Fast-PINN for Complex Geometry: Solving PDEs with Boundary. . . TL;DR: We present a fast-PINN method based on the incorporation of boundary connectivity constraints into training loss, which can efficiently produce accurate solutions with order of magnitude fewer training samples, across multiple fluid dynamic problems
Δ-PINNs: Physics-informed neural networks on complex . . . We test our methodology by solving an inverse problem with the Eikonal equation, a Poisson, heat transfer and hyperelastic forward problem, and an operator learning problem for inferring the geodesic distance between two points on a complex manifold
Physics informed neural networks for solving Partial . . . Boundary conditions: solution to a PDE often depends not only on the equation itself but also on the boundary and initial conditions If these conditions are complex or not well-defined, finding a closed-form solution becomes exceedingly challenging;
Physics Informed Neural Networks (PINNs) in TorchPhysics In this tutorial we present a first basic example of solving a PDE with boundary constraints in TorchPhysics using a PINN approach You will also learn about the different components of this library and main steps for finding a neural network that approximates the solution of a PDE