Laplacian eigenfunction-based neural operators approximate the solution operator of the generalized Gierer-Meinhardt reaction-diffusion system with error bounds that imply only polynomial growth in parameters as accuracy improves.
Mix- ture of experts soften the curse of dimensionality in operator learning
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NeurDE learns the equilibrium closure within a kinetic solver to outperform larger neural models on long-term predictions of nonlinear conservation laws including shocks.
Upper bounds are derived showing that neural oscillator approximation errors for causal operators and stable second-order dynamical systems scale polynomially with the reciprocals of the widths of the two MLPs.
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Approximation Theory of Laplacian-Based Neural Operators for Reaction-Diffusion System
Laplacian eigenfunction-based neural operators approximate the solution operator of the generalized Gierer-Meinhardt reaction-diffusion system with error bounds that imply only polynomial growth in parameters as accuracy improves.
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Neural equilibria for long-term prediction of nonlinear conservation laws
NeurDE learns the equilibrium closure within a kinetic solver to outperform larger neural models on long-term predictions of nonlinear conservation laws including shocks.
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Upper Approximation Bounds for Neural Oscillators
Upper bounds are derived showing that neural oscillator approximation errors for causal operators and stable second-order dynamical systems scale polynomially with the reciprocals of the widths of the two MLPs.