent negative results for several classical baselines (e.g., MDMin's 46% average failure rate) and demonstrates that the final energy distributions of MACS and the baselines broadly overlap. The significance for real crystal-structure-prediction workflows, however, is conditional on the fidelity of CHGNet to the true DFT potential in the highly distorted AIRSS starting structures used here, and that condition is not tested in the manuscript.

major comments (3)
  1. [Abstract, Section 6 (Limitations), Section 3.1, Appendix B.3] The abstract and conclusion claim that MACS optimizes periodic crystal structures 'significantly faster' and that it has 'the potential to become a universal geometric optimizer,' but every experiment evaluates the optimization under the CHGNet potential, and success is defined by CHGNet force norms below 0.05 eV/Å (Section 3.1). The AIRSS starting structures are generated with minimum interatomic distances down to 1 Å (Appendix B.3), which is far from the near-equilibrium distribution on which CHGNet is typically validated. No DFT re-evaluation of the final structures and no cross-potential transfer test are reported, and the Limitations paragraph explicitly defers a 'train-with-CHGNet-run-with-DFT' workflow to future work. The practical claim is therefore load-bearing on an unverified surrogate-fidelity assumption. A concrete test would be to re-optimize a random subset (e.g., 50-100 structures per composition) of the MACS and strongest-baseline final configurations with DFT and report the DFT force maxima, the DFT energy differences between the methods' final structures, and whether the ordering of the methods by required steps is preserved when MACS is queried with DFT gradients. If such an experiment is not added, the abstract and conclusion should explicitly scope all speedup claims to optimization under the CHGNet potential.
  2. [Section 5.1, Section 6 (Contributions)] The 'zero-shot transferability' claim is supported only by test sets of Sr2TiO4, Sr3Ti2O7, and Sr4Ti3O10, which are homologous Ruddlesden-Popper phases derived from the training composition SrTiO3, with the same three elements and closely related local coordination. While the stoichiometries are technically unseen, the abstract and contribution bullet state the result as 'unseen compositions' without qualification, which suggests a stronger form of generalization than is demonstrated. The paper should either add a test set with a chemically unrelated composition (e.g., a system with different elements and bonding) or qualify the claim to 'unseen compositions within the same chemical family.'
  3. [Section 5.3, Figs. 2b-c, Figs. 12-13] The paper asserts that 'MACS and the baselines sample from the same distribution of local minima' on the basis of histogram overlays. This claim is load-bearing because a speed advantage would be misleading if it came at the cost of systematically worse local minima. The current support is qualitative only. I request a quantitative comparison of the final-energy distributions, for example the mean and standard deviation of final CHGNet energies per method and test set, the fraction of structures for which MACS ends at an energy higher than the best baseline by more than a specified tolerance, or a two-sample test for distributional equivalence.
minor comments (8)
  1. [Section 6 heading] The heading contains a typo: 'otpimization' should be 'optimization.'
  2. [Table 1] The average row is labeled 'A VERAGE2' with a stray superscript '2'; the footnote about how the average is computed should be attached as a proper table footnote rather than appearing as an inline label.
  3. [Section 5.3] The sentence 'MACS ranks first or second after BFGS' for Ca3Al2Si3O12 is ambiguous: Table 6 shows that BFGS has lower Cmean for all three sizes of Ca3Al2Si3O12, while Table 5 shows BFGS lower Tmean only for the 80-atom set. Please rephrase to state explicitly which metric and which size.
  4. [Appendix B.6, Table 9] The footnote reports that the Cu28S16 88-atom test set optimization was interrupted by cluster maintenance. Since the numbers for that row are incomplete, this row should be excluded from Table 9 or clearly marked as partial, rather than being included with a footnote that the aggregate relies on other test sets.
  5. [Abstract and Section 5.3] The abstract claims 'the lowest failure rate,' but Table 1 shows that BFGSLS has the same PF value (0.36%) as MACS; consider saying 'joint-lowest' or 'matching the lowest failure rate.'
  6. [Section 5.3] The word 'significantly' in the abstract and Section 5.3 is not supported by a statistical test. Because the comparisons are paired (the same 300 structures per test set), a paired Wilcoxon signed-rank test or a paired bootstrap across the 24 test-set means would directly substantiate the claim; the per-test-set standard errors in Appendix B are not sufficient by themselves for readers to assess the paired comparison.
  7. [Section 4 and Appendix A.5] The statement 'We train MACS for ~80000 steps in total' is ambiguous: please specify whether a step is one joint action (a move of all atoms) or one per-atom update, and report the total wall-clock training time for reproducibility.
  8. [General] The manuscript does not include a data or code availability statement. Providing the trained policy, the AIRSS generation scripts, and the evaluation scripts would substantially improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper's central claim is an empirical benchmark, the reward/success alignment is a deliberate design choice, and the acknowledged CHGNet-only evaluation is a limitation on external validity rather than a circular step.

