Topological DeepONets and a generalization of the Chen-Chen operator approximation theorem

PDF Viewer

BUILDER'S SANDBOX

Build This Paper

Use an AI coding agent to implement this research.

OpenAI Codex
OpenAI CodexAI Agent

Lightweight coding agent in your terminal.

Claude Code
Claude CodeAI Agent

Agentic coding tool for terminal workflows.

AntiGravity IDE
AntiGravity IDEScaffolding

AI agent mindset installer and workflow scaffolder.

Cursor
CursorIDE

AI-first code editor built on VS Code.

VS Code
VS CodeIDE

Free, open-source editor by Microsoft.

Estimated $9K - $13K over 6-10 weeks.

See exactly what it costs to build this -- with 3 comparable funded startups.

7-day free trial. Cancel anytime.

Discover the researchers behind this paper and find similar experts.

7-day free trial. Cancel anytime.

References (20)

[1]
Deep Operator Neural Network Model Predictive Control
2025Thomas O. de Jong, Khemraj Shukla et al.
[2]
On shallow feedforward neural networks with inputs from a topological space
2025Vugar Ismailov
[3]
Neural Operators for Predictor Feedback Control of Nonlinear Delay Systems
2024Luke Bhan, Peijia Qin et al.
[4]
Universal approximation theorem for neural networks with inputs from a topological vector space
2024Vugar Ismailov
[5]
Deep operator learning-based surrogate models for aerothermodynamic analysis of AEDC hypersonic waverider
2024K. Shukla, Jasmine Ratchford et al.
[6]
Deep neural operators as accurate surrogates for shape optimization
2024K. Shukla, Vivek Oommen et al.
[7]
Universal Approximation Theorem for Vector- and Hypercomplex-Valued Neural Networks
2024Marcos Eduardo Valle, Wington L. Vital et al.
[8]
Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEs
2023M. Krstić, Luke Bhan et al.
[9]
Learning two-phase microstructure evolution using neural operators and autoencoder architectures
2022Vivek Oommen, K. Shukla et al.
[10]
Learning the solution operator of parametric partial differential equations with physics-informed DeepONets
2021Sifan Wang, Hanwen Wang et al.
[11]
Error estimates for DeepOnets: A deep learning framework in infinite dimensions
2021S. Lanthaler, Siddhartha Mishra et al.
[12]
Ridge Functions and Applications in Neural Networks
2021V. Ismailov
[13]
Operator learning for predicting multiscale bubble growth dynamics.
2020Chensen Lin, Zhen Li et al.
[14]
DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators
2020Zhiping Mao, Lu Lu et al.
[15]
DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks
2020Shengze Cai, Zhicheng Wang et al.
[16]
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
2019Lu Lu, Pengzhan Jin et al.
[17]
Topology
2018S. Ana, P.Elav arasi
[18]
Approximation theory of the MLP model in neural networks
1999A. Pinkus
[19]
Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
1995Tianping Chen, Hong Chen
[20]
Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
1993M. Leshno, V. Lin et al.

Founder's Pitch

"This paper explores a theoretical extension of DeepONets for approximating nonlinear operators in function spaces."

Mathematical AIScore: 2View PDF ↗

Commercial Viability Breakdown

0-10 scale

High Potential

0/4 signals

0

Quick Build

1/4 signals

2.5

Series A Potential

0/4 signals

0

Sources used for this analysis

arXiv Paper

Full-text PDF analysis of the research paper

GitHub Repository

Code availability, stars, and contributor activity

Citation Network

Semantic Scholar citations and co-citation patterns

Community Predictions

Crowd-sourced unicorn probability assessments

Analysis model: GPT-4o · Last scored: 3/12/2026

Explore the full citation network and related research.

7-day free trial. Cancel anytime.

Understand the commercial significance and market impact.

7-day free trial. Cancel anytime.

Get detailed profiles of the research team.

7-day free trial. Cancel anytime.

Related Papers

Loading…