Examining the robustness of Physics-Informed Neural Networks to noise for Inverse Problems
This work addresses the robustness of PINNs for inverse problems with noisy data, which is relevant for engineering and science applications, but it is incremental as it confirms existing limitations.
The study compared Physics-Informed Neural Networks (PINNs) to traditional finite element methods for solving inverse problems in fluid mechanics, finding that PINNs were outperformed in accuracy and computation time, though the gap decreased with higher dimensions and more data.
Approximating solutions to partial differential equations (PDEs) is fundamental for the modeling of dynamical systems in science and engineering. Physics-informed neural networks (PINNs) are a recent machine learning-based approach, for which many properties and limitations remain unknown. PINNs are widely accepted as inferior to traditional methods for solving PDEs, such as the finite element method, both with regard to computation time and accuracy. However, PINNs are commonly claimed to show promise in solving inverse problems and handling noisy or incomplete data. We compare the performance of PINNs in solving inverse problems with that of a traditional approach using the finite element method combined with a numerical optimizer. The models are tested on a series of increasingly difficult fluid mechanics problems, with and without noise. We find that while PINNs may require less human effort and specialized knowledge, they are outperformed by the traditional approach. However, the difference appears to decrease with higher dimensions and more data. We identify common failures during training to be addressed if the performance of PINNs on noisy inverse problems is to become more competitive.