arXiv AI
Jul 20
GA-VINO: A Geometry-Aware Variational Physics-informed Neural Operator for Mindlin-Reissner Plates
arXiv:2606. 16624v2 Announce Type: replace Abstract: Plate and shell structures are widely used in engineering fields.
MR-GVNO: A Geometry-Aware Variational Physics-Informed Neural Operator for Mindlin-Reissner Plates on Irregular Domains
arXiv:2606. 16624v1 Announce Type: new Abstract: Plate and shell structures are widely used in engineering, making rapid response prediction under varying geometries, materials, and loads highly desirable.
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arXiv AI
2d ago
ArGEnT: Arbitrary Geometry-encoded Transformer for Operator Learning
arXiv:2602. 11626v3 Announce Type: replace-cross Abstract: Learning solution operators on arbitrary geometries remains a central challenge in scientific machine learning, especially for many-query simulation, physics-informed learning, and evolving geometries requiring accurate, geometry-aware predictions at arbitrary spatial locations.
arXiv Machine Learning
Jul 21
WINO: A Weak-Form Physics Informed Neural Operator for Hyperelasticity on Variable Domains
arXiv:2605. 24651v2 Announce Type: replace-cross Abstract: We propose a Weak-form Physics-Informed Neural Operator (WINO), a data-free framework that combines the efficiency of neural operators with the geometric flexibility of the $\varphi$-finite element method ($\varphi$-FEM).
arXiv Machine Learning
Jul 2
GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problems
arXiv:2607. 01128v1 Announce Type: new Abstract: Operator learning for partial differential equations (PDEs) on arbitrary geometries builds fast neural surrogates for large-scale simulation.
arXiv Machine Learning
Jun 17
INI-VPINN: A Variational Physics-Informed Neural Network with Implicit Neumann and Interface Handling for Multi-Material Domains with Geometric Singularities
arXiv:2606. 18032v1 Announce Type: cross Abstract: We propose a new weak-form Physics-Informed Neural Network approach (named INI-VPINN).
arXiv Machine Learning
Jun 9
Mesh Graph Neural Network Framework for Accelerating Finite Element Simulation for Arbitrary Geometries
arXiv:2606. 08287v1 Announce Type: new Abstract: Finite element analysis (FEA) is essential for structural design but remains computationally expensive, particularly when evaluating multiple design iterations or load scenarios.
arXiv Machine Learning
Jun 16
Petrov-Galerkin Variational Physics-Informed Neural Network Framework for Two-Dimensional Singularly Perturbed Problems
arXiv:2606. 16510v1 Announce Type: cross Abstract: This study proposes a Petrov-Galerkin based Variational Physics-Informed Neural Network (VPINN) for efficiently solving two-dimensional singularly perturbed problems (SPPs) with one and two small perturbation parameters.
arXiv AI
Jun 10
Structure-Preserving Learning Improves Geometry Generalization in Neural PDEs
arXiv:2602. 02788v2 Announce Type: replace-cross Abstract: We aim to develop physics foundation models for science and engineering that provide real-time solutions to Partial Differential Equations (PDEs) which preserve structure and accuracy under adaptation to unseen geometries.
arXiv Machine Learning
Aug 4
Convex Neural Energy Elements: Monolithic Finite-Element Assembly of Geometry-Parameterized Neural Operators with Stability and Error Guarantees
arXiv:2608. 02036v1 Announce Type: new Abstract: Extending the neural-operator element method from individually trained, fixed-geometry neural elements to a library of reusable, geometry-parameterized element types fails structurally: a field-predicting operator trained by value regression induces an energy whose assembled Hessian is indefinite, and Newton converges to spurious minima (247% error) even with 1%-accurate field predictions.
arXiv Machine Learning
Jun 11
HAMNO: A Hierarchical Adaptive Multi-scale Neural Operator with Physics-Informed Learning for Dynamical Systems
arXiv:2606. 11963v1 Announce Type: new Abstract: Neural operators provide a powerful framework for learning solution mappings of partial differential equations directly in function space.
arXiv Machine Learning
Jul 31
Learning the Helmholtz equation operator with DeepONet for non-parametric 2D geometries
arXiv:2605. 00760v2 Announce Type: replace Abstract: This paper deals with solving the 2D Helmholtz equation on non-parametric domains, leveraging a physics-informed neural operator network, the DeepONet framework.
arXiv Machine Learning
Jun 10
Non-linear mechanical field reconstruction coupling recurrent neural networks with physics-informed graph neural networks
arXiv:2606. 10909v1 Announce Type: cross Abstract: Reconstructing local stress fields in heterogeneous microstructures under non-linear, history-dependent loading remains a major computational bottleneck in multi-scale simulations.