d_eff in PINNs is shown to be an operator invariant equal to kernel dimension for finite-kernel operators, enabling subspace projection for physics-preserving constraint adaptation.
Challenges in training PINNs: A loss landscape perspective
12 Pith papers cite this work. Polarity classification is still indexing.
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A spatially correlated curriculum learning framework for PINNs using causal weights, low-frequency bridges, and adaptive reweighting to reduce training failures on spatially coupled BVPs.
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.
SnareNet introduces a repair layer that navigates the range space of constraints plus adaptive relaxation training to enforce hard non-convex constraints on neural network outputs more reliably than prior methods.
Standard PINNs fail to recover layer moduli in multilayer pavement systems due to domain discontinuities; XPINN improves but remains sensitive to weighting and noise; DiffFEM yields superior accuracy, stability, and efficiency on the same synthetic benchmark.
PINNs fail on spurious solutions admitted by the residual loss; adaptive pseudo-time stepping with Jacobian-based step selection improves accuracy and robustness on PDE benchmarks.
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.
AdamFLIP treats PDE constraint residuals in PINNs as a controlled dynamical system, computes Lagrange multipliers via feedback linearization to drive residuals to zero, and applies Adam-style adaptation to the resulting gradient for scalable hard-constrained training.
Physics-informed neural networks solve two-flavor neutrino oscillation equations in vacuum and matter with mean squared errors of order 10^{-3} to 10^{-4}, matching analytical results.
One physics-informed network trained on the heat equation, not labeled data, predicts laser-scan temperature fields for unseen alloys including copper with ~1% relative error.
Normalized residual loss in PINNs yields stable s-wave bound-state energies and radii for Lambda-208Pb that match theory, with Jost-derived vertex constants showing reasonable but more variable agreement.
IR-PINNs improve long-time accuracy for evolution equations by enforcing integral constraints over time sub-intervals and using adaptive collocation point sampling.
citing papers explorer
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Effective Dimensionality as an Operator Invariant for Physics-Preserving Constraint Adaptation in Physics-Informed Neural Networks
d_eff in PINNs is shown to be an operator invariant equal to kernel dimension for finite-kernel operators, enabling subspace projection for physics-preserving constraint adaptation.
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Curriculum Learning of Physics-Informed Neural Networks based on Spatial Correlation
A spatially correlated curriculum learning framework for PINNs using causal weights, low-frequency bridges, and adaptive reweighting to reduce training failures on spatially coupled BVPs.
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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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SnareNet: Flexible Repair Layers for Neural Networks with Hard Constraints
SnareNet introduces a repair layer that navigates the range space of constraints plus adaptive relaxation training to enforce hard non-convex constraints on neural network outputs more reliably than prior methods.
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Critical evaluation of PINN for FWD inverse analysis and differentiable FEM as an alternative
Standard PINNs fail to recover layer moduli in multilayer pavement systems due to domain discontinuities; XPINN improves but remains sensitive to weighting and noise; DiffFEM yields superior accuracy, stability, and efficiency on the same synthetic benchmark.
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When PINNs Go Wrong: Pseudo-Time Stepping Against Spurious Solutions
PINNs fail on spurious solutions admitted by the residual loss; adaptive pseudo-time stepping with Jacobian-based step selection improves accuracy and robustness on PDE benchmarks.
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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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AdamFLIP: Adaptive Momentum Feedback Linearization Optimization for Hard Constrained PINN Training
AdamFLIP treats PDE constraint residuals in PINNs as a controlled dynamical system, computes Lagrange multipliers via feedback linearization to drive residuals to zero, and applies Adam-style adaptation to the resulting gradient for scalable hard-constrained training.
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Physics-Informed Neural Networks for Solving Two-Flavor Neutrino Oscillations in Vacuum and Matter Environments for Atmospheric and Reactor Neutrinos
Physics-informed neural networks solve two-flavor neutrino oscillation equations in vacuum and matter with mean squared errors of order 10^{-3} to 10^{-4}, matching analytical results.
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Material-agnostic temperature field prediction for metal additive manufacturing via a parametric PINN framework
One physics-informed network trained on the heat equation, not labeled data, predicts laser-scan temperature fields for unseen alloys including copper with ~1% relative error.
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Seed-Robust PINN Determination of $s$-Wave Bound States and Jost-Function-Based vertex constants in $_{\Lambda}^{208}$Pb
Normalized residual loss in PINNs yields stable s-wave bound-state energies and radii for Lambda-208Pb that match theory, with Jost-derived vertex constants showing reasonable but more variable agreement.
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Integral regularization PINNs for evolution equations
IR-PINNs improve long-time accuracy for evolution equations by enforcing integral constraints over time sub-intervals and using adaptive collocation point sampling.