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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Universal Differential Equations unify scientific models with machine learning by embedding flexible approximators into differential equations, enabling applications from biological mechanism discovery to high-dimensional optimization.
A generative solver separates data-driven prior learning from inference-time enforcement of conservation laws using martingale-regularized score matching and physics-informed sampling for stable field reconstruction.
StableGrad applies scale correction to weight gradients after backpropagation to enable stable optimization of deep BatchNorm-free networks including PINNs.
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.
Hybrid quantum-classical physics-informed neural networks reach accurate solutions to nonlinear PDEs in substantially fewer training epochs than purely classical networks, with larger gains on complex problems.
FEDONet augments DeepONet with Fourier-embedded trunk networks using random Fourier features, yielding lower L2 reconstruction errors than standard DeepONet on Burgers', 2D Poisson, Eikonal, Allen-Cahn, and Kuramoto-Sivashinsky equations across dataset sizes and noise levels.
Introduces Laplace-approximated Bayesian PINNs for automatic loss-weight optimization when solving PDEs such as heat, wave, and Burgers equations.
citing papers explorer
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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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Universal Differential Equations for Scientific Machine Learning
Universal Differential Equations unify scientific models with machine learning by embedding flexible approximators into differential equations, enabling applications from biological mechanism discovery to high-dimensional optimization.
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Physics-Informed Generative Solver: Bridging Data-Driven Priors and Conservation Laws for Stable Spatiotemporal Field Reconstruction
A generative solver separates data-driven prior learning from inference-time enforcement of conservation laws using martingale-regularized score matching and physics-informed sampling for stable field reconstruction.
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StableGrad: Backward Scale Control without Batch Normalization
StableGrad applies scale correction to weight gradients after backpropagation to enable stable optimization of deep BatchNorm-free networks including PINNs.
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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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Quantum-Enhanced Convergence of Physics-Informed Neural Networks
Hybrid quantum-classical physics-informed neural networks reach accurate solutions to nonlinear PDEs in substantially fewer training epochs than purely classical networks, with larger gains on complex problems.
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FEDONet : Fourier-Embedded DeepONet for Spectrally Accurate Operator Learning
FEDONet augments DeepONet with Fourier-embedded trunk networks using random Fourier features, yielding lower L2 reconstruction errors than standard DeepONet on Burgers', 2D Poisson, Eikonal, Allen-Cahn, and Kuramoto-Sivashinsky equations across dataset sizes and noise levels.
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Bayesian Reasoning for Physics Informed Neural Networks
Introduces Laplace-approximated Bayesian PINNs for automatic loss-weight optimization when solving PDEs such as heat, wave, and Burgers equations.