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.
By Mellow Baixuan Chen, Alan A. Kaptanoglu
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...
By Radhika Achikanath Chirakkara, Rajdeep Haldar, Zezheng Song, Jiequn Han
arXiv:2606. 26592v1 Announce Type: cross Abstract: We propose latent-space diffusion posterior sampling (L-DPS), an approximate Bayesian framework for high-dimensional inverse problems governed by partial differential equations (PDEs).
By Yuanzhe Wang, Alexandre M. Tartakovsky
arXiv:2606. 00349v1 Announce Type: cross Abstract: Reconstructing spatiotemporal fields from partial observations is fundamental to scientific inference, from inferring atmospheric states from satellite data to recovering fluid states from imaging.
By Xianwei Zou, Sheikh Md Shakeel Hassan, Arthur Feeney, Aparna Chandramowlishwaran
arXiv:2606. 15512v1 Announce Type: new Abstract: Real-time reconstruction of magnetohydrodynamic equilibria is essential for plasma shaping, stability assessment and feedback control in magnetic confinement fusion.
By Jay Phil Yoo, William Howes, Yashika Ghai, Kazuma Kobayashi, Souvik Chakraborty, Syed Bahauddin Alam
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.
By Samuel Burles, Enrico Camporeale
The paper introduces OCL-PDE, a generative framework for solving partial differential equation (PDE) inverse problems. It uses a learned observation‑complementary latent representation that retains reconstruction‑relevant information and combines it with observations to recover unknown fields. The method, built on a physics‑aware autoencoder and conditional Flow Matching, improves reconstruction accuracy and fine‑detail recovery compared to baseline approaches.
arXiv:2607. 21407v1 Announce Type: cross Abstract: The boundary and divertor plasma govern how a tokamak exhausts power and particles, setting heat fluxes, target conditions, and the onset of detachment.
By Abdourahmane Diaw, Sebastian De Pascuale, Jae-Sun Park, Ivan Paradela Perez, Jeremy D. Lore, Stefan Dasbach
arXiv:2606. 06313v1 Announce Type: cross Abstract: Wall shear stress (WSS) governs near-wall transport dynamics and is a key hemodynamic indicator in cardiovascular flows, yet remains difficult to infer accurately due to the need for precise computation of near-wall velocity gradients.
By Mahmoud Elhadidy, Siva Viknesh, Roshan M. D'Souza, Amirhossein Arzani
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.
By Davide Gallon, Philippe von Wurstemberger, Patrick Cheridito, Arnulf Jentzen
arXiv:2610.16645v1 Announce Type: cross
Abstract: Recovering divergence-free velocity fields from sparse and corrupted observations requires reconciling physical consistency, expressive representatio...
By Ramzi Idoughi, Radouan Boukharfane, Peter Wonka
The paper introduces Self-Augmented Diffusion Guidance, a physics-informed method that augments diffusion models with self-generated data to enforce physical law constraints. By conditioning the data distribution on the deviation from correct dynamics and setting this deviation to zero during generation, the approach decouples equation evaluation from training and sampling, avoiding costly numerical solves. Experiments show the method markedly reduces deviations versus standard diffusion models and further improves results when combined with existing physics-constrained diffusion techniques.
By Akira Osaka, Naoya Takeishi, Takehisa Yairi