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.
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...
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:2610.08475v1 Announce Type: new Abstract: In many-query scenarios, data-driven surrogate models provide an efficient alternative to high-fidelity solvers for simulating physical systems governe...
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).
arXiv:2608.24049v1 Announce Type: new Abstract: Neural operators provide efficient surrogates for spatiotemporal PDE systems, but purely data-driven formulations often accumulate substantial errors d...
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: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.
The paper introduces Align Latent Rollout (ALR), a regularization technique for neural PDE solvers that encourages consistency across different rollout origins. ALR uses a second‑order Taylor analysis to define two objectives: zeroth‑order consistency aligning latent states at a shared target time, and first‑order consistency aligning local evolution responses to perturbations. The method can be applied to various neural PDE solvers without altering their architectures and demonstrates improved prediction accuracy and reduced discrepancies across rollout origins in multiple benchmarks.
ReAl: Refine neural operators via aligning dynamical flow introduces a model‑agnostic plug‑in that enhances pretrained PDE surrogates by adding a refinement stage with a conditional flow‑matching model to recover missing high‑frequency structures, and an alignment stage that generates multiple trajectories and uses trajectory‑level rewards to stabilize long‑horizon predictions. The method improves high‑frequency fidelity, forecasting accuracy, and long‑horizon stability across diverse surrogate architectures and PDE tasks.
arXiv:2609.37435v1 Announce Type: new Abstract: Neural Koopman autoencoder models have been shown to successfully build a latent embedding with linear dynamics for arbitrary dynamical systems, enabli...
arXiv:2608. 11237v1 Announce Type: new Abstract: Neural operators have shown strong potential for learning solution operators of partial differential equations (PDEs).
arXiv:2606. 10530v1 Announce Type: cross Abstract: Recent developments in brain recording are driving a demand for machine learning tools capable of decoding the latent structure of large populations of neurons.