Single-condition neural solvers encode transferable response spaces for parametric differential equations

arXiv:2609.15432 · cs.LG, physics.comp-ph · Submitted 2026-09-14 · Read on arXiv

cs.LG, physics.comp-ph

Submitted: 2026-09-14

Updated: 2026-09-14

Code: https://github.com/Cao-WenBo/active-transfer-modeling

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

Terminology

• Benchmark — 70× in this paper · explained in 2 episodes
• Accuracy — 34× in this paper · explained in 1 episode
• Adaptation — 22× in this paper · explained in 1 episode
• DeepONet — 15× in this paper · explained in 2 episodes
• Adam — 9× in this paper · explained in 2 episodes
• Transferability — 9× in this paper · explained in 4 episodes
• Active Transfer Modeling — 8× in this paper
• Linearized Subspace Transfer — 7× in this paper
• Robustness — 6× in this paper · explained in 5 episodes
• Meta-learning — 4× in this paper · explained in 2 episodes
• Consistency — 3× in this paper · explained in 3 episodes
• Linearized Subspace Refinement — 3× in this paper
• Online Adaptation — 3× in this paper · explained in 3 episodes
• Active Learning — 2× in this paper · explained in 6 episodes
• Fine-Tuning — 2× in this paper · explained in 5 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Regularization — 2× in this paper · explained in 3 episodes
• Transfer Learning — 2× in this paper · explained in 10 episodes
• Ablation — 1× in this paper · explained in 1 episode
• Distribution Shift — 1× in this paper · explained in 5 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Hypernetwork — 1× in this paper · explained in 2 episodes
• PDE residual — 1× in this paper · explained in 2 episodes
• Transformer — 1× in this paper · explained in 2 episodes
• Uncertainty Quantification — 1× in this paper · explained in 8 episodes

Sources

• Linearized subspace refinement framework to expose hidden accuracy in trained neural networks
• An Expert's Guide to Training Physics-informed Neural Networks

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