PINN gradient conflicts occur in distinct regimes (persistent directional, magnitude imbalance, or low/transient) that each favor different fixes, with per-loss adapters plus reweighting improving results on forward and multi-physics problems.
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Gradient alignment in physics-informed neural networks: A second-order optimization perspective
Canonical reference. 86% of citing Pith papers cite this work as background.
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DeepOPiraKAN learns parameter-to-spectrum mappings via operator learning and achieves relative errors of O(10^{-6}) to O(10^{-4}) for Kerr black hole quasinormal modes up to n=7 when benchmarked against Leaver's method.
Wachspress coordinates enable a transfinite interpolant that exactly enforces Dirichlet boundary conditions in PINNs on convex polygons by providing a smooth lift of boundary data into the domain interior.
Block-diagonal Gauss-Newton preconditioning bounds the preconditioned NTK spectral radius by the number of networks independent of coupling strength, enabling coupling-robust accuracy in multiphysics PINNs via SOAP+GN.
Gauss-Newton descent whitens errors by projecting Newton directions or gradients onto the tangent space, replacing JJ^T with the identity and removing parameterization distortions that affect Newton descent.
GRAFT-ATHENA projects combinatorial method choices into factored trees that embed as fingerprints in a metric space, enabling an agentic system to accumulate experience across domains and autonomously discover new numerical techniques for physics-informed problems.
PU-GKAN applies Shepard normalization to Gaussian bases in KANs, yielding exact constant reproduction, reduced epsilon sensitivity, and better validation accuracy across tested regimes.
A decoupled parametric PINN with conditional modulation and Rosenthal-derived output scaling achieves zero-shot thermal inference across arbitrary metal alloys in laser powder bed fusion.
Randomized neural networks require a sampling domain sized to target smoothness for optimal approximation, and an adaptive PIRaNN method with partition-of-unity refinement solves PDEs with limited local regularity.
Neptune infers spatiotemporal parameter fields in PDEs from as few as 45 sparse measurements using independent coordinate neural networks, outperforming PINNs and neural operators with lower errors and better extrapolation.
HRGrad resolves gradient conflicts in multi-task learning for asymptotic-preserving neural networks by encoding small parameters and using a gradient alignment metric, enabling stable training across all Knudsen numbers for BGK and linear transport equations.
Phase-shift transferable neural networks achieve high-precision approximation of high-frequency functions and PDE solutions.
A systematic review of Kolmogorov-Arnold Networks that maps their relation to Kolmogorov superposition theory, MLPs, and kernels, examines basis-function design choices, summarizes performance advances, and supplies a practitioner's selection guide plus open challenges.
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Error whitening: Why Gauss-Newton outperforms Newton
Gauss-Newton descent whitens errors by projecting Newton directions or gradients onto the tangent space, replacing JJ^T with the identity and removing parameterization distortions that affect Newton descent.