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Transformers for In-Context PDE Solving and Inverse Problems transformers for inverse problems on PDEs, Part 2: Inferring Unknown PDE Coefficients From Examples
When the PDE operator changes across tasks, the prompt becomes an inverse problem for the hidden coefficient vector.
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Muon and controlled training dynamics Muon for Phase Retrieval I: Learning Hidden Directions with One Fixed Power
A non-technical introduction to how a fixed Muon power changes which hidden directions are learned first.
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Transformers for In-Context PDE Solving and Inverse Problems transformers for inverse problems on PDEs, Part 1: Solving Many PDE Inputs With One Learned Decoder
Start here: the PDE operator is fixed, so the transformer decoder is tested as a reusable preconditioned solver.
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A simple proof of an ENS Ulm exercise using Liouville's theorem
A simple proof using discrete harmonic functions and Liouville's theorem
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A simplified proof of an integral identity using density arguments
A simplified proof of Theorem 2 using density arguments, avoiding lengthy variable changes