Thomas D Swinburne

Thomas D Swinburne, Danny Perez

Bayesian regression determines model parameters by minimizing the expected loss, an upper bound to the true generalization error. However, the loss ignores misspecification, where models are imperfect. Parameter uncertainties from Bayesian regression are thus significantly underestimated and vanish in the large data limit. This is particularly problematic when building models of low-noise, or near-deterministic, calculations, as the main source of uncertainty is neglected. We analyze the generalization error of misspecified, near-deterministic surrogate models, a regime of broad relevance in science and engineering. We show posterior distributions must cover every training point to avoid a divergent generalization error and design an ansatz that respects this constraint, which for linear models incurs minimal overhead. This is demonstrated on model problems before application to thousand dimensional datasets in atomistic machine learning. Our efficient misspecification-aware scheme gives accurate prediction and bounding of test errors where existing schemes fail, allowing this important source of uncertainty to be incorporated in computational workflows.

Fraser Birks, Matthew Nutter, Thomas D Swinburne et al.

Machine-learned interatomic potentials can offer near first-principles accuracy but are computationally expensive, limiting their application to large-scale molecular dynamics simulations. Inspired by quantum mechanics/molecular mechanics methods we present ML-MIX, a CPU- and GPU-compatible LAMMPS package to accelerate simulations by spatially mixing interatomic potentials of different complexities allowing deployment of modern MLIPs even under restricted computational budgets. We demonstrate our method for ACE, UF3, SNAP and MACE potential architectures and demonstrate how linear 'cheap' potentials can be distilled from a given 'expensive' potential, allowing close matching in relevant regions of configuration space. The functionality of ML-MIX is demonstrated through tests on point defects in Si, Fe and W-He, in which speedups of up to 11x over ~ 8,000 atoms are demonstrated, without sacrificing accuracy. The scientific potential of ML-MIX is demonstrated via two case studies in W, measuring the mobility of b = 1/2 111 screw dislocations with ACE/ACE mixing and the implantation of He with MACE/SNAP mixing. The latter returns He reflection coefficients which (for the first time) match experimental observations up to an He incident energy of 80 eV - demonstrating the benefits of deploying state-of-the-art models on large, realistic systems.