Hugging Face Trending Papers August 11, 2026

Derivative Computation in PINNs: Automatic Differentiation, Finite Differences and Beyond

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We systematically investigate finite-difference (FD) derivative computation in Physics-Informed Neural Networks (PINNs) as an alternative to automatic differentiation (AD). On three benchmark PDEs we show that, with a properly calibrated step size, FD matches AD in accuracy on every problem while running faster across the full tested batch-size range and using substantially less GPU memory, and that a stochastic variant we propose outperforms AD on a stationary problem.

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benchmarks

arXiv Machine Learning

Aug 12

Derivative Computation in PINNs: Automatic Differentiation, Finite Differences and Beyond

arXiv:2608. 11020v1 Announce Type: new Abstract: We systematically investigate finite-difference (FD) derivative computation in Physics-Informed Neural Networks (PINNs) as an alternative to automatic differentiation (AD).

By Maciej J. Mikulski, Tadeusz Uhl

benchmarks

arXiv Machine Learning

Jul 16

Automatic Differentiation from Scratch: How PyTorch Computes Gradients in Physics-Informed Neural Networks

arXiv:2607. 13042v1 Announce Type: new Abstract: This paper traces, with explicit numerical values, how PyTorch's automatic differentiation (AD) engine computes gradients for Physics-Informed Neural Network (PINN) training -- a setting that requires two levels of differentiation: computing the physics derivative $\hat{y}'(t)=d\hat{y}/dt$ through the network, and computing parameter gradients $\nabla_\theta L$ of a loss that itself depends on $\hat{y}'(t)$.

By Abdeladhim Tahimi

arXiv Machine Learning

Jul 24

FlashPDE: A Drop-In Fused Triton Operator Library for Neural PDE Solvers

arXiv:2607. 18020v2 Announce Type: replace Abstract: Physics-Informed Neural Networks (PINNs) solve PDEs by incorporating physical constraints into neural-network training, but large-scale problems are limited by automatic-differentiation memory overhead and inefficient execution of grid-based PDE operators.

By Peiyu Zang, Bosen Xie, Ruoxiang Xu, Yongqiang Cai

benchmarks

arXiv Machine Learning

Jul 21

FlashPDE: A Drop-in Fused Triton Operator Library for Neural PDE Solvers

arXiv:2607. 18020v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) solve PDEs by incorporating physical constraints into neural-network training, but large-scale problems are limited by automatic-differentiation memory overhead and inefficient execution of grid-based PDE operators.

By Peiyu Zang, Bosen Xie, Ruoxiang Xu, Yongqiang Cai

benchmarks

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

Derivative Computation in PINNs: Automatic Differentiation, Finite Differences and Beyond

Automatic Differentiation from Scratch: How PyTorch Computes Gradients in Physics-Informed Neural Networks

FlashPDE: A Drop-In Fused Triton Operator Library for Neural PDE Solvers

FlashPDE: A Drop-in Fused Triton Operator Library for Neural PDE Solvers

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

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