full rationale

The derivation chain is not deductive; the paper's central claim is an empirical benchmark measured on held-out structures. Section 3.1 defines success as the maximum atomic force falling below 0.05 eV/A as computed by CHGNet, and Eq. 5 defines the per-agent reward as the decrease in the log force norm. This is an intentional alignment of the training objective with the evaluation metric, not a fitted parameter renamed as a prediction: the reported Tmean, Cmean, Nmean, and PF values in Table 1 are obtained by executing the trained policy and external baselines on AIRSS-generated test sets, including unseen compositions and larger sizes. The aggregate 34%/28% speedup is not implied by the reward definition alone, since it depends on the learned policy's step counts and wall-clock behavior. The equality Cmean = Nmean for MACS follows from its one-energy-evaluation-per-step action design, but the comparison against baselines that use line search is a transparent engineering choice rather than a hidden equivalence. Self-citations (refs. 10, 11, 20, 56) supply training compositions and related-work context; none is load-bearing for the speedup claim. The limitation acknowledged in Sec. 6, that only CHGNet and not DFT was used as the energy/force oracle, is a genuine external-validity caveat, because MACS-optimized structures may not be DFT minima and the learned policy is specialized to CHGNet gradients; however, this is not circularity, since CHGNet is an externally pretrained potential and the benchmark is self-consistent under that oracle. No step in the paper reduces by construction to its own input.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claim rests on hyperparameters (k, g_max, c_max, gamma, target entropy, batch size) that are chosen by hand and on the domain assumptions that CHGNet is an accurate force oracle, that AIRSS random structures are representative, and that the success criterion is appropriate. No new physical entities are introduced. The hyperparameter selection includes some use of test sets, which is a form of leakage rather than circular derivation.

free parameters (6)
  • k (number of nearest neighbors) = 12
    Selected by comparing policies with k=10, 12, 15 on training curves and test sets of Y2O3, SrTiO3, and Ca3Al2Si3O12 (Appendix A.2). This is a hyperparameter, not a fitted physical constant.
  • g_max (gradient scaling threshold) = 5
    Tuned by training runs; g_max=5 gives the lowest mean episode length (Appendix A.3).
  • c_max (action scaling cap) = 0.4
    Chosen from two variants based on higher episodic reward and lower episode length (Appendix A.4).
  • gamma (discount factor) = 0.995
    Set to encourage fast force reduction; no sensitivity analysis is reported.
  • target entropy = -8
    SAC hyperparameter; chosen among -7, -8, -9 based on training curves (Appendix A.5).
  • training batch size = 8192
    SAC hyperparameter; chosen among 1024, 4096, 8192 based on training curves (Appendix A.5).
assumptions (5)
  • domain assumption The CHGNet machine-learned potential provides sufficiently accurate energy and force estimates for crystal structures.
    Used as the oracle for energies and forces throughout training and evaluation (Section 1). The paper plans a future train-with-CHGNet-run-with-DFT workflow, so the current results are not validated against DFT.
  • domain assumption AIRSS-generated random structures with volumes within ±5% of the experimental structure and interatomic distances at least 1 Å are representative of realistic geometry optimization tasks.
    Training and test structures are generated this way (Section 5.1 and Appendix B.3). The conclusions about speedups and failure rates are conditional on this distribution.
  • domain assumption The convergence criterion of maximum atomic force below 0.05 eV/Å within 1000 steps is a standard and sufficient measure of successful optimization.
    Stated in Section 3.1 and used to define Nmean, Cmean, and the failure rate.
  • domain assumption Independent SAC with shared policy and Q-networks can solve the partially observable Markov game formulated for geometry optimization.
    The paper assumes that the decentralized training converges to a useful policy; no optimality guarantees are given.
  • standard math Standard RL machinery (SAC, replay buffer, twin Q-networks) works as described in the cited literature.
    Section 4 uses SAC as implemented in RLlib, with standard hyperparameters; the design is not derived in the paper.

