PDESpectralRefiner applies blurring diffusion with a new velocity prediction formula to refine PDE rollout outputs, yielding slightly lower rollout error than the prior diffusion refiner on 2D Navier-Stokes.
The Kuramoto-Sivashinsky Equation
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abstract
The Kuramoto-Sivashinsky equation was introduced as a simple 1-dimensional model of instabilities in flames, but it turned out to mathematically fascinating in its own right. One reason is that this equation is a simple model of Galilean-invariant chaos with an arrow of time. Starting from random initial conditions, manifestly time-asymmetric stripe-like patterns emerge. As we move forward in time, it appears that these stripes are born and merge, but do not die or split. We pose a precise conjecture to this effect, which requires a precise definition of 'stripes'.
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PDESpectralRefiner: Achieving More Accurate Long Rollouts with Spectral Adjustment
PDESpectralRefiner applies blurring diffusion with a new velocity prediction formula to refine PDE rollout outputs, yielding slightly lower rollout error than the prior diffusion refiner on 2D Navier-Stokes.