Scalable Bayesian Uncertainty Quantification for Neural Network Potentials: Promise and Pitfalls

Abstract

Neural network (NN) potentials promise highly accurate molecular dynamics (MD) simulations within the computational complexity of classical MD force fields. However, when applied outside their training domain, NN potential predictions can be inaccurate, increasing the need for Uncertainty Quantification (UQ). Bayesian modeling provides the mathematical framework for UQ, but classical Bayesian methods based on Markov chain Monte Carlo (MCMC) are computationally intractable for NN potentials. By training graph NN potentials for coarse-grained systems of liquid water and alanine dipeptide, we demonstrate here that scalable Bayesian UQ via stochastic gradient MCMC (SG-MCMC) yields reliable uncertainty estimates for MD observables. We show that cold posteriors can reduce the required training data size and that for reliable UQ, multiple Markov chains are needed. Additionally, we find that SG-MCMC and the Deep Ensemble method achieve comparable results, despite shorter training and less hyperparameter tuning of the latter. We show that both methods can capture aleatoric and epistemic uncertainty reliably, but not systematic uncertainty, which needs to be minimized by adequate modeling to obtain accurate credible intervals for MD observables. Our results represent a step toward accurate UQ that is of vital importance for trustworthy NN potential-based MD simulations required for decision-making in practice.

Raman Spectra of Amino Acids and Peptides from Machine Learning Polarizabilities

“…It is important to note that, in our case, the CEE always underestimates the RMSE and is therefore only an estimation. Additionally, CEE only accounts for the epistemic uncertainty, 82 while other sources of errors such as DFT approximations, accuracy of classical force fields, and limited MD sampling are not included.…”

Developing an Implicit Solvation Machine Learning Model for Molecular Simulations of Ionic Media

“…In the future, the salt concentration could be added as an additional input feature of the NN, making the model directly concentration-dependent. Similar approaches were previously proposed to include the temperature dependency of the CG models . To emphasize the importance of capturing the many-body term of the PMF, a pure sodium chloride solution at 5.0 mol kg –1 has been performed following the computational detail of Shen et al, the detailed results are provided in the Supporting Information (Section 4.3).…”

“…Similar approaches were previously proposed to include the temperature dependency of the CG models. 63 To emphasize the importance of capturing the many-body term of the PMF, a pure sodium chloride solution at 5.0 mol kg –1 has been performed following the computational detail of Shen et al, 83 the detailed results are provided in the Supporting Information (Section 4.3). The DIS model and two other implicit models, i.e., the IBI potential 76 , 128 fitted at 5.0 mol kg –1 and the transferable effective potential of the cited paper.…”

“…The pioneering work of Behler showcased that deep neural networks (NN) could be employed to learn a computationally cheaper surrogate model for the density functional theory potential energy surface of bulk silicon . Following the initial studies, other ML algorithms and NN architectures rapidly emerged. − ML algorithms can be utilized to construct not only all-atom models but also CG models. , Previous studies demonstrated a successful reproduction of structural − and dynamical − properties. However, most considered pure water solvent or implicitly treated the ions, even though they play a vital role in biological processes.…”

Active learning graph neural networks for partial charge prediction of metal-organic frameworks via dropout Monte Carlo

“…Consequently, AL efficacy critically depends on the quality of the employed uncertainty quantification (UQ) scheme to estimate the prediction error. For state-ofthe-art graph neural network (GNN) surrogate models, popular UQ schemes include the Deep Ensemble method 54,55 , stochastic-gradient Markov chain Monte Carlo (SG-MCMC) [56][57][58][59] and Dropout Monte Carlo 60,61 (DMC). However, the former two methods are inefficient for AL given that they require retraining of several models at each AL iteration.…”