arXiv:2609.36216v1 Announce Type: new Abstract: Neural operators are typically trained in a supervised fashion, which requires a dataset to be generated with a classical solver. Training them physics...
arXiv:2601. 00672v2 Announce Type: replace-cross Abstract: In this paper, we study the finite element operator network (FEONet), an operator-learning method for parametric problems, originally introduced in J.
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:2507.07292v2 Announce Type: replace Abstract: We develop a new and general encode-approximate-reconstruct operator learning model that leverages learned neural representations of bases for inpu...
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:2606. 19754v1 Announce Type: new Abstract: Partial differential equations (PDEs) play a central role in modeling complex physical, biological, and engineering systems.
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:2606. 18032v1 Announce Type: cross Abstract: We propose a new weak-form Physics-Informed Neural Network approach (named INI-VPINN).
arXiv:2609.07437v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) represent a growing frontier in using artificial intelligence to solve partial differential equations (PDEs)...
arXiv:2606. 05199v1 Announce Type: cross Abstract: The identification of constitutive neural network models from heterogeneous full-field deformation data provides a robust alternative to traditional calibration methods based on homogeneous stress-strain experiments, particularly given the high dimensionality of trainable parameters.
arXiv:2607. 20378v1 Announce Type: new Abstract: Physics-informed learning of partial differential equations (PDEs) has been dominated by multilayer perceptrons (MLPs), whose spectral bias and dense parameterization limit both accuracy and interpretability.
arXiv:2607. 12570v1 Announce Type: cross Abstract: Multiscale problems are notoriously difficult to tackle using traditional numerical methods, as accurately resolving fine-scale features often requires prohibitively fine discretizations.