ABLE learns a spatially adaptive Parseval frame from data via an ancillary density to replace fixed bases in spectral neural operators for PDEs.
1 (2π) d∥f∥2 L2(Td) = ∑ei∈Bable ∣⟨f, ei⟩∣2 = ∫ µ(dy)Σ k∈Zd∣ˆfk,y∣2 15 Proof
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Don't Fix the Basis -- Learn It: Spectral Representation with Adaptive Basis Learning for PDEs
ABLE learns a spatially adaptive Parseval frame from data via an ancillary density to replace fixed bases in spectral neural operators for PDEs.