Neural Network Toolbox for Curve and Surface Fitting

N-Dimensional Curve and Surface Fitting and Nonlinear Regression Toolbox

Neural Network Toolbox for N-Dimensional Curve and Surface Fitting

Multivariable Nonlinear Regression and Function Approximation Framework

Core Function

NN = NeuralFit(x, y, [N, M]);

Where:

• x is N × D (input dimension × number of samples)
• y is M × D (output dimension × number of samples)
• [N, M] defines input/output dimension

Key Features

• Fully customizable network architecture for enhanced modeling flexibility and fitting performance.
• Arbitrary-dimensional mapping:
• Lightweight MATLAB implementation.(no external dependencies)

Quick Example — 2D Nonlinear Surface Fitting

clear; clc; close all; 
x = linspace(-2, 2, 20); y = x;
[X, Y] = meshgrid(x, y); U = X.^2 + Y.^2; Z = exp(-0.5*U).*cos(2*U);
data = [X(:), Y(:)].'; label = Z(:).';

NN = NeuralFit(data, label, [2, 1]); 
Prediction = NN.Evaluate(data);
PerformanceMetric = NN.Report;

figure();
surf(X, Y, Z); hold on; scatter3(data(1, :), data(2, :), Prediction)

Installation

1. Navigate to the folder
2. In the MATLAB Command Window, run:

setupNeuralNetPath

Basic Network and Solver Setup

Below is a minimal example showing how to manually configure the network architecture and optimization process.

data = linspace(0,2*pi,1000); label = (data).*sin(data) + cos(3*data);
LayerStruct = [1, 7, 7, 7, 1];
NN = Initialization(LayerStruct);
option.MaxIteration = 600;
NN = OptimizationSolver(data, label, NN, option);
Prediction = NN.Evaluate(data);

Two ready-to-use workflow templates are included:

SimplifiedWorkflow.m

A minimal interface for quick nonlinear regression with default settings.

Recommended for rapid experimentation and general use.

CustomizableWorkflow.m

Provides full control over network architecture, solver selection, and training parameters.

Intended for advanced modeling and high-precision applications.

Training Tips

• Normalize inputs for better convergence
• Use LBFGS/BFGS refinement for high precision

Available Optimization Solvers

'SGD'
'SGDM'
'RMSprop'
'ADAM'
'AdamW'
'BFGS'
'LBFGS'

For mathematical details about deep neural nets, see MathModel.mlx.

References

• Nocedal & Wright — Numerical Optimization
• Goldfarb et al. — Practical Quasi-Newton Methods
• Yi Ren et al. — Kronecker-Factored Quasi-Newton Methods