how reviews work

0 comments
Cite this review

Pith. "Pith review of MACS: Multi-Agent Reinforcement Learning for Optimization of Crystal Structures." pith.science (2026). https://pith.science/paper/B3BW6WTY

@misc{pith2026250604195,
  author       = {Pith},
  title        = {Pith review of: MACS: Multi-Agent Reinforcement Learning for Optimization of Crystal Structures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/B3BW6WTY}},
  note         = {Machine review of arXiv:2506.04195}
}
read the original abstract

Geometry optimization of atomic structures is a common and crucial task in computational chemistry and materials design. Following the learning to optimize paradigm, we propose a new multi-agent reinforcement learning method called Multi-Agent Crystal Structure optimization (MACS) to address periodic crystal structure optimization. MACS treats geometry optimization as a partially observable Markov game in which atoms are agents that adjust their positions to collectively discover a stable configuration. We train MACS across various compositions of reported crystalline materials to obtain a policy that successfully optimizes structures from the training compositions as well as structures of larger sizes and unseen compositions, confirming its excellent scalability and zero-shot transferability. We benchmark our approach against a broad range of state-of-the-art optimization methods and demonstrate that MACS optimizes periodic crystal structures significantly faster, with fewer energy calculations, and the lowest failure rate.

Figures

Figures reproduced from arXiv: 2506.04195 by the authors.

Figure 1
Figure 1. Our overall MACS architecture. We use the SrTiO [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. (a) Unit cells and nearest neighbors in two dimensions for a structure with three atoms. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. (a, d) Energy evolution averaged over all successfully optimized structures of 80 atoms [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: Two-dimensional structure with three atoms, and the three nearest neighbors for one of the [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: Mean episodic reward and mean episode length achieved by MACS with different numbers [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 6
Figure 6. Figure 6: The gradient norm during training for MACS with different [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]
Figure 7
Figure 7. Figure 7: Performance comparison of MACS with different values of [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]
Figure 8
Figure 8. Figure 8: Performance comparison of MACS with different values of [PITH_FULL_IMAGE:figures/full_fig_p017_8.png]
Figure 9
Figure 9. Figure 9: Performance comparison of MACS with different action space bounds and target entropy [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]
Figure 10
Figure 10. Figure 10: Performance comparison of MACS with different values of the replay buffer capacity and [PITH_FULL_IMAGE:figures/full_fig_p018_10.png]
Figure 11
Figure 11. Figure 11: Performance comparison of MACS with different values of the target entropy, entropy/ac [PITH_FULL_IMAGE:figures/full_fig_p019_11.png]
Figure 12
Figure 12. Figure 12: The energy distribution of the local minima obtained by all different methods. The vertical [PITH_FULL_IMAGE:figures/full_fig_p023_12.png]
Figure 13
Figure 13. Figure 13: The energy distribution of the local minima obtained by all different methods. The vertical [PITH_FULL_IMAGE:figures/full_fig_p024_13.png]
Figure 14
Figure 14. Figure 14: Energy evolution averaged over all successfully optimized structures for all methods on [PITH_FULL_IMAGE:figures/full_fig_p025_14.png]
Figure 15
Figure 15. Figure 15: Energy evolution averaged over all successfully optimized structures for all methods on [PITH_FULL_IMAGE:figures/full_fig_p026_15.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

