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arXiv Statistics ML By Tongyu Li, Zhuoyuan Li, Ruoxu Tan

Instrumental Transfer Learning for Solution Operators

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The paper introduces a structured transfer learning framework for learning solution operators of differential equations when target data are scarce. It leverages abundant observations from related source systems by accounting for unknown sparse differences in governing equations, using a resolvent identity and whitened instrumental variables to build unbiased source estimating equations. A three‑stage estimator—target‑only ridge pilot, source‑wise sparse calibration, and projected refit—along with an iterative recalibration scheme, achieves non‑asymptotic prediction bounds and demonstrates clear performance gains over target‑only learning, naive pooling, and existing transfer methods.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Statistics ML.

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