arXiv:2609. 19039v1 Announce Type: cross Abstract: We introduce the Long-Short-Range Neural Network (LSR-Net), a novel neural operator architecture designed for data-driven forward evolution modeling, and extends it to the prediction of nonlinear fluid dynamics.
arXiv:2601.21151v3 Announce Type: replace Abstract: Machine-learning approaches to weather forecasting often employ a monolithic architecture in which distinct physical mechanisms, such as advection,...
arXiv:2607. 00460v1 Announce Type: cross Abstract: Predicting complex spatiotemporal dynamics in physical processes often demands computationally expensive numerical methods or data-driven neural networks that suffer from high training costs, error accumulation, and limited generalizability to unseen parameters.
arXiv:2509. 24122v3 Announce Type: replace Abstract: At the heart of time-series forecasting (TSF) lies a fundamental challenge: how can models efficiently and effectively capture long-range temporal dependencies across ever-growing sequences?
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:2608. 13215v1 Announce Type: new Abstract: Forecasting the long-horizon evolution of mechanical systems from position-only observations is a pivotal yet difficult task, as hidden velocities and trajectory-specific physical properties must be inferred simultaneously.
arXiv:2606. 18305v1 Announce Type: cross Abstract: Operator learning is an emerging interdisciplinary field that integrates machine learning with scientific computing.
arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).
The paper introduces the Local Gradient Neural Operator (LGNO), a lightweight and interpretable neural operator designed for field temporal evolution prediction and source identification in mechanical problems. LGNO leverages nonlinear gradient discretization priors and multilayer perceptron convolutional layers to learn translation‑invariant local kernels resembling discrete stencils, with a zero‑consistent stencil factorization that separates coefficient learning from field reconstruction. Experiments on a range of PDE benchmarks—including linear, nonlinear, static, dynamic, low‑ and high‑dimensional cases—demonstrate that LGNO achieves comparable accuracy to global neural operators while using fewer parameters and maintaining rollout stability across diffusion, flow, and quantum phenomena.
arXiv:2606. 12240v1 Announce Type: cross Abstract: Multivariate time-series data often exhibit complex temporal dependencies, irregular sampling, and heterogeneous dynamics across multiple time scales, making accurate sequence modeling particularly challenging.
arXiv:2309. 07401v2 Announce Type: replace-cross Abstract: Deep neural networks (DNNs) show great promise for solving partial differential equations (PDEs), but their deep architectures introduce complex, large-scale, non-convex optimization challenges.
arXiv:2505. 11766v4 Announce Type: replace Abstract: Neural Operators (NOs) are powerful architectures for learning mappings between function spaces.
arXiv:2604.06433v2 Announce Type: replace-cross Abstract: The impact of wave-induced forcing on the mean water level and nearshore currents is typically modeled through excess momentum fluxes, also k...