FO-PINNs: A First-Order formulation for Physics Informed Neural Networks
This work addresses accuracy and efficiency issues in PINNs for solving parameterized physical systems, representing an incremental improvement over existing methods.
The paper tackles the problem of reduced accuracy and soft boundary conditions in Physics-Informed Neural Networks (PINNs) for parameterized systems by proposing FO-PINNs, which use a first-order formulation of the PDE loss, resulting in significantly higher accuracy and reduced training time per iteration.
Physics-Informed Neural Networks (PINNs) are a class of deep learning neural networks that learn the response of a physical system without any simulation data, and only by incorporating the governing partial differential equations (PDEs) in their loss function. While PINNs are successfully used for solving forward and inverse problems, their accuracy decreases significantly for parameterized systems. PINNs also have a soft implementation of boundary conditions resulting in boundary conditions not being exactly imposed everywhere on the boundary. With these challenges at hand, we present first-order physics-informed neural networks (FO-PINNs). These are PINNs that are trained using a first-order formulation of the PDE loss function. We show that, compared to standard PINNs, FO-PINNs offer significantly higher accuracy in solving parameterized systems, and reduce time-per-iteration by removing the extra backpropagations needed to compute the second or higher-order derivatives. Additionally, FO-PINNs can enable exact imposition of boundary conditions using approximate distance functions, which pose challenges when applied on high-order PDEs. Through three examples, we demonstrate the advantages of FO-PINNs over standard PINNs in terms of accuracy and training speedup.