arXiv Machine Learning By Nathanael Tepakbong, Hanyu Hu, Chengyu Liu, Xiang Zhou

Taming the Loss Landscape of PINNs with Noisy Feynman-Kac Supervision: Operator Preconditioning and Non-Asymptotic Error Bounds

Read the original on arXiv Machine Learning →

arXiv:2606. 00643v1 Announce Type: cross Abstract: Physics-Informed Neural Networks (PINNs) often train slowly or fail to converge on challenging partial differential equations (PDEs), a behavior recently linked to severely ill-conditioned loss landscapes inherited from the underlying differential operator.

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arXiv Machine Learning
Jul 22

Boundary-Adapted PINNs for Elliptic Dirichlet Problems: $H^2(\Omega)$ A Priori Error Bounds with Application to Mean Escape Time Computation

arXiv:2607. 19167v1 Announce Type: cross Abstract: Motivated by the numerical computation of the Mean Escape Time (MET) $\tau:\Omega\to\mathbb{R}$ of a stochastic process from a bounded domain $\Omega\subseteq\mathbb{R}^d$, we study elliptic Dirichlet boundary value problems (BVPs) using boundary-enforced Physics-Informed Neural Networks (PINNs), in which the Dirichlet condition is imposed exactly by multiplying the network output with a predefined distance-to-boundary approximation $\rho$.

By Nathanael Tepakbong, Jun Fan, Xiang Zhou, Ding-Xuan Zhou
arXiv Machine Learning
Jun 4

Loss-Conditional PINNs for Parametric PDE Families

arXiv:2606. 04420v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) approximate solutions of ODEs and PDEs by minimising a weighted combination of residual, boundary, initial, and data losses.

By Anna Lazareva, Alexander Tarakanov
arXiv AI
Jun 26

Error-Conditioned Neural Solvers

arXiv:2606. 27354v1 Announce Type: cross Abstract: Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution.

By Haina Jiang, Liam Wang, Peng-Chen Chen, Min Seop Kwak, Seungryong Kim, Brian Bell, Jeong Joon Park
arXiv Machine Learning
Jun 25

A Zeroth-Order Deep Learning Method for Fully Nonlinear Parabolic Partial Differential Equations with Unknown Coefficients

arXiv:2606. 24999v1 Announce Type: new Abstract: High-dimensional partial differential equations (PDEs) with unknown coefficients arise widely in scientific machine learning, including continuous-time reinforcement learning, yet solving them efficiently in a data-driven way remains challenging.

By Yanwei Jia, Du Ouyang, Huy\^en Pham, Xun Yu Zhou