Machine-learning accelerated geometry optimization in molecular simulation
Yilin Yang, Omar A. Jiménez-Negrón and John R. Kitchin, “Machine-learning accelerated geometry optimization in molecular simulation”, The Journal of Chemical Physics 154(23) (2021). https://doi.org/10.1063/5.0049665
This summary was written by a language model from the paper and has not been checked line by line. Rely on the published paper for details.
Question
Finding relaxed structures and transition states with DFT means many sequential force calls, and geometry optimization is often the rate-limiting step in building adsorption energy datasets. Earlier surrogate-accelerated optimizers, notably Gaussian process schemes built on Cartesian coordinates, relax one configuration at a time and cannot reuse information from other configurations of different size or composition. The paper asks whether a neural network ensemble surrogate with active learning can cut the number of DFT calls, how much more is gained by relaxing many related configurations together or by pretraining on prior data, and how to keep the surrogate’s retraining cost from growing as data accumulate (Yang et al. 2021).
Approach
The surrogate is a SingleNN model (a Behler-Parrinello style network with one output per element and atom-centered symmetry function fingerprints), with two hidden layers of 50 tanh neurons and early stopping. Uncertainty comes from an ensemble of 10 such networks trained on the same data with different random initializations, deliberately overparameterized so that the members differ. A configuration is flagged as uncertain when the ensemble variance of its total energy exceeds a multiple alpha of the largest variance seen on the training set; alpha of 2 to 3 worked for all examples and 2 is the default. The surrogate drives the optimizer until a configuration becomes uncertain or converged, uncertain structures are sent to DFT, and the model is retrained. Several configurations share one ensemble, and the training set can be restricted to the most recent steps, by analogy with L-BFGS keeping only recent gradients.
Three modes were compared: single-configuration relaxation, simultaneous relaxation of multiple configurations, and multiple configurations with a warm-up (pretraining on related prior trajectories), plus a fully offline mode using a model trained on many existing trajectories. Test systems were Au (100), (111), (211) and (643) slabs, propylene on Au(111), a bare AuPd(111) slab, acrolein on AgPd(111), and CO on an edge of an AuPd icosahedron, all with VASP and PBE, compared against VASP’s RMM-DIIS quasi-Newton optimizer with a 0.05 eV/Å force criterion. Two climbing-image NEB cases were also run: Pt heptamer rearrangement on Pt(111) with EMT (343 Pt atoms) and acetylene hydrogenation on Pd(111) with DFT. Code is released as the NN-ensemble-relaxer ASE optimizer package.
Key findings
For single Au slabs, the savings were modest for simple bare surfaces and larger for Au(643) and the propylene adsorbate case; the authors conclude DFT calls can be cut by a factor of two to four for optimizations needing 20 or more steps, since the surrogate needs some data before it helps. For 13 acrolein/AgPd(111) configurations, which took about 193 DFT steps on average with the quasi-Newton optimizer, a literature-parameterized GP gave roughly four times fewer calls, single-configuration NN active learning about 11 times fewer, multiple-configuration mode about 13 times fewer, and the warm-up mode the largest reduction. In the offline mode, a network trained on 243 acrolein/AgPd trajectories lowered the maximum force of 13 new configurations from about 0.7 to below 0.1 eV/Å without any DFT call, which could serve as a better initial guess.
Across the bare AuPd slab, CO on the AuPd icosahedron and acrolein on AgPd, active learning saved about 50% of calls for the simple slab and over 90% for the lower-symmetry systems. In the NEB cases, the transition states matched the reference with activation energy errors of 6 meV (EMT) and 4 meV (DFT), using 9 instead of 596 EMT calls and 30 instead of 1109 VASP calls. Because convergence was checked only on the highest-energy image, intermediate image energies in the acetylene band did not all match DFT. Training time grew linearly with training set size, but a Pearson correlation analysis of fingerprints showed that configurations more than about five steps apart are weakly correlated, so training on only recent steps kept retraining time nearly constant; a single acrolein/AgPd DFT call took about 1.5 hours, much longer than training. This summary is based on the arXiv v2 preprint text.
Significance
The work shows that an atom-centered NN ensemble, unlike a coordinate-based GP, can pool information across configurations of different size and composition, so batch relaxations of related structures (adsorbate sites, alloy arrangements) become cheaper as the campaign proceeds. It also offers a practical ensemble-variance threshold for deciding when to trust the surrogate, and frames a continuum from on-the-fly learning to offline relaxation with pretrained models. Later work in the group replaced the from-scratch ensemble with pretrained graph neural networks fine-tuned during relaxation (Wang et al. 2024).