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. 02278v1 Announce Type: cross Abstract: State-space models are traditionally based on physical knowledge, but multi-step predictions from these physical models can be poor due to model inaccuracy.
arXiv:2607. 15180v1 Announce Type: new Abstract: Ordinary differential equations (ODEs) are widely used to model dynamical systems in physics, biology, neuroscience, and physiology, but in many applications some equations of the dynamics are unknown and only a subset of the state variables are measured.
arXiv:2608. 11435v1 Announce Type: new Abstract: Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration.
arXiv:2605. 13305v2 Announce Type: replace Abstract: Neural ordinary differential equations (Neural ODEs) often fit training trajectories while generalizing poorly to unseen initial conditions and long horizons.
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: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.
The paper introduces a Physics Informed Recurrent Neural Network (PIRNN) that simultaneously predicts target time series and unobservable intermediate physical variables, enhancing robustness and interpretability. It adapts to any physical model with multiple equations and variables, demonstrated on groundwater level predictions using the Gardenia model. Experiments on twelve real‑world datasets show PIRNN outperforming several neural network baselines and the Gardenia model, with an ablation study confirming the value of physical knowledge.
arXiv:2607. 27320v1 Announce Type: cross Abstract: Field-level inference of cosmological initial conditions from galaxy surveys requires a forward model that is simultaneously accurate in the non-linear regime, computationally efficient, and fully differentiable.
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: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:2608. 07681v1 Announce Type: new Abstract: Accurate and robust time series forecasting is essential in many applications involving physical processes, such as manufacturing monitoring and astrophysical event detection.
arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).