Robust Regression with Highly Corrupted Data via Physics Informed Neural Networks
This addresses the challenge of sensor failures in physics-informed machine learning for researchers in computational science, though it is incremental as it builds on existing PINN frameworks.
The authors tackled the problem of solving partial differential equations (PDEs) with highly corrupted data by proposing LAD-PINN and MAD-PINN methods, achieving robust reconstruction and parameter recovery even with large percentages of outliers, as demonstrated across examples like Navier-Stokes equations.
Physics-informed neural networks (PINNs) have been proposed to solve two main classes of problems: data-driven solutions and data-driven discovery of partial differential equations. This task becomes prohibitive when such data is highly corrupted due to the possible sensor mechanism failing. We propose the Least Absolute Deviation based PINN (LAD-PINN) to reconstruct the solution and recover unknown parameters in PDEs - even if spurious data or outliers corrupt a large percentage of the observations. To further improve the accuracy of recovering hidden physics, the two-stage Median Absolute Deviation based PINN (MAD-PINN) is proposed, where LAD-PINN is employed as an outlier detector followed by MAD screening out the highly corrupted data. Then the vanilla PINN or its variants can be subsequently applied to exploit the remaining normal data. Through several examples, including Poisson's equation, wave equation, and steady or unsteady Navier-Stokes equations, we illustrate the generalizability, accuracy and efficiency of the proposed algorithms for recovering governing equations from noisy and highly corrupted measurement data.