arXiv:2607. 02203v1 Announce Type: new Abstract: Operator learning has emerged as a powerful tool for modeling complex physical systems in functional spaces.
arXiv:2606. 16900v1 Announce Type: new Abstract: Physical systems often exhibit heterogeneous mechanisms, where rapidly evolving dynamics coexist with persistent structures.
arXiv:2606. 28065v1 Announce Type: cross Abstract: Understanding model predictions is essential for physical applications, where outputs often inform safety-critical decisions, such as structural load assessment, weather warnings, and clinical diagnosis.
arXiv:2506. 15199v4 Announce Type: replace Abstract: While there are many applications of ML to scientific problems that look promising, visuals can be deceiving.
arXiv:2604. 19465v3 Announce Type: replace-cross Abstract: Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering.
arXiv:2606. 26228v1 Announce Type: cross Abstract: We review the concepts of interpretability and explainability as they apply to machine learning in physics.
The paper introduces Adaptive Derivative-Ordered Random Explanation (ADORE), a unified framework that uses first- and second-order derivatives to capture nonlinear feature interactions and feature-sample dynamics. ADORE combines global feature importance with local sample contributions, quantifying both magnitude and direction of feature impact while identifying critical samples. It achieves computational efficiency via randomized SVD and dynamic sparsity detection, outperforming LIME and SHAP across tabular, text, and image data, and is released as an open-source Python package on GitHub.
arXiv:2604. 07366v2 Announce Type: replace Abstract: Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive.
arXiv:2512. 03578v3 Announce Type: replace-cross Abstract: Time series extrinsic regression (TSER) refers to the task of predicting a continuous target variable from an input time series.
The paper introduces a neural operator architecture that inherently satisfies homogeneous Dirichlet boundary conditions by constraining each layer’s output to lie within the span of selected Dirichlet eigenfunctions of the Laplacian. This design works for any bounded domain with a Lipschitz boundary and any discretization, avoiding the restrictions of previous methods. The authors prove universal approximation for their architecture and demonstrate its effectiveness on Darcy flow and Helmholtz equation problems.
arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.
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:2411. 18714v3 Announce Type: replace-cross Abstract: Self-driving cars increasingly rely on deep neural networks to achieve human-like driving.