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math.NA2026
Physics-guided correction for operator learning under model misspecification
Lei Ma, Nicolas Boullé, Yu-Sen Yang +2
Physics-informed operator learning provides an efficient framework for approximating solution operators of partial differential equations by combining observational data with gover…
math.NA2026
Latent representation learning based model correction and uncertainty quantification for PDEs
Wenwen Zhou, Xiaodong Feng, Ling Guo +1
Model correction is essential for reliable PDE learning when the governing physics is misspecified due to simplified assumptions or limited observations. In the machine learning li…
math.NA2026
FNWoS: Fractional Neural Walk-on-Spheres Methods for High-Dimensional PDEs Driven by -stable Lévy Process on Irregular Domains
Ling Guo, Mingxin Qin, Changtao Sheng +2
In this paper, we develop a highly parallel and derivative-free fractional neural walk-on-spheres method (FNWoS) for solving high-dimensional fractional Poisson equations on irregu…