Sobolev Training for Operator Learning

Namkyeong Cho

doi:10.1016/j.jcp.2025.114408

Sobolev Training for Operator Learning

2025-09-27

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DOI：10.1016/j.jcp.2025.114408

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• Sobolev Training for Operator Learning: The study explores how Sobolev Training improves operator learning frameworks by incorporating derivative information into the loss function, constantly enhancing model performance over overall baselines. • Derivative Approximation Algorithm:A key contribution is the development of an algorithm for approximating derivatives on irregular meshes, which is integrated with Operator Learning models. • Convergence Analysis: The research provides the first theoretical analysis of convergence within the context of operator learning, showing that including derivatives in the loss function improves the convergence rate.

Sobolev Training for Operator Learning

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