4 papers
Data-free neural PDE solvers based on Graph Neural Networks and weak forms
Mikel M. Iparraguirre, Iciar Alfaro, David Gonzalez +1
We present a physics-informed, data-free neural solver for partial differential equations, built on a graph neural network architecture that utilises message passing. By relying on…
MeshGraphNet-Transformer: Scalable Mesh-based Learned Simulation for Solid Mechanics
Mikel M. Iparraguirre, Iciar Alfaro, David Gonzalez +1
We present MeshGraphNet-Transformer (MGN-T), a novel architecture that combines the global modeling capabilities of Transformers with the geometric inductive bias of MeshGraphNets,…
On the under-reaching phenomenon in message-passing neural PDE solvers: revisiting the CFL condition
Lucas Tesan, Mikel M. Iparraguirre, David Gonzalez +2
This paper proposes sharp lower bounds for the number of message passing iterations required in graph neural networks (GNNs) when solving partial differential equations (PDE). This…
On the feasibility of foundational models for the simulation of physical phenomena
Alicia Tierz, Mikel M. Iparraguirre, Iciar Alfaro +3
We explore the feasibility of foundation models for the simulation of physical phenomena, with emphasis on continuum (solid and fluid) mechanics. Although so-called learned simulat…