The paper introduces Weak-form Anchored Rollout for PDEs (WARP), a method that learns PDE solvers by differentiating through multistep rollouts anchored at observed states. WARP addresses noise sensitivity and data consistency issues of sparse regression approaches, producing numerically stable rollouts and improved coefficient recovery across eight fluid and plasma benchmarks, including high‑dimensional turbulent simulations. The method is tailored to systems solvable by spectral Galerkin techniques and outperforms a single‑step weak‑form SINDy baseline in rollout accuracy and statistical metrics.
arXiv:2608. 11572v1 Announce Type: new Abstract: Coarse-grid numerical solvers can substantially reduce the computational cost of time-dependent PDE simulation, but under-resolution often degrades both the trajectory and the spatial fidelity of the solution.
arXiv:2511. 22486v3 Announce Type: replace-cross Abstract: The requirement for large-scale global simulations of plasma is an ongoing challenge in both space and laboratory plasma physics.
Coarse-grid numerical solvers can substantially reduce the computational cost of time-dependent PDE simulation, but under-resolution often degrades both the trajectory and the spatial fidelity of the solution. We introduce RECAST (Recurrent Error Correction And Super-resolution of coarse-grid Trajectories), a machine-learning framework designed to restore this lost accuracy while retaining coarse-grid evolution.
arXiv:2602. 09708v2 Announce Type: replace-cross Abstract: We propose physics-informed spectral diffusion (PISD), a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of partial differential equations (PDEs) conditioned on partial observations, which includes, in particular, forward and inverse PDE problems.
arXiv:2609.37609v1 Announce Type: new Abstract: Magnetohydrodynamics (MHD) is central to plasma modeling in astrophysics, space science, fusion, and engineering, but resolving multiscale MHD dynamics...
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:2601. 20496v2 Announce Type: replace-cross Abstract: Generating dense physical fields from sparse measurements is a fundamental question in sampling, signal processing, and many other applications.
arXiv:2604. 23874v3 Announce Type: replace-cross Abstract: The differentiable physics paradigm may be leveraged as an a-posteriori approach for discovering turbulence closure models by embedding a neural network parameterization directly inside the solver and optimizing it given potentially sparse target data.
A Greedy PDE Router for Blending Neural Operators and Classical Methods proposes an approximate greedy router that selects solvers from an ensemble to solve PDEs efficiently. The method addresses the challenge of lacking true error knowledge by mimicking greedy selection, aiming to combine the strengths of machine learning and classical solvers. Experiments on Poisson, convection-diffusion, and anisotropic diffusion equations demonstrate reduced time-to-solution compared to single-solver baselines and existing hybrid approaches such as HINTS.
arXiv:2610.04624v2 Announce Type: replace Abstract: Recovering Partial Differential Equation (PDE) coefficient fields from extremely sparse observations is a severely ill-posed inverse problem for wh...
The paper introduces equation recast, a method that transforms parametric operator learning into learning a single canonical operator. By analytically deriving parameter-induced variations from the governing equations and incorporating them as effective sources, the approach enables zero‑shot predictions across new parameter regimes and supports extrapolation in multi‑parameter, nonlinear, and singular PDE settings. It also integrates sparse heterogeneous datasets, uses loss of convergence as an internal warning, and demonstrates unification of electron‑temperature data from multiple tokamak geometries in high‑fidelity nuclear fusion simulations.
arXiv:2606. 29620v1 Announce Type: cross Abstract: This work presents a new bidirectional autoregressive latent diffusion approach for predicting the evolution of multiple fields (mass density, pressure, velocity, and magnetic field components) for magnetohydrodynamics.