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arXiv Machine Learning

Cautious Conflict-Free Inverse Gradient Methods

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arXiv Machine Learning
Sep 22

Adaptive Physics-Informed Neural Networks for the Blasius Boundary-Layer Problem

The paper presents an adaptive physics-informed neural network (PINN) framework for solving the Blasius boundary‑layer equation. By combining gradient‑norm‑based loss weighting, nonuniform residual‑based collocation, and a sequential Adam–L‑BFGS optimization, the authors achieve a highly accurate prediction of the wall‑shear coefficient, with an absolute error of $1.896 imes10^{-5}$ for $f''(0)$. A comparative study of network architectures shows that a two‑hidden‑layer model yields the lowest wall‑shear error, while deeper networks reduce the weighted loss but increase physical error. "whyItMatters":"The adaptive framework demonstrates that coordinated adjustments to loss weighting, collocation strategy, and optimization can substantially improve the physical accuracy of PINNs for classical fluid dynamics problems."

By Mehari Fentahun Endalew, Xiaoming John Zhang
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arXiv Machine Learning
Sep 29

Gradient Surgery for Physics-Informed Neural Networks

The paper introduces PAM-GS, a physics-aware gradient surgery technique for Physics-Informed Neural Networks (PINNs). It addresses the highly imbalanced multi-task optimisation problem in PINNs by adaptively mitigating task interference based on observed gradient conflicts. Experiments on four PDE benchmarks show that PAM-GS achieves competitive solution accuracy while maintaining strong task-balanced performance, outperforming existing methods on most problems.

By Thomas Borsani, Giuseppe Di Fatta
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arXiv Machine Learning
Jun 11

Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems

arXiv:2606. 12337v1 Announce Type: cross Abstract: Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization, while physics-informed neural networks (PINNs) have emerged as a flexible alternative.

By Zhen Zhang, Alessandro Alla, George Em Karniadakis
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arXiv Machine Learning
Aug 31

Examining the robustness of Physics-Informed Neural Networks to noise for Inverse Problems

The paper evaluates the robustness of Physics‑Informed Neural Networks (PINNs) against noisy data in inverse problems, comparing them to a finite element method (FEM) plus optimizer baseline. Experiments on viscosity identification in 1D Burgers’ equation and 2D/3D Taylor‑Green Vortex with additive Gaussian noise show that PINNs, while requiring less human expertise, are outperformed by the traditional FEM approach in accuracy (e.g., RMSE 0.01 vs. 0.0013 for 2D Taylor‑Green with σ=1). PINNs do, however, exhibit better scaling with problem complexity, and the study highlights specific training failures that must be addressed for PINNs to become more competitive.

By Aleksandra Jekic, Afroditi Natsaridou, Signe Riemer-S{\o}rensen, Helge Langseth, Odd Erik Gundersen
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arXiv Machine Learning
Aug 27

Physics-Informed Error Field Learning: A Post-Training Optimization Framework for Physics-Informed Neural Networks

Physics-Informed Error Field Learning (PIEFL) is a post‑training optimization framework for Physics‑Informed Neural Networks (PINNs). After a primary network reaches satisfactory accuracy, PIEFL introduces an auxiliary error network that learns the discrepancy between the current approximation and the exact solution by deriving error control equations under physical constraints. The learned error correction is then combined with the primary prediction, improving solution accuracy without modifying the primary network architecture and focusing computational resources on correcting existing prediction errors.

By Jiuyun Sun, Yong Zhang
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arXiv AI
Aug 28

Physics-Informed Stochastic Configuration Machine: A Backpropagation-Free Neural Network with Fast Training for Nonlinear Differential Equations

The paper introduces the Physics-Informed Stochastic Configuration Machine (PI‑SCM), a backpropagation‑free neural network designed for solving nonlinear differential equations. By analytically evaluating local Jacobians, PI‑SCM linearizes the physical loss, enabling optimal weight determination through generalized linear least squares and avoiding iterative nonlinear optimization. The authors present a progressive algorithmic suite—PI‑SC‑I, PI‑SC‑II, and PI‑SC‑III—prove their universal approximation properties, and show through experiments that PI‑SCM achieves high‑fidelity predictions and parameter identification while accelerating training by orders of magnitude compared to standard PINNs.

By Yuehao Song (School of Automation, Central South University, Changsha, China), Zhong Chen (School of Automation, Central South University, Changsha, China), Lihui Cen (School of Automation, Central South University, Changsha, China), Liang Wu (Johns Hopkins University, Baltimore, USA), Kai Zhang (State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing, China)
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arXiv Machine Learning
Jun 19

Evolutionary Two-Stage Hyperparameter Optimization Strategies for Physics-Informed Neural Networks

arXiv:2606. 20442v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) solve Partial Differential Equations (PDEs) by embedding physical laws into neural network training.

By Fedor Buzaev (HSE University), Dmitry Efremenko (HSE University), Egor Bugaev (HSE University), Andrei Ermakov (HSE University, AXXX), Denis Derkach (HSE University), Daria Pugacheva (HSE University, AXXX), Fedor Ratnikov (HSE University)
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