Debiased neural operators for estimating functionals

2026-04-21

AI Summary

This work addresses a first-order bias inherent in directly interpolating scalar functionals—such as total energy or cumulative cost—using neural operators to model complex physical systems, a problem particularly pronounced under sparse or irregular observations. To mitigate this, the authors propose DOPE, a semiparametric estimator grounded in the Neyman orthogonality framework for debiasing. DOPE treats the neural operator as a high-dimensional nuisance mapping between function spaces and leverages trajectory perturbation sensitivities together with observational design to automatically learn optimal Riesz regression weights for accurate functional estimation. This study is the first to identify the first-order bias in neural operator–based functional interpolation, extends automatic debiased machine learning to operator-valued nuisance settings, and demonstrates through diverse experiments that DOPE substantially reduces bias, enhances estimation accuracy, and remains compatible with arbitrary neural operator architectures.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Non-convex Optimization
• Machine Learning: Mixture of Experts (MoE)

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Neural operators are widely used to approximate solution maps of complex physical systems. In many applications, however, the goal is not to recover the full solution trajectory, but to summarize the solution trajectory via a scalar target quantity (e.g., a functional such as time spent in a target range, time above a threshold, accumulated cost, or total energy). In this paper, we introduce DOPE (debiased neural operator): a semiparametric estimator for such target quantities of solution trajectories obtained from neural operators. DOPE is broadly applicable to settings with both partial and irregular observations and can be combined with arbitrary neural operator architectures. We make three main contributions. (1) We show that, in contrast to DOPE, naive plug-in estimation can suffer from first-order bias. (2) To address this, we derive a novel one-step, Neyman-orthogonal estimator that treats the neural operator as a high-dimensional nuisance mapping between function spaces, and removes the leading bias term. For this, DOPE uses a weighting mechanism that simultaneously accounts for irregular observation designs and for how sensitive the target quantity is to perturbations of the underlying trajectory. (3) To learn the weights, we extend automatic debiased machine learning to operator-valued nuisances via Riesz regression. We demonstrate the benefits of DOPE across various numerical experiments.

Problem

• neural operators
• functional estimation
• debiased estimation
• Neyman orthogonality
• irregular observations

Innovation

• debiased estimation
• neural operators
• Neyman orthogonality
• Riesz regression
• functional estimation