Deep nurbs – admissible neural networks

10/25/2022
by   Hamed Saidaoui, et al.
0

In this study, we propose a new numerical scheme for physics-informed neural networks (PINNs) that enables precise and inexpensive solution for partial differential equations (PDEs) in case of arbitrary geometries while strictly enforcing Dirichlet boundary conditions. The proposed approach combines admissible NURBS parametrizations required to define the physical domain and the Dirichlet boundary conditions with a PINN solver. The fundamental boundary conditions are automatically satisfied in this novel Deep NURBS framework. We verified our new approach using two-dimensional elliptic PDEs when considering arbitrary geometries, including non-Lipschitz domains. Compared to the classical PINN solver, the Deep NURBS estimator has a remarkably high convergence rate for all the studied problems. Moreover, a desirable accuracy was realized for most of the studied PDEs using only one hidden layer of neural networks. This novel approach is considered to pave the way for more effective solutions for high-dimensional problems by allowing for more realistic physics-informed statistical learning to solve PDE-based variational problems.

READ FULL TEXT

page 10

page 13

page 15

research
07/10/2020

Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions

In recent work it has been established that deep neural networks are cap...
research
04/17/2021

Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks

In this paper, we introduce a new approach based on distance fields to e...
research
12/14/2022

Guiding continuous operator learning through Physics-based boundary constraints

Boundary conditions (BCs) are important groups of physics-enforced const...
research
06/07/2022

Solving Non-local Fokker-Planck Equations by Deep Learning

Physics-informed neural networks (PiNNs) recently emerged as a powerful ...
research
04/22/2021

Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domains

Physics-informed neural networks (PINNs) are increasingly employed to re...
research
05/05/2022

Lagrangian PINNs: A causality-conforming solution to failure modes of physics-informed neural networks

Physics-informed neural networks (PINNs) leverage neural-networks to fin...
research
08/13/2023

The Hard-Constraint PINNs for Interface Optimal Control Problems

We show that the physics-informed neural networks (PINNs), in combinatio...

Please sign up or login with your details

Forgot password? Click here to reset