Geometry Optimization
Geometry optimization searches for atomic positions that minimize the energy (or, in nudged elastic band methods, locate a minimum energy path and its saddle point) by iteratively moving atoms along computed forces with optimizers such as BFGS, conjugate gradients or quasi-Newton schemes. With DFT each step needs an expensive force call, so the number of steps dominates the cost, and surrogate models that take many cheap steps between reference calculations are a common way to accelerate it.
Surrogate-accelerated relaxations with a neural network ensemble (2021)
Yang, Jiménez-Negrón and Kitchin showed that an ensemble of atom-centered neural networks, retrained as DFT data arrive, reduced DFT calls by about 50% for a bare AuPd slab and by over 90% for adsorbates and a nanoparticle compared with VASP’s RMM-DIIS optimizer, with gains largest for low-symmetry systems needing many steps (Yang et al. 2021). A network trained on 243 earlier acrolein/AgPd trajectories relaxed new configurations offline from about 0.7 to below 0.1 eV/Å maximum force, and training only on the most recent five or so steps kept retraining time roughly constant. Summary: yang2021.
Direct prediction versus ML-driven relaxation of adsorbate structures (2022)
Kolluru et al. (2022) compared predicting relaxed adsorbate-slab energies and structures in one model call with running an ML-force-driven optimizer (typically 200 to 300 calls). For relaxed energies the two were close, with direct models trained on about 300 times less data nearly matching relaxation-based ones, though relaxations generalized better out of distribution. For relaxed structures the gap was large: direct models matched distance-based ADwT (about 46 to 48%) but almost never gave low DFT forces (AFbT near 0%), while relaxation-based GemNet-dT reached 60.88% ADwT and 20.35% AFbT. Distance metrics cannot replace DFT force checks, and the authors suggest counting the DFT steps needed to finish an ML-relaxed structure as a practical measure of savings. Summary: kolluru2022.
Fine-tuned GNN relaxations outside the pretraining domain (2024)
Wang and coworkers tested Finetuna, which relaxes structures with an Open Catalyst pretrained GemNet potential driving an ASE BFGS optimizer and fine-tunes it on the fly with occasional VASP single points, on systems unlike its training data (Wang et al. 2024). Relative to pure VASP BFGS relaxations, an OC20 model converged 81% of alcohol adsorbate runs using 18% of the DFT calls, and 92% of zeolite and MOF runs using 19% when an extra query was triggered whenever the retrained force error stayed above 0.05 eV/Å. Spin-polarized oxides were harder: the OC20 model converged none, while an OC22 model converged 90% using 58% of the DFT calls. Most failed runs showed ML forces above 5 eV/Å somewhere along the trajectory, which the authors propose as a signal to fall back to plain DFT. Summary: wang2024.