Physics-informed neural networks with hard constraints for inverse design

4 code implementations • 9 Feb 2021 • Lu Lu, Raphael Pestourie, Wenjie Yao, Zhicheng Wang, Francesc Verdugo, Steven G. Johnson

We achieve the same objective as conventional PDE-constrained optimization methods based on adjoint methods and numerical PDE solvers, but find that the design obtained from hPINN is often simpler and smoother for problems whose solution is not unique.

The aggregated unfitted finite element method on parallel tree-based adaptive meshes

no code implementations • 9 Jun 2020 • Santiago Badia, Alberto F. Martín, Eric Neiva, Francesc Verdugo

In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement.

Numerical Analysis Computational Engineering, Finance, and Science Mathematical Software Numerical Analysis

A user-guide to Gridap -- grid-based approximation of partial differential equations in Julia

2 code implementations • 3 Oct 2019 • Francesc Verdugo, Santiago Badia

We present Gridap, a new scientific software library for the numerical approximation of partial differential equations (PDEs) using grid-based approximations.

Mathematical Software