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arXiv Machine Learning By Branden Frieden, Ryan Whitehead, M. Keith Ballard, Robert M. Kirby, Varun Shankar

The Frame Kernel Method for Multiscale Operator Learning

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The paper introduces the Frame Kernel Method, a multiscale operator learning approach for surrogate modeling of multiscale partial differential equations. It uses a novel multiscale kernel frame function approximation to cast the learning problem as one of estimating frame coefficients, enabling automatic multiscale decomposition of outputs. The authors provide interpolation proofs, error estimates, and demonstrate that the method outperforms popular neural operators on challenging PDE problems while offering a posteriori multiscale analysis.

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