An Efficient Framework for Encoding Nonlinear Dynamics of Nuclear Systems

In this research, we propose an application of convolutional autoencoders (CAEs) and the sparse identification of nonlinear dynamics (SINDy) algorithm to learn and model nonlinear dynamics. This particular method aims to extract essential features and compress them into a lower dimension before learning the governing equations in this new space. CAEs are powerful tools that can efficiently reduce the dimensionality of large, complex datasets and find an accurate low order representation beyond traditional linear embedding. Once the dynamics have been compressed into a latent space, SINDy is applied to discover equations that determine the trajectory of that latent representation through time. With these reduced equations, one is able to interpolate and extrapolate the system in time and extract information beyond what was in the training set. Being a data-driven approach, it provides a generic framework for learning nonlinear dynamics, whether in time-dependent applications or in parametric exploration for uncertainty quantification purposes.