Operator inference with roll outs for learning reduced models from scarce and low-quality data

TL;DR

This paper introduces a method combining operator inference with neural ODE roll outs to improve the learning of reduced models from scarce, noisy, and low-quality data in scientific computing.

Contribution

It presents a novel approach that enhances traditional operator inference by integrating dynamic roll outs, increasing stability and robustness in low-quality data scenarios.

Findings

Effective with sparse, noisy data up to 10% noise.

Produces accurate predictive models from limited data.

Demonstrated on shallow water and geophysical dynamics.

Abstract

Data-driven modeling has become a key building block in computational science and engineering. However, data that are available in science and engineering are typically scarce, often polluted with noise and affected by measurement errors and other perturbations, which makes learning the dynamics of systems challenging. In this work, we propose to combine data-driven modeling via operator inference with the dynamic training via roll outs of neural ordinary differential equations. Operator inference with roll outs inherits interpretability, scalability, and structure preservation of traditional operator inference while leveraging the dynamic training via roll outs over multiple time steps to increase stability and robustness for learning from low-quality and noisy data. Numerical experiments with data describing shallow water waves and surface quasi-geostrophic dynamics demonstrate that operator inference with roll outs provides predictive models from training trajectories even if data are sampled sparsely in time and polluted with noise of up to 10%.