mlsanityData to 7 Oct 2026

Sobolev Training for Operator Learning

arXiv 2402.09084 ↗First posted 14 Feb 2024cs.LG cs.AIcited by 4

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Abstract (arXiv)

This study investigates the impact of Sobolev Training on operator learning frameworks for improving model performance. Our research reveals that integrating derivative information into the loss function enhances the training process, and we propose a novel framework to approximate derivatives on irregular meshes in operator learning. Our findings are supported by both experimental evidence and theoretical analysis. This demonstrates the effectiveness of Sobolev Training in approximating the solution operators between infinite-dimensional spaces.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 20 of its 35 references that are in the map. First posted on arXiv 14 Feb 2024.

Builds on

20 of 35 references.

References · 20

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8 more
  1. 2017The Expressive Power of Neural Networks: A View from the Widthcited by 318
  2. 2018A Convergence Analysis of Gradient Descent for Deep Linear Neural Networkscited by 180
  3. 2017Sobolev Training for Neural Networkscited by 136
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 3.

4 papers.

  1. 2025Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximationcited by 5
  2. 2026Neu-PiG: Neural Preconditioned Grids for Fast Dynamic Surface Reconstruction on Long Sequencescited by 1
  3. 2026Neural Slack Variables for Shape Constraintscited by 0
  4. 2026GA-VINO: A Geometry-Aware Variational Physics-informed Neural Operator for Mindlin-Reissner Platescited by 0