(411j) Uncertainty Measurement Method for Machine Learned Potentials

Machine learned potentials (MLPs) have been used to accelerate molecular simulations such as molecular dynamics (MD) and Monte Carlo simulations. Selecting data for training the machine learned models is challenging because the space of atomic structures is often large, not well understood, and not possible to enumerate. In addition, atomic structures are translated into fingerprints which are high dimensional and less human-interpretable than the original atom configurations. Commonly used MLPs such as neural networks will unreliably extrapolate on inputs much different from their training data, and how to select enough of the relevant training space to avoid this is nonobvious. Hence, we require a way to determine the uncertainty of a prediction from a MLP to determine if it is reliable. We propose an uncertainty measurement method for neural network potentials. The uncertainty measure is based on the multiparameter delta method from statistics, which gives the standard error of the prediction. The uncertainty measure is calculated after the MLP is trained, and requires the gradient of the MLP prediction with respect to model parameters and the Hessian of the loss function with respect to model parameters. Both the gradient and Hessian can be obtained from most neural network training frameworks. The method gives a measure of uncertainty for an input that depends on training data, and model parameters. We use examples of intuitive molecular systems to show that the uncertainty measure is large for input space regions not part of the training data. The uncertainty method can be used in combination with MD as an on-the-fly method, and it can aid in selecting training data.