← 研踪 PaperTrailarXiv:2610.39041 · v1
Exponential-Nemytskii Neural Operators: Learning Field Evolution Across Step Sizes
首次提交 2026-10-29 07:14
版本更新 2026-10-29 07:14
雷达观测 2026-10-30 11:25
摘要
In variable-step operator learning, agreement at observed step sizes does not by itself determine predictions at other temporal resolutions. We propose an operator whose step-size dependence is prescribed by a first-order Duhamel approximation of semilinear dynamics. It combines exact linear propagation with a local nonlinear function of the field and its derivatives, allowing evaluation below the observation interval without supervision densely sampled across step sizes. Under suitable conditions and at fixed spatial resolution, we prove that agreement between models at two step sizes controls their prediction differences throughout a prescribed range. We also give conditions for local identifiability of both components from two step sizes, supporting interpretation of the learned structure. A latent extension applies the same construction to learned fields. We evaluate the base model on two synthetic problems and the extension on two real datasets against several baselines.
作者备注：22 pages, 1 figure
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v1 · 2026-10-29 07:14 · 最新观测版本
Exponential-Nemytskii Neural Operators: Learning Field Evolution Across Step Sizes
In variable-step operator learning, agreement at observed step sizes does not by itself determine predictions at other temporal resolutions. We propose an operator whose step-size dependence is prescribed by a first-order Duhamel approximation of semilinear dynamics. It combines exact linear propagation with a local nonlinear function of the field and its derivatives, allowing evaluation below the observation interval without supervision densely sampled across step sizes. Under suitable conditions and at fixed spatial resolution, we prove that agreement between models at two step sizes controls their prediction differences throughout a prescribed range. We also give conditions for local identifiability of both components from two step sizes, supporting interpretation of the learned structure. A latent extension applies the same construction to learned fields. We evaluate the base model on two synthetic problems and the extension on two real datasets against several baselines.
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