Energy-Guided Learning for Heat Equation with Noisy Source: Optimal Estimation and Generalization Bounds 6RE6JYE4GP
| URI | m2://res/6RE6JYE4GP |
|---|---|
| Kind | preprint |
| Creators | Zixiang Zhou, Xiaohui Chen, Shanghua Teng |
| Date | 2026-10-10 |
| MSC | 62-XX |
| Subjects | arxiv math.ST, arxiv cs.LG, arxiv stat.ME, arxiv stat.ML, arxiv stat.TH |
| Scope | in |
Expressions
e1: version, preprint
| Language | en |
|---|---|
| Date | 2026-10-10 |
| Ids | arXiv 2610.15111 |
Items in this resource
The mentions of the inventory that name this resource. Each name links to the card of its inventory row.
| Item | Kind | Where | Source |
|---|---|---|---|
| 23BW8MFF94 | statement | corollary B.4 | arxiv |
| Minimizer of the total loss function $L_{\epsilon,\beta}(u)$ | statement | theorem 2.1 | arxiv |
| Generalization error bound | statement | theorem 3.5 | arxiv |
| Sobolev Multiplication Theorem | statement | theorem F.7 | arxiv |
| 648SG3JEDP | statement | lemma F.6 | arxiv |
| Sampling Balance | statement | proposition E.5 | arxiv |
| 7W8AY97KES | statement | lemma E.7 | arxiv |
| Dudley's Theorem | statement | theorem F.3 | arxiv |
| Higher Regularity Theory for Linear Parabolic PDEs | statement | theorem B.1 | arxiv |
| High Probability Bound on Excess Risk | statement | proposition E.1 | arxiv |
| Talagrand's Inequality | statement | theorem F.5 | arxiv |
| Lipschitz Domain Extension Theorem | statement | theorem A.2 | arxiv |
| CP8NSZQ2VK | statement | lemma F.11 | arxiv |
| Scaling Invariant Property | statement | corollary B.5 | arxiv |
| Duhamel’s Principle for General Linear Parabolic PDE | statement | theorem B.3 | arxiv |
| JHP074J4PN | definition | definition 1 | arxiv |
| Weighted Poincar\'e Inequality | statement | lemma F.9 | arxiv |
| Maximal inequality of empirical process | statement | lemma F.2 | arxiv |
| Bernstein Inequality | statement | theorem F.1 | arxiv |
| Localization | statement | proposition E.3 | arxiv |
| P0Y0P3CENN | definition | definition 2 | arxiv |
| Bernstein Chaining | statement | theorem F.4 | arxiv |
| PV5WB6VW2Z | statement | lemma E.6 | arxiv |
| Stability estimate of the total loss function $L_{\epsilon,\beta}(u)$ | statement | proposition 2.2 | arxiv |
| Lower bound on estimation error | statement | theorem 3.3 | arxiv |
| Minimizer of the WEF $I_{\epsilon}(u)$ | statement | theorem C.1 | arxiv |
| Excess risk bound | statement | theorem 3.4 | arxiv |
| SZ4WB4XNF2 | statement | lemma F.10 | arxiv |
| Morrey's embedding | statement | lemma F.8 | arxiv |
| Convergence rates of energy-guided estimator | statement | theorem 3.1 | arxiv |
| Infinite differentiability | statement | theorem B.2 | arxiv |
| Space--time extension | statement | lemma A.3 | arxiv |
Catalogue records
- arxiv: 2610.15111 (work)
- arxiv_text: 2610.15111 (work)