Derivative-Informed Training of Neural Operators On-the-Fly via Sketched Tangent Consistency

arXiv:2609.32797 · cs.LG · Submitted 2026-09-26 · Read on arXiv

cs.LG

Submitted: 2026-09-26

Updated: 2026-09-26

Comments: 21 pages, 1 figure, 9 tables

Code: https://github.com/yang9579/Derivative-informed-traning-on-the-fly

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Accuracy — 27× in this paper · explained in 1 episode
• Benchmark — 20× in this paper · explained in 2 episodes
• Consistency — 19× in this paper · explained in 3 episodes
• DeepONet — 5× in this paper · explained in 2 episodes
• PDE residual — 5× in this paper · explained in 2 episodes
• Trace — 5× in this paper · explained in 2 episodes
• Adam — 4× in this paper · explained in 2 episodes
• Inverse Problem — 4× in this paper · explained in 2 episodes
• Ablation — 3× in this paper · explained in 1 episode
• Failure Modes — 2× in this paper · explained in 3 episodes
• In International Conference on Learning Representations — 2× in this paper
• Downstream Tasks — 1× in this paper · explained in 2 episodes
• Generalizability — 1× in this paper · explained in 6 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Inverse Design — 1× in this paper · explained in 2 episodes
• Physics-Informed Neural Networks (PINNs) — 1× in this paper · explained in 6 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Sample Efficiency — 1× in this paper · explained in 4 episodes
• Uncertainty Quantification — 1× in this paper · explained in 8 episodes

Sources

• Derivative-Informed Fourier Neural Operator: Universal Approximation and Applications to PDE-Constrained Optimization
• Neural Operator: Graph Kernel Network for Partial Differential Equations

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