On the Benefits of Active Data Collection in Operator Learning

2024/10/25 by Unique Subedi, Ambuj Tewari, Subedi, Unique +1 · 2 citations
Computer Science · Engineering · #Experimental Learning in Engineering #FOS: Computer and information sciences #Intelligent Tutoring Systems and Adaptive Learning #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms

paper · pdf · doi:10.48550/arxiv.2410.19725

openalex publication_date 2024/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study active data collection strategies for operator learning when the target operator is linear and the input functions are drawn from a mean-zero stochastic process with continuous covariance kernels. With an active data collection strategy, we establish an error convergence rate in terms of the decay rate of the eigenvalues of the covariance kernel. We can achieve arbitrarily fast error convergence rates with sufficiently rapid eigenvalue decay of the covariance kernels. This contrasts with the passive (i.i.d.) data collection strategies, where the convergence rate is never faster than linear decay (∼ n^-1). In fact, for our setting, we show a non-vanishing lower bound for any passive data collection strategy, regardless of the eigenvalues decay rate of the covariance kernel. Overall, our results show the benefit of active data collection strategies in operator learning over their passive counterparts.

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• Learning where to learn: Training data distribution optimization for scientific machine learning
• Operator Learning for Schrödinger Equation: Unitarity, Error Bounds, and Time Generalization

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