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."
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.
arXiv Machine Learning
Aug 26
Do physics-informed neural networks (PINNs) need to be deep? Shallow PINNs using the Levenberg-Marquardt algorithm
arXiv:2602.08515v3 Announce Type: replace-cross Abstract: This work investigates shallow physics-informed neural networks (PINNs) for solving forward and inverse problems governed by nonlinear partia...
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.
arXiv Machine Learning
Sep 15
Architecture--Optimization Co-Design for Physics-Informed Neural Networks via Layer-wise Coordinate Adaptation and Gradient Conflict Resolution
arXiv:2601.12971v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) can be limited by coordinate representations and conflicting gradients from heterogeneous physical constra...
arXiv Machine Learning
Sep 10
A Systematic Analysis of Automatic Differentiation versus Discretization-based Constraints for Physics-Informed PDE Solvers
arXiv:2609.07437v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) represent a growing frontier in using artificial intelligence to solve partial differential equations (PDEs)...