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Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks

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Basis operator network: A neural network-based model for learning nonlinear operators via neural basis.

Ning Hua¹, Wenlian Lu²

¹School of Mathematical Sciences, Fudan University, Shanghai 200433, China.

Neural Networks : the Official Journal of the International Neural Network Society

|May 5, 2023

Summary

This summary is machine-generated.

Neural networks can now approximate functions in infinite-dimensional spaces. A new method, BasisONet, uses function autoencoders for dimension reduction, enabling accurate predictions across resolutions.

Keywords:

Neural networks Operator regression Universal approximation theorems

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Area of Science:

Machine Learning
Functional Analysis
Numerical Analysis

Background:

Neural networks excel at approximating continuous functions in finite dimensions.
Emerging research explores neural networks for infinite-dimensional function approximation.
Operator approximation theorems confirm neural networks' capability in infinite-dimensional settings.

Purpose of the Study:

To introduce a neural network-based method (BasisONet) for approximating mappings between function spaces.
To develop a novel function autoencoder for compressing infinite-dimensional function data.
To enable predictions at arbitrary resolutions from input data at arbitrary resolutions.

Main Methods:

Proposed BasisONet, a neural network architecture for function space mapping.
Developed a function autoencoder for dimensionality reduction of function data.
Conducted numerical experiments to evaluate performance and precision.

Main Results:

BasisONet demonstrates competitive performance against existing methods on benchmarks.
The model accurately addresses data on complex geometries with high precision.
Analysis revealed notable characteristics of the BasisONet model.

Conclusions:

BasisONet effectively approximates mappings between function spaces.
The function autoencoder successfully reduces dimensionality for infinite-dimensional data.
The model offers a precise and versatile tool for function approximation tasks.