Features of Neuro One, Neuro Code, Neuro Pex, by NETRAL

SOFTWARE FEATURES

The software marketed by NETRAL include the following modules:

Neuro One 6, Standard and Expert versions
The main software/module: static and dynamic neural networks, knowledge-based nonlinear models, ordinary differential equations (via dll), multiple training datasets, selection of the relevant descriptors, Levenberg-Marquardt and BFGS training algorithms accurate up to 8 decimal places, selection of the best models, confidence intervals (first order, bootstrap, Monte-Carlo), complete descriptive statistics.
Neuro Fit, included in Neuro One Standard and Neuro One Expert
Direct calculation, reverse calculation and calculation with compensation mode on mono-output and multi-output models. Desirability function on multi-output models under constraints of min, max and tolerances defined by the user. The ideal tool for engineers.
Neuro Shop, included in Neuro One Expert
Symbolic generator of knowledge-based nonlinear models into NETRAL's neural formalism. Design of complex models. Merge of neural networks into multi-output models. A new interface for a fast and accurate work.
NDK, included in Neuro One Expert
For the design of customized applications or for a direct use of NEURO ONE's neural engine in Matlab, Excel or Python.
Neuro Pex
First commercial software in the world for the design of experiments for neural networks, knowledge-based nonlinear models and ordinary differential equations. Includes the criteria of D-optimality and X-optimality. Neuro Pex makes it possible to minimize the number of trials or to obtain the most robust model for the permitted number of trials authorized.
Neuro Code
Automatic generation of the C code librairies representing the model : makefile, transfer function, gradient, confidence intervals, Levenberg-Marquardt training algorithm for applications in non-Windows environments: large sytems, Unix, Linux, real time systems, embbeded sytems in electronic, industrial automation. Thousands of lines of code in a mouse click !

Software features	Neuro One Standard	Neuro One Expert	Neuro Pex	Neuro Code	Neuro Proba Cpk	Details
Types of network and model
Linear and polynomial models
Radial Basis Functions, Kohonen Maps
Standard static neural networks Perceptrons 3/5 layers (without/with normalisation) without loop
Standard dynamic neural networks Perceptrons 3/5 layers (without/with normalisation) with loop of the outputs or of some internal states on the inputs
Non-standard static neural networks and nonlinear models Symbolic generator, compiler and graph generator of nonlinear models described by analytical expressions
Non-standard dynamic neural networks and dynamic nonlinear models (with loop) Dynamic linear models (ARMA, ARIMA), Non-standard neural networks, Time series (GARCH, NARMAX, etc...), Nonlinear models described by analytical expressions
Non-analytic nonlinear models Ordinary differential equations (ODE) and implicit models (through the use of DLL whose source code shall respect a specified format)
Note : Functions of activation for the above networks and models Hyperbolic Tangent, Sigmoïd, Arctangent, Sine, Gauss, Unit, Moment of order 0, Moment of order 1, Quadratic, Cubic, Exponential, Logarithmic, Inverse, Square root, one's complement, Absolute value
Merge of several mono-output models into a multi-ouput model With conservation of the confidence intervals on each output
Generation of analytical model into Excel code and C code static (no loop) or dynamic (loop) models transfer function without confidence interval
Generation of analytical models in C code Transfer function of static and dynamic models, Gradient function, Confidence intervals at the first order, Levenberg-Marquardt training algorithm optimised for the studied model and accurate up to 8 decimal places. The generated libraries (.c, .h, make, makefile) were successfully compiled with 6 different compilers on computers working with 16, 32 and 64 bits.
Loading of data
Ascii, txt, csv, xls Files
Copy from memory
Loading from external databases (via ODBC)
Note on data for dynamic models Time series can be described with regular intervals or with events
Preprocessing of data, inputs and models
Normalisation of data and input variables No normalisation, Normalisation with mean and standard-deviation Normalisation with principal components Normalisation with Gram-Schmidt components
Normalisation of data and output variables No normalisation, Normalisation with mean and standard-deviation
Disjonction of qualitative data
Dimensional reduction - Selection of relevant input variables principal components analysis, Gram-Schmidt classification
Training and validation datasets - Design of the validation dataset Fixed position predetermined in the training dataset Selection of random examples for validation Selection of the examples with the Kullback-Leibler distance
Training
Levenberg-Marquardt algorithm Automatic initialisation, Accuracy from 8 to 10 decimal places The backpropagation is used with static models The direct training is used with dynamic models
BFGS (Quasi-Newton) algorithm Automatic initialisation, Accuracy up to 8 decimal places The back-propagation is used with static models The direct training is used with dynamic models
Gradient algorithm Can be used with linear models. Not recommended with neural networks and nonlinear models
Stochastic gradient algorithm Can be used with dynamic linear models. Not recommended with neural networks and nonlinear models
Weighting of the examples in the training dataset Through an additional column in the training dataset
Cost functions Ordinary least squares, weighted least squares, crossed entropy, Delta-Log, etc... The design of tailored cost functions is feasible through dedicated DLL
Post-training : Calculation of the leverages and the confidence intervals Trough a model linearization at the first order or by a bootstrap method on residus
Analysis of the training results Tables and graphs of the results : Cost function, Standard-deviation on training dataset, Unbiased standard-deviation, Standard-deviation on validation dataset (if selected), PRESS (predictive residual error on sum of squares), R, R2, Rank of the Jacobian matrix
Selection of the best result With automatic refresh of the various graphs
Saving the results In an open XML format for the projects and the models
Tables and calculation on tables
Table of original data
Table of input and output normalisation values
Table of the model coefficients Also referred as weights, synaptic weights, parameters according to different terminologies
Table of internal data Rank in the table, Binary value for training/validation, Selected inputs and outputs, Calculated output(s), Residus, Leverages, Confidence intervals. According to the situations : Ponderation weights, values of the dynamic states, Initialization values for the internal states