57 extracted references · 48 canonical work pages

  1. [1]

    Learning to optimize molecular geometries using reinforcement learning.Journal of Chemical Theory and Computation, 17(2):818–825, 2021

    Kabir Ahuja, William H Green, and Yi-Pei Li. Learning to optimize molecular geometries using reinforcement learning.Journal of Chemical Theory and Computation, 17(2):818–825, 2021

    work page 2021

  2. [2]

    Stridernet: A graph reinforcement learning approach to optimize atomic structures on rough energy landscapes

    Vaibhav Bihani, Sahil Manchanda, Srikanth Sastry, Sayan Ranu, and NM Anoop Krishnan. Stridernet: A graph reinforcement learning approach to optimize atomic structures on rough energy landscapes. InInternational Conference on Machine Learning, pages 2431–2451. PMLR, 2023

    work page 2023

  3. [3]

    Structural relaxation made simple.Physical review letters, 97:170201, 2006

    Erik Bitzek, Pekka Koskinen, Franz Gähler, Michael Moseler, and Peter Gumbsch. Structural relaxation made simple.Physical review letters, 97:170201, 2006

    work page 2006

  4. [4]

    The convergence of a class of double-rank minimization algorithms 1

    Charles George Broyden. The convergence of a class of double-rank minimization algorithms 1. general considerations.IMA Journal of Applied Mathematics, 6(1):76–90, 1970

    1970

  5. [5]

    Christian J Burnham and Niall J English. Crystal structure prediction via basin-hopping global optimization employing tiny periodic simulation cells, with application to water–ice.Journal of Chemical Theory and Computation, 15(6):3889–3900, 2019

    work page 2019

  6. [6]

    Learning to optimize in swarms

    Yue Cao, Tianlong Chen, Zhangyang Wang, and Yang Shen. Learning to optimize in swarms. Advances in neural information processing systems, 32, 2019

    work page 2019

  7. [7]

    Integrating chemical information into reinforcement learning for enhanced molecular geometry optimization.Journal of Chemical Theory and Computation, 19(23):8598–8609, 2023

    Yu-Cheng Chang and Yi-Pei Li. Integrating chemical information into reinforcement learning for enhanced molecular geometry optimization.Journal of Chemical Theory and Computation, 19(23):8598–8609, 2023

    work page 2023

  8. [8]

    Learning to optimize: A primer and a benchmark.Journal of Machine Learning Research, 23(189):1–59, 2022

    Tianlong Chen, Xiaohan Chen, Wuyang Chen, Howard Heaton, Jialin Liu, Zhangyang Wang, and Wotao Yin. Learning to optimize: A primer and a benchmark.Journal of Machine Learning Research, 23(189):1–59, 2022

    2022

Show all 57 references
  1. [9]

    Learning to learn without gradient descent by gradient descent

    Yutian Chen, Matthew W Hoffman, Sergio Gómez Colmenarejo, Misha Denil, Timothy P Lillicrap, Matt Botvinick, and Nando Freitas. Learning to learn without gradient descent by gradient descent. InInternational Conference on Machine Learning, pages 748–756. PMLR, 2017

    2017

  2. [10]

    The flexible unit structure engine (fuse) for probe structure-based composition prediction.Faraday Discussions, 211:117–131, 2018

    Christopher M Collins, George R Darling, and Matthew J Rosseinsky. The flexible unit structure engine (fuse) for probe structure-based composition prediction.Faraday Discussions, 211:117–131, 2018

    2018

  3. [11]

    Integration of generative machine learning with the heuristic crystal structure prediction code fuse.Faraday Discussions, 256:85–103, 2025

    Christopher M Collins, Hasan M Sayeed, George R Darling, John B Claridge, Taylor D Sparks, and Matthew J Rosseinsky. Integration of generative machine learning with the heuristic crystal structure prediction code fuse.Faraday Discussions, 256:85–103, 2025. 10

