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MACS: Multi-Agent Reinforcement Learning for Optimization of Crystal Structures
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Proposes MACS, a multi-agent SAC-based reinforcement learning method that treats each atom as an agent to learn decentralized policies for periodic crystal structure geometry optimization, using CHGNet forces.
Problem
Geometry optimization of periodic crystal structures is slow and costly in energy/force evaluations, which bottlenecks crystal structure prediction workflows that require thousands of local relaxations.
Approach
Formulates crystal structure geometry optimization as a partially observable Markov game in which each atom is an agent observing its own gradient-based features and k=12 nearest periodic neighbors, trained with independent SAC and a log-gradient-norm reward, with a gradient-norm-scaled action space.
Key results
- MACS reduces mean optimization time by 34% and energy calculations by 28% relative to the best baseline BFGSLS on average across test sets.
- MACS achieves the lowest failure rate (0.36%) among all methods, comparable to BFGSLS (0.36%), while CG fails 18.22% of the time.
- MACS outperforms all baselines in T_mean and C_mean on the unseen compositions Sr2TiO4, Sr3Ti2O7, and Sr4Ti3O10.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use MACS instead of BFGSLS | Crystal structure optimization · All test sets (average) | mean optimization time: 99 vs 152; 34% less | Helped |
| use MACS instead of BFGSLS | Crystal structure optimization · All test sets (average) | mean energy calculations: 28% fewer energy calculations | Helped |
| use MACS instead of BFGSLS | Crystal structure optimization · All test sets | failure rate: 0.36% vs 0.36% | No clear effect |
| use MACS instead of BFGSLS | Crystal structure optimization · All test sets (average) | mean optimization steps: BFGSLS requires 5% fewer steps on average | Mixed |
| remove selected force-related and history features (ablation) | MACS observation space · Crystal optimization test sets | mean optimization time: MACS substantially better than feat.7 and feat.8 | Hurt |
| use feat.9 reduced observation features (ablation) | MACS observation space · SrTiO3 test sets | mean optimization time: 96 vs 87 average | Helped |
| use feat.9 reduced observation features (ablation) | MACS observation space · Remaining test sets | mean optimization steps: ~7.7% more optimization steps | Hurt |
| add a fixed per-step penalty of -0.05 to the reward (ablation) | MACS reward · SrTiO3 test sets | mean optimization time: 50; 88; 154 vs 57; 90; 142 | Mixed |
| add the average reward across agents to each agent's reward (ablation) | MACS reward · SrTiO3 test sets | mean optimization time: 54; 83; 161 vs 57; 90; 142 | Mixed |
| use direct displacement actions without the gradient-dependent scaling factor (ablation) | MACS action design · Training | mean episode length | Hurt |
| use 15 nearest neighbors instead of 12 (ablation) | MACS local observation · Y2O3, SrTiO3, Ca3Al2Si3O12 test sets | mean optimization time: 140 vs 120 | Hurt |
| use 10 nearest neighbors instead of 12 (ablation) | MACS local observation · Y2O3, SrTiO3, Ca3Al2Si3O12 test sets | mean optimization time: 122 vs 120 | No clear effect |
Surprising findings
- BFGSLS takes about 5% fewer steps than MACS on average, so MACS wins on time and energy calls rather than steps.
- BFGS outperforms MACS on Ca3Al2Si3O12 (the most complex composition), which the authors attribute to limited training diversity; a composition-specific MACS model beats BFGS there.
Limitations
- Only the covalent radius distinguishes atomic species in the observations.
- Relies on CHGNet energies/forces, not DFT; the trained policy is tied to this estimator.
- Cell-vector optimization is not included; the unit cell is held fixed.
Experimental setup
Datasets: AIRSS-generated random crystal structures for Y2O3, Cu28S16, SrTiO3, Ca3Ti2O7, Ca3Al2Si3O12, K3Fe5F15
Benchmarks: Y2O3, Cu28S16, SrTiO3, Ca3Ti2O7, Ca3Al2Si3O12, K3Fe5F15 test sets (larger sizes) Sr2TiO4, Sr3Ti2O7, Sr4Ti3O10 unseen compositions
Metrics: mean optimization time T_mean mean steps N_mean mean energy calculations C_mean failure rate P_F
Baselines: BFGS BFGSLS FIRE FIRE+BFGSLS MDMin CG
Builds on: soft actor-critic learning to optimize CHGNet RLlib
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