Multi-Fidelity Modeling of Spatio-Temporal Fields

Sudeepta Mondal, Soumalya Sarkar

Keywords: multi-fidelity modeling, machine learning, spatio-temporal emulation

TL;DR: This paper proposes a methodology of combining the so-called inaccurate (but inexpensive) low-fidelity information with expensive high-fidelity training data for efficiently emulating spatio-temporal fields under data limitations.

Abstract: Devising emulation frameworks for predicting the spatio-temporal behavior of nonlinear dynamical systems is a challenging problem which has generated significant interest lately. However, scarcity of data often plagues the prevalent approaches, particularly when the cost of procuring spatio-temporal data from the underlying physical processes is high. However, the data sources for a particular spatio-temporal process may present a hierarchy of fidelities with respect to their computational cost/accuracy, such that higher fidelity levels are more accurate (and also more expensive) than the lower fidelity levels. This paper presents a novel multi-fidelity spatio-temporal modeling approach (MF-STM), whereby the lower fidelity data source for a dynamical process is gainfully utilized in increasing the accuracy of predicting the higher fidelity fields. The methodology is based on non-intrusive reduced order modeling using deep convolutional autoencoders, combined with a latent-space evolution framework based on multi-fidelity Gaussian processes. This framework results in probabilistic spatio-temporal predictions for unknown operating conditions of the dynamical system, which provides the end user with quantified levels of uncertainties associated with the data-driven predictions. The framework is validated on an advection-dominated fluid flow process described by the inviscid shallow water equations, which is a well-studied benchmark problem.