    2025

  4. [12]

    CHGNet as a pretrained universal neural network potential for charge- informed atomistic modelling.Nature Machine Intelligence, 5(9):1031–1041, September 2023

    Bowen Deng, Peichen Zhong, Kyujung Jun, Janosh Riebesell, Kevin Han, Christopher J Bartel, and Gerbrand Ceder. CHGNet as a pretrained universal neural network potential for charge- informed atomistic modelling.Nature Machine Intelligence, 5(9):1031–1041, September 2023

    2023

  5. [13]

    The double-funnel energy landscape of the 38-atom lennard-jones cluster.The Journal of Chemical Physics, 110(14):6896–6906, 1999

    Jonathan PK Doye, Mark A Miller, and David J Wales. The double-funnel energy landscape of the 38-atom lennard-jones cluster.The Journal of Chemical Physics, 110(14):6896–6906, 1999

    1999

  6. [14]

    A new approach to variable metric algorithms.The Computer Journal, 13(3):317–322, 1970

    Roger Fletcher. A new approach to variable metric algorithms.The Computer Journal, 13(3):317–322, 1970

    1970

  7. [15]

    The general utility lattice program (gulp).Molecular Simulation, 29(5):291–341, 2003

    Julian D Gale and Andrew L Rohl. The general utility lattice program (gulp).Molecular Simulation, 29(5):291–341, 2003

    2003

  8. [16]

    A family of variable-metric methods derived by variational means.Mathe- matics of computation, 24(109):23–26, 1970

    Donald Goldfarb. A family of variable-metric methods derived by variational means.Mathe- matics of computation, 24(109):23–26, 1970

    1970

  9. [17]

    Learning conditional policies for crystal design using offline reinforcement learning.Digital Discovery, 3(4):769–785, 2024

    Prashant Govindarajan, Santiago Miret, Jarrid Rector-Brooks, Mariano Phielipp, Janarthanan Rajefndran, and Sarath Chandar. Learning conditional policies for crystal design using offline reinforcement learning.Digital Discovery, 3(4):769–785, 2024

    2024

  10. [18]

    Learning to optimize multigrid pde solvers

    Daniel Greenfeld, Meirav Galun, Ronen Basri, Irad Yavneh, and Ron Kimmel. Learning to optimize multigrid pde solvers. InInternational Conference on Machine Learning, pages 2415–2423. PMLR, 2019

    2019

  11. [19]

    Lattice relaxation at a metal surface.Physical Review B, 23(12):6265, 1981

    Raju P Gupta. Lattice relaxation at a metal surface.Physical Review B, 23(12):6265, 1981

    1981

  12. [20]

    Optimality guarantees for crystal structure prediction.Nature, 619(7968):68 72, 2023

    Vladimir V Gusev, Duncan Adamson, Argyrios Deligkas, Dmytro Antypov, Christopher M Collins, Piotr Krysta, Igor Potapov, George R Darling, Matthew S Dyer, Paul Spirakis, and Matthew J Rosseinsky. Optimality guarantees for crystal structure prediction.Nature, 619(7968):68 72, 2023

    2023

  13. [21]

    Soft actor-critic: Off- policy maximum entropy deep reinforcement learning with a stochastic actor

    Tuomas Haarnoja, Aurick Zhou, Pieter Abbeel, and Sergey Levine. Soft actor-critic: Off- policy maximum entropy deep reinforcement learning with a stochastic actor. InInternational Conference on Machine Learning, pages 1861–1870. PMLR, 2018

    2018

  14. [22]

    Structure cristalline du bronze pseudo- quadratique K0.6FeF3: transition pyrochlore-quadratique pour les composés KMM’X6.Acta Crystallographica Section B, 29(8):1654–1658, Aug 1973

    Anne-Marie Hardy, Antoine Hardy, and Gérard Ferey. Structure cristalline du bronze pseudo- quadratique K0.6FeF3: transition pyrochlore-quadratique pour les composés KMM’X6.Acta Crystallographica Section B, 29(8):1654–1658, Aug 1973

    1973

  15. [23]

    The atomic simulation environmenta python library for working with atoms.Journal of Physics: Condensed Matter, 29(27):273002, 2017

    Ask Hjorth Larsen, Jens Jrgen Mortensen, Jakob Blomqvist, Ivano E Castelli, Rune Christensen, Marcin Duak, Jesper Friis, Michael N Groves, Bjrk Hammer, Cory Hargus, Eric D Hermes, Paul C Jennings, Peter Bjerre Jensen, James Kermode, John R Kitchin, Esben Leonhard Kols- bjerg, ...

