14 Feb 2020 | LU LU*, XUHUI MENG*, ZHIPING MAO*, AND GEORGE EM KARNIADAKIS*†
DeepXDE is a Python library designed for solving partial differential equations (PDEs) using physics-informed neural networks (PINNs). PINNs embed PDEs into the loss function of neural networks using automatic differentiation, enabling them to solve both forward and inverse problems efficiently. DeepXDE supports complex geometries through constructive solid geometry (CSG) and provides a user-friendly interface that closely resembles mathematical formulations. The library allows for the solution of various PDE types, including integro-differential, fractional, and stochastic equations. It also includes a residual-based adaptive refinement (RAR) method to enhance training efficiency by dynamically adjusting residual points. DeepXDE is customizable, enabling users to define new geometries, neural networks, and callback functions for monitoring and modifying the training process. The library has been demonstrated through five examples, showcasing its effectiveness in solving both forward and inverse problems. DeepXDE contributes to the development of scientific machine learning by providing a versatile tool for computational science and engineering. Despite its advantages, PINNs face challenges such as slower performance for forward problems and the need for further research in neural network architecture optimization. Overall, DeepXDE offers a powerful and flexible solution for solving PDEs using deep learning.DeepXDE is a Python library designed for solving partial differential equations (PDEs) using physics-informed neural networks (PINNs). PINNs embed PDEs into the loss function of neural networks using automatic differentiation, enabling them to solve both forward and inverse problems efficiently. DeepXDE supports complex geometries through constructive solid geometry (CSG) and provides a user-friendly interface that closely resembles mathematical formulations. The library allows for the solution of various PDE types, including integro-differential, fractional, and stochastic equations. It also includes a residual-based adaptive refinement (RAR) method to enhance training efficiency by dynamically adjusting residual points. DeepXDE is customizable, enabling users to define new geometries, neural networks, and callback functions for monitoring and modifying the training process. The library has been demonstrated through five examples, showcasing its effectiveness in solving both forward and inverse problems. DeepXDE contributes to the development of scientific machine learning by providing a versatile tool for computational science and engineering. Despite its advantages, PINNs face challenges such as slower performance for forward problems and the need for further research in neural network architecture optimization. Overall, DeepXDE offers a powerful and flexible solution for solving PDEs using deep learning.