7 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…
A Graph Neural Network approach to zero-shot Digital Twins
Alicia Tierz, Icíar Alfaro, David González +1
Traditional Predictive Digital Twins often remain geometrically rigid, requiring extensive retraining or fine-tuning whenever the underlying physical domain or boundary conditions…
Variational Graph Neural Networks for Uncertainty Quantification in Inverse Problems
David Gonzalez, Alba Muixi, Beatriz Moya +1
The increasingly wide use of deep machine learning techniques in computational mechanics has significantly accelerated simulations of problems that were considered unapproachable j…
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…
Graph neural networks informed locally by thermodynamics
Alicia Tierz, Iciar Alfaro, David González +2
Thermodynamics-informed neural networks employ inductive biases for the enforcement of the first and second principles of thermodynamics. To construct these biases, a metriplectic…