Deep Learning-based surrogate models for parametrized PDEs: handling geometric variability through graph neural networks

by   Nicola Rares Franco, et al.

Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, require the solution of parametrized time-dependent nonlinear partial differential equations (PDEs). In this context, full order models (FOMs), such as those relying on the finite element method, can reach high levels of accuracy, however often yielding intensive simulations to run. For this reason, surrogate models are developed to replace computationally expensive solvers with more efficient ones, which can strike favorable trade-offs between accuracy and efficiency. This work explores the potential usage of graph neural networks (GNNs) for the simulation of time-dependent PDEs in the presence of geometrical variability. In particular, we propose a systematic strategy to build surrogate models based on a data-driven time-stepping scheme where a GNN architecture is used to efficiently evolve the system. With respect to the majority of surrogate models, the proposed approach stands out for its ability of tackling problems with parameter dependent spatial domains, while simultaneously generalizing to different geometries and mesh resolutions. We assess the effectiveness of the proposed approach through a series of numerical experiments, involving both two- and three-dimensional problems, showing that GNNs can provide a valid alternative to traditional surrogate models in terms of computational efficiency and generalization to new scenarios. We also assess, from a numerical standpoint, the importance of using GNNs, rather than classical dense deep neural networks, for the proposed framework.


page 14

page 16

page 17

page 18

page 20

page 22

page 23

page 26


GrADE: A graph based data-driven solver for time-dependent nonlinear partial differential equations

The physical world is governed by the laws of physics, often represented...

Learning Mesh-Based Simulation with Graph Networks

Mesh-based simulations are central to modeling complex physical systems ...

Graph Neural Network Based Surrogate Model of Physics Simulations for Geometry Design

Computational Intelligence (CI) techniques have shown great potential as...

Learning Controllable Adaptive Simulation for Multi-resolution Physics

Simulating the time evolution of physical systems is pivotal in many sci...

Learning the Solution Operator of Boundary Value Problems using Graph Neural Networks

As an alternative to classical numerical solvers for partial differentia...

Universal Solution Manifold Networks (USM-Nets): non-intrusive mesh-free surrogate models for problems in variable domains

We introduce Universal Solution Manifold Network (USM-Net), a novel surr...

Please sign up or login with your details

Forgot password? Click here to reset