I. Introduction
Last decade has witnessed a surge of machine-learning applications to model complex electronic dynamics due to underlying quantum mechanics [1]. An example is neural network quantum molecular dynamics (NNQMD), where neural network is trained to reproduce quantum-mechanically obtained atomic energy or force to perform MD simulations [2]-[6]. NNQMD has attracted great attention because of its algorithmic scalability, orders of magnitude faster time-to-solution (T2S), and quantum-mechanically accurate trajectory. SC20 has marked a milestone, demonstrating a 100-million atom NNQMD simulation on the Summit supercomputer at ORNL [7]. Such a NNQMD simulation has opened up a possibility of novel materials simulations. However, NNQMD simulations have thus far been limited to gentle equilibrium conditions, and those involving excited electrons have been hindered due to the complex energy landscape far-from-equilibrium. Such highly-nontrivial interatomic interaction suffers from uncertainty in model prediction due to unseen atomic configuration. The prediction uncertainty results in unphysical atomic force, which quickly deteriorates the fidelity of obtained atomic trajectory, or even worse, cause unpredictable termination of the simulation. The number of unphysical predictions is expected to scale with respect to the simulation size and length, therefore the scaling of simulation fidelity becomes a critical issue for large-scale NNQMD on soon arriving exascale supercomputing platforms. Conventional active learning approaches to this problem generate new training data and retrain the model when a simulation failed. This cycle of simulation failure and model rebuilding is too costly for forthcoming exascale NNQMD simulations. Another commonly used method is NVT ensemble, such as Nose-Hoover thermostat [8], to keep atomic velocity fluctuates around a specified temperature. The use of thermostat algorithm helps to regulate atomic velocities to some extent, however, it does not provide a mean to control unphysical prediction beyond a certain threshold. A potential light-overhead alternative may use inductive bias [9], [10], which is a set of assumptions for a machine learning model to predict when training data does not exist, e.g., margin maximization in support vector machine. Though a good inductive bias may substantially improve the fidelity of generalization performance, it is rarely discussed in the materials simulation context.