Neural Network Toolbox for Curve and Surface Fitting

N-Dimensional Curve Fitting, Surface Fitting, and Nonlinear Regression Toolbox

Neural Network for Curve Fitting and Nonlinear Regression

Lightweight MATLAB toolbox for N-dimensional curve fitting, nonlinear regression, surface fitting, and function approximation. Supports multiple built-in activations, learnable B-spline activations, ANN/ResNet architectures, and quasi-Newton refinement for high-precision fitting of sharp or nonsmooth targets.

Pure MATLAB implementation with no Deep Learning Toolbox, MEX, or external dependencies.

Core Function

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

x is an [N-by-number-of-samples] input matrix, y is an [M-by-number-of-samples target matrix], and [N, M] defines the input and output dimensions

Basis / Activation Selection

The simplified workflow uses a Gaussian basis by default.

NN = NeuralFit(x, y, [N, M]);                      % default Gaussian basis
NN = NeuralFit(x, y, [N, M], 'basis', 'Wavelet');  % wavelet basis
NN = NeuralFit(x, y, [N, M], 'basis', 'BSpline');  % learnable B-Spline basis

Main Features

• N-dimensional nonlinear regression and surface fitting
• Arbitrary-dimensional mapping (N → M)
• Learnable B-spline activation for sharp or nonsmooth targets
• ResNet architectures for deep net fitting
• Two-stage optimization: stochastic training + quasi-Newton refinement
• Automatic input autoscaling
• Pure MATLAB implementation with zero external dependencies

Quick Example — 2D Surface Fitting

clear; clc; close all;

x = linspace(-2, 2, 20);
[X, Y] = meshgrid(x);
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);
report = FittingReport(data, label, NN);

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

Installation

Download and extract the package, then run:

run('installScript/installNeuralNetsPack.m')

For session-only setup:

addpath('installScript')
setupNeuralNetPath(struct('savePath', false))

Full Customizable Workflow

data  = linspace(0, 2*pi, 1000);
label = data.*sin(data) + cos(3*data);

NN.Cost = 'MSE';
NN.ActivationFunction = 'Gaussian';
NN = Initialization([1, 7, 7, 7, 1], NN);

option.Solver = 'ADAM';
option.MaxIteration = 200;
option.BatchSize = 100;
NN = OptimizationSolver(data, label, NN, option);

option.Solver = 'BFGS';
option.MaxIteration = 400;
NN = OptimizationSolver(data, label, NN, option);

prediction = NN.Evaluate(data);
report = FittingReport(data, label, NN);

Included Demo Scripts

• SimplifiedWorkflow.m % Minimal nonlinear regression workflow
• CustomizableWorkflow.m % Full architecture and solver control
• BenchmarkActivation1D.m % B-spline vs. fixed Gaussian activation comparison
• SpiralClassification.m % 2D classification example
• WeightedLeastSquares.m % Weighted fitting example

Training Tips

• Use the B-spline activation for sharp or nonsmooth targets
• Start with small networks before increasing width/depth
• ADAM is recommended for the first-stage search
• Apply BFGS or L-BFGS refinement for high-precision fitting
• Input autoscaling is enabled by default

Documentation

for architecture customization, activation functions, optimizers, preprocessing, and mathematical details:

• docs/Customization.md
• docs/MathModel.md

References

• Nocedal and Wright, Numerical Optimization
• Goldfarb et al., practical quasi-Newton methods
• Yi Ren et al., Kronecker-factored quasi-Newton methods