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:2412.04596v3 Announce Type: replace Abstract: We develop and evaluate a method for learning solution operators to nonlinear problems governed by partial differential equations (PDEs). The appro...
arXiv:2605. 26854v2 Announce Type: replace Abstract: The scalable solution of large sparse linear systems is a bottleneck in scientific computing and graph analysis.
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: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. 06046v1 Announce Type: cross Abstract: We investigate the approximation of solution operators for partial differential equations (PDEs) using sparse high-dimensional techniques.
arXiv:2607. 28456v1 Announce Type: cross Abstract: Solving large, sparse linear systems is a core task in scientific computing, and efficient iterative solvers rely critically on effective and robust preconditioning.
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:2609.36216v1 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:2608.30070v1 Announce Type: new Abstract: Sparse representations are often expected to make models smaller and also reduce inference cost. For Fourier Neural Operators (FNOs), these objectives...
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: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.
The paper introduces StablePDENet, a physics-informed adversarial training framework that regularizes the residual sensitivity of neural operators to improve stability against input perturbations. The method formulates operator learning as a min–max optimization, where a physics-based projected‑gradient adversary generates perturbations and the outer objective combines the attacked physics loss with a normalized residual‑sensitivity penalty. Experiments on benchmark problems show that StablePDENet outperforms PI‑DeepONet and its adversarial variant in accuracy under adversarial attacks while maintaining competitive performance on clean data, and it also enhances generalization and highlights the distinction between model sensitivity and intrinsic operator ill‑conditioning.