DeepXDE

DeepXDE is a library for scientific machine learning and physics-informed learning. DeepXDE includes the following algorithms. Physics-informed neural network (PINN). Solving different problems. Solving forward/inverse ordinary/partial differential equations (ODEs/PDEs) [SIAM Rev.] Solving forward/inverse integro-differential equations (IDEs) [SIAM Rev.] fPINN: solving forward/inverse fractional PDEs (fPDEs) [SIAM J. Sci. Comput.] NN-arbitrary polynomial chaos (NN-aPC): solving forward/inverse stochastic PDEs (sPDEs) [J. Comput. Phys.] PINN with hard constraints (hPINN): solving inverse design/topology optimization [SIAM J. Sci. Comput.] Residual-based adaptive sampling [SIAM Rev., arXiv] Gradient-enhanced PINN (gPINN) [Comput. Methods Appl. Mech. Eng.] PINN with multi-scale Fourier features [Comput. Methods Appl. Mech. Eng.]