    2017

  16. [24]

    Deep reinforcement learning for inverse inorganic materials design.npj Computational Materials, 10(1):287, 2024

    Christopher Karpovich, Elton Pan, and Elsa A Olivetti. Deep reinforcement learning for inverse inorganic materials design.npj Computational Materials, 10(1):287, 2024

    2024

  17. [25]

    Adam: A method for stochastic optimization.arXiv preprint arXiv:1412.6980, 2014

    Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization.arXiv preprint arXiv:1412.6980, 2014

    2014 arXiv

  18. [26]

    On the determination of molecular fields.i

    JE Lennard and I Jones. On the determination of molecular fields.i. from the variation of the viscosity of a gas with temperature.Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 106(738):441–462, 1924

    1924

  19. [27]

    Learning to optimize.arXiv preprint arXiv:1606.01885, 2016

    Ke Li and Jitendra Malik. Learning to optimize.arXiv preprint arXiv:1606.01885, 2016

    2016 arXiv

  20. [28]

    B2opt: Learning to optimize black-box optimization with little budget

    Xiaobin Li, Kai Wu, Xiaoyu Zhang, and Handing Wang. B2opt: Learning to optimize black-box optimization with little budget. InProceedings of the AAAI Conference on Artificial Intelligence, volume 39, pages 18502–18510, 2025. 11

    2025

  21. [29]

    Rllib: Abstractions for distributed reinforcement learning

    Eric Liang, Richard Liaw, Robert Nishihara, Philipp Moritz, Roy Fox, Ken Goldberg, Joseph Gonzalez, Michael Jordan, and Ion Stoica. Rllib: Abstractions for distributed reinforcement learning. InInternational Conference on Machine Learning, pages 3053–3062. PMLR, 2018

    2018

  22. [30]

    Computational prediction of muon stopping sites using ab initio random structure searching (airss).The Journal of Chemical Physics, 148(13):134114, 2018

    Leandro Liborio, Simone Sturniolo, and Dominik Jochym. Computational prediction of muon stopping sites using ab initio random structure searching (airss).The Journal of Chemical Physics, 148(13):134114, 2018

    2018

  23. [31]

    Markov games as a framework for multi-agent reinforcement learning

    Michael L Littman. Markov games as a framework for multi-agent reinforcement learning. In William W Cohen and Haym Hirsh, editors,Machine Learning Proceedings 1994, pages 157–163. Morgan Kaufmann, San Francisco (CA), 1994

    1994

  24. [32]

    Multi-agent actor-critic for mixed cooperative-competitive environments

    Ryan Lowe, YI WU, Aviv Tamar, Jean Harb, OpenAI Pieter Abbeel, and Igor Mordatch. Multi-agent actor-critic for mixed cooperative-competitive environments. In I. Guyon, U. V on Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, editors,Advances in Neura...

    2017

  25. [33]

    Nanostructure and nanomechanics of cement: polydisperse colloidal packing.Physical review letters, 109(15):155503, 2012

    Enrico Masoero, E Del Gado, RJ-M Pellenq, F-J Ulm, and Sidney Yip. Nanostructure and nanomechanics of cement: polydisperse colloidal packing.Physical review letters, 109(15):155503, 2012

    2012

  26. [34]

    Learn2hop: Learned optimization on rough landscapes

    Amil Merchant, Luke Metz, Samuel S Schoenholz, and Ekin D Cubuk. Learn2hop: Learned optimization on rough landscapes. InInternational Conference on Machine Learning, pages 7643–7653. PMLR, 2021

