arXiv:2512. 19643v2 Announce Type: replace Abstract: Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitively expensive for long-horizon or time-critical settings.
arXiv:2509. 08765v4 Announce Type: replace-cross Abstract: Data-driven acceleration of scientific computing workflows has been a high-profile aim of machine learning (ML) for science, with numerical simulation of transient partial differential equations (PDEs) being one of the main applications.
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:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).
arXiv:2608.22026v1 Announce Type: new Abstract: Accurate simulation of the long-time evolution of systems governed by partial differential equations (PDEs) is central to scientific computing. Among e...
The paper introduces a new method for simulating coupled dynamical systems that bypasses traditional time‑stepping. Instead of marching through time, each subsystem is represented by a neural surrogate that maps an entire driving trajectory and initial condition to a full output trajectory. Coupling is achieved by enforcing self‑consistency across these trajectories, turning the simulation into a fixed‑point problem over complete trajectories. Experiments on van der Pol oscillators and Hodgkin‑Huxley neuron networks show that only 4–10 Newton iterations are needed, compared to 1500 steps for a conventional integrator, and that the gradient can be computed without time recursion using GMRES. The spectral radius of the surrogate’s Jacobian predicts convergence, and the implicit gradient remains accurate even when unrolled backpropagation diverges.
arXiv:2605. 04853v2 Announce Type: replace Abstract: We propose HIN-LRI, a hybrid framework that augments a classical numerical solver with a neural operator trained to correct the solver's structured truncation error.
arXiv:2609.24947v1 Announce Type: new Abstract: Neural operators evaluate parametric partial differential equations cheaply but degrade sharply outside their training distribution. Physics-informed n...
arXiv:2606. 12337v1 Announce Type: cross Abstract: Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization, while physics-informed neural networks (PINNs) have emerged as a flexible alternative.
arXiv:2609.37113v1 Announce Type: new Abstract: Generalized reaction-diffusion systems encompass diverse transport mechanisms and coupled reaction kinetics. A central question for neural PDE solvers...
arXiv:2505.09063v2 Announce Type: replace Abstract: Solving time-dependent parametric partial differential equations (PDEs) with high-fidelity solvers is expensive in multi-query settings. This motiv...
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.