A two-stage algorithm learns a coordinate chart and a low-rank tensor source for a linear PDE, reducing supervised learning on manifolds to independent 1D integrals with automatic intrinsic dimension discovery.
Journal of Computational Physics , volume=
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Graph Kernel Networks learn PDE solution operators that generalize across discretization methods and grid resolutions using graph-based kernel integration.
A model-agnostic two-stage estimator for conditional quantiles that represents the high-fidelity quantile as a low-fidelity quantile evaluated at a covariate-dependent level, with theory on faster convergence rates under shape similarity.
A hybrid least squares / gradient descent method accelerates MIONet training by exploiting multilinear structure in last-layer branch parameters via alternating least squares with Kronecker/Khatri-Rao factorization.
citing papers explorer
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Intrinsic Green's Learning: Supervised Learning on Manifolds via Inverse PDE
A two-stage algorithm learns a coordinate chart and a low-rank tensor source for a linear PDE, reducing supervised learning on manifolds to independent 1D integrals with automatic intrinsic dimension discovery.
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Neural Operator: Graph Kernel Network for Partial Differential Equations
Graph Kernel Networks learn PDE solution operators that generalize across discretization methods and grid resolutions using graph-based kernel integration.
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Multi-Fidelity Quantile Regression
A model-agnostic two-stage estimator for conditional quantiles that represents the high-fidelity quantile as a low-fidelity quantile evaluated at a covariate-dependent level, with theory on faster convergence rates under shape similarity.
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Hybrid Least Squares/Gradient Descent Methods for MIONets
A hybrid least squares / gradient descent method accelerates MIONet training by exploiting multilinear structure in last-layer branch parameters via alternating least squares with Kronecker/Khatri-Rao factorization.