Nonintrusive Reduced-Order Models for Parametric Partial Differential Equations via Data-Driven Operator Inference

This work formulates a new approach to reduced modeling of parameterized, time-dependent partial differential equations (PDEs). The method employs Operator Inference, scientific machine learning framework combining data-driven and physics-based modeling. parametric structure the governing is embedded directly into reduced-order model, parameterized operators are learned via linear regression problem. result model that can be solved rapidly map parameter values approximate PDE solutions. Such models may used as surrogates for uncertainty quantification inverse problems require many forward solves PDEs. Numerical issues such well-posedness need appropriate regularization in problem considered, an algorithm hyperparameter selection presented. illustrated heat equation demonstrated FitzHugh–Nagumo neuron model.