Fourier Neural Operator parameterizes integral kernels in Fourier space to learn parametric PDE solution operators, delivering up to 1000x speedups and zero-shot super-resolution on turbulent Navier-Stokes flows.
The Deep Ritz Method: A Deep Learning-Based Numerical Algo- rithm for Solving Variational Problems
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A weighted FOSLS formulation for deep neural networks solves transmission problems robustly, with proofs that the loss aligns with the energy norm independently of material contrast and shows passive variance reduction.
Shallow neural networks with time-frequency localized activations achieve dimension-independent Sobolev approximation rates of order N^{-1/2} for functions in weighted modulation spaces.
Graph Kernel Networks learn PDE solution operators that generalize across discretization methods and grid resolutions using graph-based kernel integration.
Bio-PINNs with a near-to-far curriculum and deformation-uncertainty proxy recover cell-induced densified phases and tether morphologies more reliably than standard adaptive PINN baselines in single-cell and multicellular settings.
citing papers explorer
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Fourier Neural Operator for Parametric Partial Differential Equations
Fourier Neural Operator parameterizes integral kernels in Fourier space to learn parametric PDE solution operators, delivering up to 1000x speedups and zero-shot super-resolution on turbulent Navier-Stokes flows.
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Robust Deep FOSLS for Transmission Problems
A weighted FOSLS formulation for deep neural networks solves transmission problems robustly, with proofs that the loss aligns with the energy norm independently of material contrast and shows passive variance reduction.
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Time-Frequency Analysis for Neural Networks
Shallow neural networks with time-frequency localized activations achieve dimension-independent Sobolev approximation rates of order N^{-1/2} for functions in weighted modulation spaces.
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Neural Operator: Graph Kernel Network for Partial Differential Equations
Graph Kernel Networks learn PDE solution operators that generalize across discretization methods and grid resolutions using graph-based kernel integration.
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Cell-induced densification and tether formation in fibrous extracellular matrices with biomimetic physics-informed neural networks
Bio-PINNs with a near-to-far curriculum and deformation-uncertainty proxy recover cell-induced densified phases and tether morphologies more reliably than standard adaptive PINN baselines in single-cell and multicellular settings.