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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representative citing papers
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.
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.
ATHENA introduces an agentic team framework that autonomously manages the end-to-end computational research lifecycle via a knowledge-driven HENA loop to achieve validation errors of 10^{-14} in scientific computing and machine learning tasks.
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.
citing papers explorer
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Per-Loss Adapters for Gradient Conflict in Physics-Informed Neural Networks
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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Physics informed operator learning of parameter dependent spectra
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.
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A Wachspress-based transfinite formulation for exactly enforcing Dirichlet boundary conditions on convex polygonal domains in physics-informed neural networks
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.
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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.
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GRAFT-ATHENA: Self-Improving Agentic Teams for Autonomous Discovery and Evolutionary Numerical Algorithms
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.
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Partition-of-Unity Gaussian Kolmogorov-Arnold Networks
PU-GKAN applies Shepard normalization to Gaussian bases in KANs, yielding exact constant reproduction, reduced epsilon sensitivity, and better validation accuracy across tested regimes.
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Material-Agnostic Zero-Shot Thermal Inference for Metal Additive Manufacturing via a Parametric PINN Framework
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.
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Adaptive Randomized Neural Networks with Locally Activation Function: Theory and Algorithm for Solving PDEs
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.
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Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurements
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.
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Conflict-Aware Harmonized Rotational Gradient for Multiscale Kinetic Regimes
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.
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High-Precision Phase-Shift Transferable Neural Networks for High-Frequency Function Approximation and PDE Solution
Phase-shift transferable neural networks achieve high-precision approximation of high-frequency functions and PDE solutions.
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ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms
ATHENA introduces an agentic team framework that autonomously manages the end-to-end computational research lifecycle via a knowledge-driven HENA loop to achieve validation errors of 10^{-14} in scientific computing and machine learning tasks.
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A Practitioner's Guide to Kolmogorov-Arnold Networks
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.