Easy to learn hard to master - how to solve an arbitrary equation with PINN
Keywords: PINN, solver, open source, XDE, differential equations
TL;DR: We present a single framework that allows to see how different features developed in the papers affect the equation solution ability of a PINN to make PINNs from an art to the technique
Abstract: Physics-informed neural networks (PINNs) offer predictive capabilities for processes defined by known equations and limited data. While custom architectures and loss computations are often designed for each equation, the untapped potential of classical architectures remains unclear. To make a comprehensive study, it is required to compare performance of a given neural network architecture and loss formulation for different types of equations. This paper introduces an open-source framework for unified handling of ordinary differential equations (ODEs), partial differential equations (PDEs), and their systems. We explore PINN applicability and convergence comprehensively, demonstrating its performance across ODEs, PDEs, ODE systems, and PDE systems.
Submission Track: Original Research
Submission Number: 1
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