This project emerged out of the frustration of there existing no differentiable PDE simulator capable of handling the diversity of problems out there. We identified Radial Basis Functions as a powerful and flexible mesh-free tool to control systems governed by partial differential equations, including non-linear PDEs like the Navier-Stokes equations. We showed that our discretise-then-optimise differentiable programming (DP) framework is superior to both the optimise-then-discretise direct-adjoint-looping (DAL) and the data-driven Physics-Informed Neural Network (PINN).
Software stack: - JAX - GMSH - PyVista
GitHub: 👉 Universal Partial Differential Equations Simulator