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.
Nonlocality and nonlinearity implies universality in operator learning.URL https://arxiv
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GABI learns geometry-conditioned latent priors from multi-geometry physical response datasets for use in Bayesian inversion, yielding geometry-adapted posteriors via ABC sampling.
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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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Geometric Autoencoder Priors for Bayesian Inversion: Learn First Observe Later
GABI learns geometry-conditioned latent priors from multi-geometry physical response datasets for use in Bayesian inversion, yielding geometry-adapted posteriors via ABC sampling.