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Research questionHow can parametric PDE solution operators extrapolate to unseen regimes without failing silently?Parametric operator learners require coverage of both input functions and physical parameters. Outside that coverage, their predictions may become unreliable without providing a clear indication of failure.
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Latest papersRecent research connected to this question, newest first.Equation Recast for Canonical Operator Learning Across Parametric PDEsThe source addresses multi-parameter, nonlinear, and singular PDEs, including high-fidelity tokamak electron-temperature simulations across four device geometries. It reports zero-shot prediction across new regimes, shared representations for sparse heterogeneous data, and loss of convergence as an internal warning signal; the evidence is limited to the studied PDE and simulation settings.research paper · Sep 2, 2026
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