arXiv subjects

Mikel M. Iparraguirre

Publications and source records attributed to Mikel M. Iparraguirre.

4 recordsLinked to original sources

arXiv2026

MeshGraphNet-Transformer: Scalable Mesh-based Learned Simulation for Solid Mechanics

We present MeshGraphNet-Transformer (MGN-T), a novel architecture that combines the global modeling capabilities of Transformers with the geometric inductive bias of MeshGraphNets, while preserving a mesh-based graph representation. MGN-T overcomes a key limitation of standard MGN, the inefficient long-range information propagation caused by iterative message passing on large, high-resolution meshes. A physics-attention Transformer serves as a global processor, updating all nodal states simultaneously while explicitly retaining node and edge attributes. By directly capturing long-range physical interactions, MGN-T eliminates the need for deep message-passing stacks or hierarchical, coarsened meshes, enabling efficient learning on high-resolution meshes with varying geometries, topologies, and boundary conditions at an industrial scale. We demonstrate that MGN-T successfully handles industrial-scale meshes for impact dynamics, a setting in which standard MGN fails due message-passing under-reaching. The method accurately models self-contact, plasticity, and multivariate outputs, including internal, phenomenological plastic variables. Moreover, MGN-T outperforms state-of-the-art approaches on classical benchmarks, achieving higher accuracy while maintaining practical efficiency, using only a fraction of the parameters required by competing baselines.

cs.LG↗

arXiv2026

Data-free neural PDE solvers based on Graph Neural Networks and weak forms

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 the weak form of the problem, we use gradients of finite-element shape functions (which are therefore polynomials) rather than automatic differentiation operators to compute the residuals of the equation from the displacements predicted by the network itself. Our approach generalises to previously unseen load cases and geometries, achieving easily convergence errors in the residuals of less than 1% and being capable of scaling up to models of considerable size and arbitrary geometries. To ensure compliance with the laws of physics and provide guarantees regarding the inference, it is possible to use the residual itself as an error indicator for the inference, and thus perform a refinement at the testing stage if the residual tolerance set in advance by the user is not met. Examples are provided to demonstrate the performance of the proposed method. This results in a method that avoids the costly process of obtaining, curating and storing high-fidelity synthetic data for training the neural network. Whilst this is not unique to our method, it is the first time it has been combined with a geometric machine learning technique capable of providing the necessary geometric bias to overcome the well-known difficulties of physics-informed neural networks.

cs.CE↗

arXiv2025

On the under-reaching phenomenon in message-passing neural PDE solvers: revisiting the CFL condition

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 significantly reduces the need for exhaustive hyperparameter tuning. Bounds are derived for the three fundamental classes of PDEs (hyperbolic, parabolic and elliptic) by relating the physical characteristics of the problem in question to the message-passing requirement of GNNs. In particular, we investigate the relationship between the physical constants of the equations governing the problem, the spatial and temporal discretisation and the message passing mechanisms in GNNs. When the number of message passing iterations is below these proposed limits, information does not propagate efficiently through the network, resulting in poor solutions, even for deep GNN architectures. In contrast, when the suggested lower bound is satisfied, the GNN parameterisation allows the model to accurately capture the underlying phenomenology, resulting in solvers of adequate accuracy. Examples are provided for four different examples of equations that show the sharpness of the proposed lower bounds.

cs.LG↗

arXiv2024

On the feasibility of foundational models for the simulation of physical phenomena

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 simulators have shown some success when applied to specific tasks, it remains to be studied to what extent they are able to undergo severe changes in domain shape, boundary conditions and/or constitutive laws and still provide robust (i.e., hallucination-free) and accurate results. In this paper we perform an exhaustive study of these features, put ourselves in the worst-case scenario and study their resistance to such strong changes in their domain of application.

cs.CE↗