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: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:2609.35938v1 Announce Type: new Abstract: This paper proposes an interpretable neural operator framework, the Kernel Operator Network (KernelOnet), which incorporates kernel functions explicitl...
arXiv:2607. 22215v1 Announce Type: new Abstract: In this study, we introduce latent PDE mapping, a broadly applicable physics-informed learning technique designed to enable efficient geometric generalization with sparse training data.
arXiv:2609.14841v1 Announce Type: new Abstract: Scientific machine learning methods such as physics-informed neural networks (PINNs) increasingly rely on domain decomposition for better scalability w...
The paper presents Finite Basis Physics-Informed Neural Networks (FBPINNs) and their multilevel extensions as a new approach to solving the Helmholtz equation. By decomposing the computational domain into overlapping sub‑domains, each governed by a local neural network, the method aims to improve accuracy and computational efficiency for high‑frequency wave problems in complex two‑dimensional domains. The authors evaluate the technique on the homogeneous Helmholtz case, showing its potential to overcome limitations of traditional finite difference and finite element methods.
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:2609.07983v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) have recently emerged as a promising approach for solving Partial Differential Equations (PDEs), offering a me...
arXiv:2512. 23192v4 Announce Type: replace Abstract: While Transformers have demonstrated remarkable potential in modeling Partial Differential Equations (PDEs), modeling large-scale unstructured meshes with complex geometries remains a significant challenge.
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:2606. 18032v1 Announce Type: cross Abstract: We propose a new weak-form Physics-Informed Neural Network approach (named INI-VPINN).
The paper introduces Cross-Physics Mapping (CPM), an operator-learning framework that enables deep learning to translate physical fields governed by different equations. By aligning latent representations and applying a dimensionless scaling principle, CPM maps between heterogeneous domains such as diffusion and wave fields. Experiments with seven neural operator architectures show directional asymmetry: diffusion-to-wave mapping is harder, while wave-to-diffusion mapping is more stable, with neural operators outperforming conventional convolutional baselines.
Can deep learning translate physical fields governed by fundamentally different equations? We address this question by introducing Cross-Physics Mapping (CPM), an operator-learning framework for mappi...