Using out-of-sample regularization of physics-informed neural networks to speed up computational fluid dynamics

PI: Alex Davis, Associate Professor, Engineering and Public Policy, College of Engineering

Co-PIs: Aarti Singh, Associate Professor, Machine Learning, School of Computer Science; Satbir SinghAssociate Teaching Professor, Mechanical Engineering, College of Engineering

Machine learning approaches such as neural networks (NNs) are being used to model many physical systems in a purely data-driven way. However, these models need significant training data for accurate prediction. Recently, there is interest in developing physics-informed NNs that use expert knowledge in the form of constraints, invariances, or equations to regularize data-driven models. For example, NNs regularized using partial differential equations (PDEs) have been used to model costly computational fluid dynamics (CFD) simulations, demonstrating significant savings in the training data needed over simply fitting a NN to CFD data.

However, existing methods do not fully leverage expert knowledge, as they impose the PDE regularization only on predictions at the training pointsand hence, do not generalize outside of the time periods and spatial locations used for training. We propose to use expert physical knowledge, in the form of the Navier-Stokes equation, to regularize a physics-informed NN beyond the original resolution of training points, with potential extrapolations in time. This will allow the NN to quickly solve fluid flow problems forward in time without using costly CFD calculations to cover the entire domain of interest. We will establish, theoretically and practically, the benefits of the proposed approach on CFD problems in collaboration with ANSYS. We will also port back the methodology to PIs Davis and A. Singh’s current collaboration with Lockheed-Martin where diverse forms of expert judgment (including e.g. differential equations characterizing machine vibrations) are being used to assist ML models for predictive maintenance of machines.