Nonlinearity encoding to improve extrapolation capabilities for unobserved physical states.

The fundamental goal of machine learning (ML) in physical science is to predict the physical properties of unobserved states. However, an accurate prediction for input data outside of training distributions is a challenging problem in ML due to the nonlinearities in input and target dynamics. For an accurate extrapolation of ML algorithms, we propose a new data-driven method that encodes the nonlinearities of physical systems into input representations. Based on the proposed encoder, a given physical system is described as linear-like functions that are easy to extrapolate. By applying the proposed encoder, the extrapolation errors were significantly reduced by 48.39% and 40.04% in n -body problem and materials property prediction, respectively.