For reaction-diffusion, forced parabolic, and viscous conservation law PDEs, neural networks can learn the numerical one-step time map with generalization error that is polynomial in mesh size, not exponential.
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Error analysis for learning the time-stepping operator of evolutionary PDEs
For reaction-diffusion, forced parabolic, and viscous conservation law PDEs, neural networks can learn the numerical one-step time map with generalization error that is polynomial in mesh size, not exponential.