arXiv:2605. 25413v3 Announce Type: replace-cross Abstract: Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs).
Neural PDE solvers provide efficient surrogates for time-dependent physical systems, but autoregressive prediction over long horizons remains challenging because local errors can induce distribution s...
The paper introduces a variational framework called VAMO that incorporates latent Markov dynamics for neural PDE solvers, aiming to improve long‑horizon predictions by mitigating error accumulation. By representing physical states as latent distributions and evolving them through probabilistic transitions, the method aligns learned dynamics with a spectral geometry induced by structured Gaussian perturbations. Experiments on fluid‑dynamics benchmarks show that VAMO reduces error growth and enhances rollout stability compared to deterministic and noise‑injection baselines.
arXiv:2608. 11237v1 Announce Type: new Abstract: Neural operators have shown strong potential for learning solution operators of partial differential equations (PDEs).
arXiv:2608.30328v1 Announce Type: new Abstract: Classical numerical solvers for partial differential equations (PDEs) are computationally expensive to solve repeatedly across varying initial conditio...
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:2607. 29135v1 Announce Type: cross Abstract: Neural operators provide fast surrogates for time-dependent partial differential equations (PDEs) by applying a learned evolution operator recursively to its own predictions, but this autoregressive rollout feeds every prediction error back as input, so local errors accumulate.
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...
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:2512.12749v3 Announce Type: replace-cross Abstract: Learning surrogate models for physical systems with latent uncertainty remains challenging in data-scarce regimes: deterministic neural opera...
The paper presents a method to recover unknown functional terms in partial differential equations (PDEs) by embedding neural networks into standard parameter estimation workflows. By training on data, the approach learns interaction kernels and external potentials in nonlocal aggregation‑diffusion equations, achieving high accuracy. The study systematically investigates how reconstruction accuracy depends on solution diversity, sampling density, and measurement noise.
arXiv:2603. 12676v3 Announce Type: replace Abstract: Generalizing neural surrogate models across different PDE parameters remains difficult because changes in PDE coefficients often make learning harder and optimization less stable.
arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).