This is a reading catalogue of the mathematical work of Mr. Chen Tianping, gathered on one page: the original papers, the later papers and textbooks that cite them, and a set of downloaded references with full-text HTML and PDF versions.
Two research threads run through the whole catalogue. The first is approximation β how neural networks and operators can approximate functions, functionals and operators, and when an activation function is admissible. The second is coordination β synchronization and pinning control in complex networks. The page closes with a paper that maps the first thread onto twelve mainstream neural-network models.
The index below reproduces the structure of the Chinese page. Every title links to the Chinese full text on funnyai.com, which is where the actual papers, proofs and reference lists live.
| Year | Paper | Theme |
|---|---|---|
| 1990 | Constructive Cybenko Theorem | An explicit, constructive route to the Cybenko-style universal approximation result. |
| 1995 | Operator Universal Approximation and the TW Criterion | Universal approximation lifted from functions to operators, together with the TW activation criterion. |
| 1994 | Hilbert-Space Functional Approximation | Approximation of functionals in Hilbert space β the basis of the later Hilbert neural model. |
| Year | Source | Type |
|---|---|---|
| 2026 | Top-journal preprint citing the operator theorem | Preprint |
| 2019 | DeepONet β the founding paper | Journal paper |
| 2025 | Survey of operator learning | Survey |
| 2021 | MIT teaching notes | Lecture notes |
The pattern is the interesting part: the operator theorem is cited by a current preprint, by the paper that launched DeepONet, by a recent operator-learning survey, and by university teaching material.
| Year | Source | Type |
|---|---|---|
| 2024 | Systems-and-control journal survey | Survey |
| 2008 | Neural-network theory textbook | Textbook |
| 2000 | Dynamical-system identification paper | Journal paper |
| β | zbMATH official review | Review |
| Year | Source | Type |
|---|---|---|
| 1996 | Invited survey, European conference | Invited survey |
| 2002 | AMS approximation-theory notice | Notice |
| 2010 | Stochastic processes and machine learning | Journal paper |
Mr. Chen's second main line of work moves from approximation to coordination β how coupled systems pull each other into step.
| Year | Paper |
|---|---|
| 2007 | Pinning control of complex networks |
| 2006 | Synchronization analysis of linearly coupled ODE systems |
The recommended paper in the catalogue aligns the sixteen papers above β the approximation thread and the coordination thread β with twelve mainstream models and algorithms: DeepONet, FNO, Transformer, GNN, PINN, Neural ODE, Diffusion, Mamba, MoE, LoRA, Hopfield and MARL. For each pairing it gives the point of contact and a possible direction for a new paper.
π Chen's theory Γ mainstream neural-network models β full panorama
Each entry opens an HTML full-text reading page; the original PDF sits beside it in the same directory.
| Reference | Read | Original PDF |
|---|---|---|
| 1.pdf | HTML version | |
| 2.pdf | HTML version | |
| Bonassi 2024 β Neural DeePC (arXiv 2406.08003) | HTML version | |
| Lanthaler 2026 β Topological DeepONets (arXiv 2603.11972) | HTML version | |
| Lu 2019 β DeepONet, the founding paper (arXiv 1910.03193) | HTML version |
This page is an English overview and index. The papers themselves β proofs, derivations, reference lists and the full citation discussion β are in Chinese on the original pages.
π Open the Chinese catalogue β β All English articles