    2021

  27. [35]

    Exploring potential energy surfaces using reinforcement machine learning.Journal of Chemical Information and Modeling, 62(13):3169–3179, 2022

    Alexis W Mills, Joshua J Goings, David Beck, Chao Yang, and Xiaosong Li. Exploring potential energy surfaces using reinforcement machine learning.Journal of Chemical Information and Modeling, 62(13):3169–3179, 2022

    2022

  28. [36]

    Molopt: Autonomous molecular geometry optimization using multiagent reinforcement learning.The Journal of Physical Chemistry B, 127(48):10295–10303, 2023

    Rohit Modee, Sarvesh Mehta, Siddhartha Laghuvarapu, and U Deva Priyakumar. Molopt: Autonomous molecular geometry optimization using multiagent reinforcement learning.The Journal of Physical Chemistry B, 127(48):10295–10303, 2023

    2023

  29. [37]

    Location of saddle points and minimum energy paths by a constrained simplex optimization procedure.Theoretica chimica acta, 53:75–93, 1979

    Klaus Müller and Leo D Brown. Location of saddle points and minimum energy paths by a constrained simplex optimization procedure.Theoretica chimica acta, 53:75–93, 1979

    1979

  30. [38]

    How evolutionary crystal structure prediction works and why.Accounts of chemical research, 44(3):227–237, 2011

    Artem R Oganov, Andriy O Lyakhov, and Mario Valle. How evolutionary crystal structure prediction works and why.Accounts of chemical research, 44(3):227–237, 2011

    2011

  31. [39]

    Geometry optimization.Wiley Interdisciplinary Reviews: Computational Molecular Science, 1(5):790–809, 2011

    H Bernhard Schlegel. Geometry optimization.Wiley Interdisciplinary Reviews: Computational Molecular Science, 1(5):790–809, 2011

    2011

  32. [40]

    Conditioning of quasi-newton methods for function minimization.Mathemat- ics of Computation, 24(111):647–656, 1970

    David F Shanno. Conditioning of quasi-newton methods for function minimization.Mathemat- ics of Computation, 24(111):647–656, 1970

    1970

  33. [41]

    An introduction to the conjugate gradient method without the agonizing pain.Technical report, Pittsburgh, PA, USA, 1994

    Jonathan Richard Shewchuk et al. An introduction to the conjugate gradient method without the agonizing pain.Technical report, Pittsburgh, PA, USA, 1994

    1994

  34. [42]

    Deep reinforcement learning in chemistry: A review.Journal of Computational Chemistry, 45(22):1886–1898, 2024

    Bhuvanesh Sridharan, Animesh Sinha, Jai Bardhan, Rohit Modee, Masahiro Ehara, and U Deva Priyakumar. Deep reinforcement learning in chemistry: A review.Journal of Computational Chemistry, 45(22):1886–1898, 2024

    2024

  35. [43]

    Local order in quenched states of simple atomic substances.Physical Review B, 34(8):5136, 1986

    Frank H Stillinger and Randall A LaViolette. Local order in quenched states of simple atomic substances.Physical Review B, 34(8):5136, 1986

    1986

  36. [44]

    Computer simulation of local order in condensed phases of silicon.Physical review B, 31(8):5262, 1985

    Frank H Stillinger and Thomas A Weber. Computer simulation of local order in condensed phases of silicon.Physical review B, 31(8):5262, 1985

    1985

  37. [45]

    Learn to optimize – a brief overview.National Science Review, 11(8):nwae132, 2024

    Ke Tang and Xin Yao. Learn to optimize – a brief overview.National Science Review, 11(8):nwae132, 2024

    2024

  38. [46]

    Digital features of chemical elements extracted from local geometries in crystal structures.Digital Discovery, 2025

    Andrij Vasylenko, Dmytro Antypov, Sven Schewe, Luke M Daniels, John B Claridge, Matthew S Dyer, and Matthew J Rosseinsky. Digital features of chemical elements extracted from local geometries in crystal structures.Digital Discovery, 2025. 12

