ModalPINN: an extension of Physics-Informed Neural Networks with enforced truncated Fourier decomposition for periodic flow reconstruction using a limited number of imperfect sensors

TL;DR

ModalPINN enhances Physics-Informed Neural Networks by incorporating Fourier mode shapes, significantly improving periodic flow reconstruction accuracy with limited and imperfect sensor data, demonstrated on vortex shedding simulations.

Contribution

It introduces ModalPINN, a novel extension of PINN that encodes Fourier modes for better interpretability and accuracy in periodic flow reconstruction from sparse, noisy data.

Findings

Up to two orders of magnitude more precise than standard PINN in test cases.

Robust flow reconstruction with limited, asymmetric, and noisy sensor data.

Effective in modeling vortex shedding phenomena.

Abstract

Continuous reconstructions of periodic phenomena provide powerful tools to understand, predict and model natural situations and engineering problems. In line with the recent method called Physics-Informed Neural Networks (PINN) where a multi layer perceptron directly approximates any physical quantity as a symbolic function of time and space coordinates, we present an extension, namely ModalPINN, that encodes the approximation of a limited number of Fourier mode shapes. In addition to the added interpretability, this representation performs up to two orders of magnitude more precisely for a similar number of degrees of freedom and training time in some cases as illustrated through the test case of laminar shedding of vortices over a cylinder. This added simplicity proves to be robust in regards to flow reconstruction using only a limited number of sensors with asymmetric data that simulates an experimental configuration, even when a Gaussian noise or a random delay is added, imitating imperfect and sparse information.