Data-driven recovery of hidden physics in reduced order modeling of fluid flows

TL;DR

This paper presents a hybrid modeling approach combining physics-based models with machine learning to uncover hidden physics in reduced order models of fluid flows, improving accuracy under uncertain conditions.

Contribution

The paper introduces a modular hybrid analysis and modeling framework that integrates first principles with data-driven neural networks to account for hidden physics in fluid flow models.

Findings

Effective correction of reduced order models using LSTM networks.

Improved modeling of hidden physics in parameterized fluid systems.

Application of Grassmannian interpolation for unseen parameters.

Abstract

In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on using the first principles to model the known physics in conjunction with utilizing the data-driven machine learning tools to model remaining residual that is hidden in data. This framework employs proper orthogonal decomposition as a compression tool to construct orthonormal bases and Galerkin projection (GP) as a model to built the dynamical core of the system. Our proposed methodology hence compensates structural or epistemic uncertainties in models and utilizes the observed data snapshots to compute true modal coefficients spanned by these bases. The GP model is then corrected at every time step with a data-driven rectification using a long short-term memory (LSTM) neural network architecture to incorporate hidden physics. A Grassmannian manifold approach is also adapted for interpolating basis functions to unseen parametric conditions. The control parameter governing the system's behavior is thus implicitly considered through true modal coefficients as input features to the LSTM network. The effectiveness of the HAM approach is discussed through illustrative examples that are generated synthetically to take hidden physics into account. Our approach thus provides insights addressing a fundamental limitation of the physics-based models when the governing equations are incomplete to represent underlying physical processes.