    2025

  39. [47]

    Scipy 1.0: fundamental algorithms for scientific computing in python.Nature methods, 17(3):261–272, 2020

    Pauli Virtanen, Ralf Gommers, Travis E Oliphant, Matt Haberland, Tyler Reddy, David Courna- peau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, et al. Scipy 1.0: fundamental algorithms for scientific computing in python.Nature methods, 17(3):261–272, 2020

    2020

  40. [48]

    Magus: machine learning and graph theory assisted universal structure searcher.National Science Review, 10(7):nwad128, 2023

    Junjie Wang, Hao Gao, Yu Han, Chi Ding, Shuning Pan, Yong Wang, Qiuhan Jia, Hui-Tian Wang, Dingyu Xing, and Jian Sun. Magus: machine learning and graph theory assisted universal structure searcher.National Science Review, 10(7):nwad128, 2023

    2023

  41. [49]

    Resolving the data ambiguity for periodic crystals

    Daniel Widdowson and Vitaliy Kurlin. Resolving the data ambiguity for periodic crystals. In Advances in Neural Information Processing Systems, 2022

    2022

  42. [50]

    Daniel Widdowson, Marco M Mosca, Angeles Pulido, Vitaliy Kurlin, and Andrew I Cooper. Average minimum distances of periodic point sets - foundational invariants for mapping periodic crystals.MATCH Communications in Mathematical and in Computer Chemistry, 87(3):529–559, 2022

    2022

  43. [51]

    Convergence conditions for ascent methods

    Philip Wolfe. Convergence conditions for ascent methods. ii: Some corrections.SIAM Review, 13(2):185–188, 1971

    1971

  44. [52]

    Crystal structure prediction from first principles.Nature materials, 7(12):937–946, 2008

    Scott M Woodley and Richard Catlow. Crystal structure prediction from first principles.Nature materials, 7(12):937–946, 2008

    2008

  45. [53]

    Structure prediction of crystals, surfaces and nanoparticles.Philosophical Transactions of the Royal Society A, 378(2186), 2020

    Scott M Woodley, Graeme M Day, and R Catlow. Structure prediction of crystals, surfaces and nanoparticles.Philosophical Transactions of the Royal Society A, 378(2186), 2020

    2020

  46. [54]

    Improved adversarial training via learned optimizer

    Yuanhao Xiong and Cho-Jui Hsieh. Improved adversarial training via learned optimizer. In Computer Vision–ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020, Proceedings, Part VIII 16, pages 85–100. Springer, 2020

    2020

  47. [55]

    Exploration and optimization in crystal structure prediction: Combining basin hopping with quasi-random sampling.Journal of Chemical Theory and Computation, 17(3):1988–1999, 2021

    Shiyue Yang and Graeme M Day. Exploration and optimization in crystal structure prediction: Combining basin hopping with quasi-random sampling.Journal of Chemical Theory and Computation, 17(3):1988–1999, 2021

    1988

  48. [56]

    Reinforcement learning in crystal structure prediction.Digital Discovery, 2(6):1831–1840, 2023

    Elena Zamaraeva, Christopher M Collins, Dmytro Antypov, Vladimir V Gusev, Rahul Savani, Matthew S Dyer, George R Darling, Igor Potapov, Matthew J Rosseinsky, and Paul G Spirakis. Reinforcement learning in crystal structure prediction.Digital Discovery, 2(6):1831–1840, 2023

    2023

  49. [57]

    Learning atoms for materials discovery.Proceedings of the National Academy of Sciences, 115(28):E6411– E6417, 2018

    Quan Zhou, Peizhe Tang, Shenxiu Liu, Jinbo Pan, Qimin Yan, and Shou-Cheng Zhang. Learning atoms for materials discovery.Proceedings of the National Academy of Sciences, 115(28):E6411– E6417, 2018. 13 A The MACS design and hyperparameter tuning A.1 The nearest neighbors example...

    2018

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.