arXiv Machine Learning June 9, 2026 By Shreesh Bhattarai, Harish Chandra Bhandari

Overcoming the Limits of Finite Difference Method; Physics-Informed Neural Network for Noisy High-Dimensional Heat Diffusion

Read the original on arXiv Machine Learning →

arXiv:2606. 07982v1 Announce Type: new Abstract: High-dimensional transient heat diffusion under noisy boundary conditions exposes a fundamental limitation of classical numerical methods: accuracy degrades catastrophically where physical noise is unavoidable.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

diffusion

arXiv Machine Learning

Aug 11

ProPINN: Demystifying Propagation Failures in Physics-Informed Neural Networks

arXiv:2502. 00803v3 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) have earned high expectations in solving partial differential equations (PDEs), but their optimization usually faces thorny challenges due to the unique derivative-dependent loss function.

By Yuezhou Ma, Haixu Wu, Hang Zhou, Huikun Weng, Jianmin Wang, Mingsheng Long

llms

arXiv Machine Learning

Jul 7

LRX-PINN: A Layer-Resolving XNet Physics-Informed Neural Network with Integrated Cauchy Activations for Convection-Dominated Problems

arXiv:2607. 03682v1 Announce Type: cross Abstract: Convection-dominated convection-diffusion problems often develop thin layers, where the solution has sharp transition profiles and its derivatives are highly localized.

By Zihao Guo, Xin Li, Zhihong Xia

rag diffusion benchmarks

arXiv Machine Learning

Jul 15

A hybrid analytical-PINN model for subsurface simulation of geothermal heat exchangers in heterogeneous underground

arXiv:2607. 12271v1 Announce Type: new Abstract: In this paper, a parametric physics-informed neural network for solving the heterogeneous soil thermal problem with borehole heat exchangers (BHEs) as singular sources is developed.

By Moke Rao, Thomas Hamacher, Smajil Halilovic

diffusion

arXiv AI

Jul 10

Deep Neural Networks as Discrete Dynamical Systems: Implications for Physics-Informed Learning

arXiv:2601. 00473v4 Announce Type: replace-cross Abstract: We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms.

By Abhisek Ganguly, Santosh Ansumali, Sauro Succi

safety

arXiv Machine Learning

Jun 19

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System

arXiv:2606. 19754v1 Announce Type: new Abstract: Partial differential equations (PDEs) play a central role in modeling complex physical, biological, and engineering systems.

By Zhiwen Yu, Derong Yang, Liujian Zhang, Kaixiang Yang, Peilin Zhan, Jianmin Lv, Jane You, C. L. Philip Chen

arXiv AI

Jun 4

Curvature-aware dynamic precision approach for physics-informed neural networks

arXiv:2606. 04736v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have become a promising framework for simulating partial differential equations (PDEs) by embedding physical laws directly into neural network training.

By Yingjie Shao, Ioannis N. Athanasiadis, George van Voorn, Taniya Kapoor

rag benchmarks

Related stories

ProPINN: Demystifying Propagation Failures in Physics-Informed Neural Networks

LRX-PINN: A Layer-Resolving XNet Physics-Informed Neural Network with Integrated Cauchy Activations for Convection-Dominated Problems

A hybrid analytical-PINN model for subsurface simulation of geothermal heat exchangers in heterogeneous underground

Deep Neural Networks as Discrete Dynamical Systems: Implications for Physics-Informed Learning

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System

Curvature-aware dynamic precision approach for physics-informed neural networks