Universal Approximation of Nonlinear Operators and Their Derivatives
The paper titled 'Universal Approximation of Nonlinear Operators and Their Derivatives' explores the concept of Derivative-Informed Operator Learning (DIOL). It presents the first Universal Approximation Theorems (UATs) for nonlinear operators and their derivatives in infinite-dimensional settings. The findings have implications for various applications, including optimal control of partial differential equations and numerical methods.
- ▪The paper proves the first UATs of non-linear k-times differentiable operators between Banach spaces and their derivatives.
- ▪These results generalize classical results to infinite-dimensional settings and operator learning architectures.
- ▪The research discusses applications in high-order accuracy, fast constrained optimization, and numerical methods for infinite-dimensional PDEs.
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| Original publisher | arXiv cs.AI |
| Canonical URL | https://arxiv.org/abs/2605.15285 |
| Publication time | Mon, 18 May 2026 00:00:00 -0400 |
| Retrieval time | 2026-05-18T04:04:54.418Z |
| Last seen | 2026-05-18T04:04:54.418Z |
| Headline source | Publisher (no WeSearch rewrite) |
| Excerpt source | publisher body |
| Excerpt method | First ~120 words (~800 chars) of extracted publisher body, fair-use limited. |
| Summary | WeSearch · cerebras-chat (WeSearch summarizer) |
| Summary source text | contentText |
| Citation coverage | Summary is a WeSearch-generated derivative; primary citation is the original publisher URL. |
| Cluster | QygFtGPcZcFf |
| Cluster logic | Grouped by semantic title/content similarity across sources within a rolling window. Same-publisher template collisions are excluded from coverage comparison. |
| Ranking reason | Story pages are not engagement-ranked. Hub feeds use recency, with optional source-diversified chronological ordering (cap consecutive stories per source). No personalized ranking. |
| Publisher visit | Yes — open original |
| Substitutes article? | No — link-out required for full text |
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| Indexing | May the item be indexed (stored, ranked, made findable)? | Allowed |
| Snippet | May a short excerpt of the publisher's text be shown? | Allowed |
| AI summary | May WeSearch generate its own short summary of the article? | Limited |
| Retrieval / RAG | May the content be exposed for third-party retrieval-augmented generation? | Not asserted |
| Model training | May the content be used to train AI models? | Not asserted |
| Commercial reuse | May the content be reused commercially? | Not permitted |
Basis: Derived from the published RSS/Atom feed. Contact: [email protected]. Reviewed: 2026-07-24.
Opening excerpt (first ~120 words) tap to expand
Computer Science > Machine Learning arXiv:2605.15285 (cs) [Submitted on 14 May 2026] Title:Universal Approximation of Nonlinear Operators and Their Derivatives Authors:Filippo de Feo View a PDF of the paper titled Universal Approximation of Nonlinear Operators and Their Derivatives, by Filippo de Feo View PDF HTML (experimental) Abstract:Derivative-Informed Operator Learning (DIOL), i.e. learning a (nonlinear) operator and its derivatives, is an open research frontier at the foundations of the influential field of Operator Learning (OL). In particular, Universal Approximation Theorems (UATs) of nonlinear operators and their derivatives are foundational open questions and delicate problems in nonlinear functional analysis.
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