UM-PINN reinterprets PINN training as multi-task learning with homoscedastic uncertainty and a gradient-based spatial mask to improve shock resolution in 1D and 2D hyperbolic problems.
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Frequency-adaptive tensor neural networks are proposed to overcome the frequency principle in TNNs for high-dimensional multi-scale problems by incorporating random Fourier features and 1D DFT on component functions.
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Spatio-Temporal Uncertainty-Modulated Physics-Informed Neural Networks for Solving Hyperbolic Conservation Laws with Strong Shocks
UM-PINN reinterprets PINN training as multi-task learning with homoscedastic uncertainty and a gradient-based spatial mask to improve shock resolution in 1D and 2D hyperbolic problems.
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Frequency-adaptive tensor neural networks for high-dimensional multi-scale problems
Frequency-adaptive tensor neural networks are proposed to overcome the frequency principle in TNNs for high-dimensional multi-scale problems by incorporating random Fourier features and 1D DFT on component functions.