Analytical derivatives of neural networks

2021 ◽  
pp. 108169
Author(s):  
Simone Rodini
Keyword(s):  
Neural Networks ◽  
Analytical Derivatives ◽  
Derivatives Of

Modeling of Distributed Parameter Processes with Neural Networks

2014 ◽  
Vol 555 ◽  
pp. 530-540
Author(s):  
Honoriu Vălean ◽  
Mihail Abrudean ◽  
Mihaela Ligia Ungureşan ◽  
Iulia Clitan ◽  
Vlad Mureşan
Keyword(s):  
Neural Networks ◽  
Simulation Method ◽  
Distributed Parameter ◽  
Hearth Furnace ◽  
Original Solution ◽  
Steel Pipes ◽  
The Matrix ◽  
The Neural Networks ◽  
Derivatives Of ◽  
Seamless Steel

In this paper an original solution for the modeling of distributed parameter processes using neural networks is presented. The proposed method represents a particular alternative to a very accurate modeling-simulation method for this kind of processes, the method based on the matrix of partial derivatives of the state vector (Mpdx), associated with Taylor series. In order to compare the performances generated by the two methods, a distributed parameter thermal process associated to a rotary hearth furnace (R.H.F) from the technological flow of producing seamless steel pipes is considered. The main similarities and differences between the two methods are highlighted in the paper. The treated solution represents a premise for the usage of the neural networks in the automatic control of the distributed parameter processes domain.

scholarly journals Speeding-up the Fitting of the Model Defining the Ribs-bounded Contour

2017 ◽  
Vol 21 (1) ◽  
pp. 66-70
Author(s):  
Mykolas J. Bilinskas ◽  
Gintautas Dzemyda ◽  
Martynas Sabaliauskas
Keyword(s):  
Mathematical Model ◽  
Local Search ◽  
Computer Tomography ◽  
Vertical Axis ◽  
Newton Methods ◽  
Optimal Parameters ◽  
Analytical Derivatives ◽  
The Mathematical Model ◽  
Quasi Newton ◽  
Derivatives Of

Abstract The method for analysing transversal plane images from computer tomography scans is considered in the paper. This method allows not only approximating ribs-bounded contour but also evaluating patient rotation around the vertical axis during a scan. In this method, a mathematical model describing the ribs-bounded contour was created and the problem of approximation has been solved by finding the optimal parameters of the mathematical model using least-squares-type objective function. The local search has been per-formed using local descent by quasi-Newton methods. The benefits of analytical derivatives of the function are disclosed in the paper.

scholarly journals Molecular docking and 3D-QSAR on 16a,17a-cycloalkanoprogesterone analogues as progesterone receptor ligands

2013 ◽  
Vol 59 (6) ◽  
pp. 622-635 ◽  
Author(s):  
I.V. Fedyushkina ◽  
V.S. Skvortsov ◽  
I.V. Romero Reyes ◽  
I.S. Levina
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Molecular Docking ◽  
Progesterone Receptor ◽  
3D Qsar ◽  
Dynamics Simulation ◽  
Receptor Ligands ◽  
Artificial Neural ◽  
Derivatives Of

A series of 42 steroid ligands was used to predict a binding affinity to progesterone receptor. The molecules were the derivatives of 16a,17a-cycloalkanoprogesterones. Different methods of prediction were used and analyzed such as CoMFA and artificial neural networks. The best result (Q2=0.91) was obtained for a combination of molecular docking, molecular dynamics simulation and artificial neural networks. A predictive power of the model was validated by a group of 8 pentarans synthesized separately and tested in vitro (R2test=0.77). This model can be used to determine the affinity level of the ligand to progesterone receptor and accurate ranking of binding compounds.

Training Feedforward Neural Networks with Gain Constraints

2000 ◽  
Vol 12 (4) ◽  
pp. 811-829 ◽  
Author(s):  
Eric Hartman
Keyword(s):  
Neural Networks ◽  
Objective Function ◽  
Network Models ◽  
Feedforward Neural Networks ◽  
Bound Constraints ◽  
Neural Network Models ◽  
Optimization Control ◽  
Input Variables ◽  
Derivatives Of ◽  
And Training

Inaccurate input-output gains (partial derivatives of outputs with respect to inputs) are common in neural network models when input variables are correlated or when data are incomplete or inaccurate. Accurate gains are essential for optimization, control, and other purposes. We develop and explore a method for training feedforward neural networks subject to inequality or equality-bound constraints on the gains of the learned mapping. Gain constraints are implemented as penalty terms added to the objective function, and training is done using gradient descent. Adaptive and robust procedures are devised for balancing the relative strengths of the various terms in the objective function, which is essential when the constraints are inconsistent with the data. The approach has the virtue that the model domain of validity can be extended via extrapolation training, which can dramatically improve generalization. The algorithm is demonstrated here on artificial and real-world problems with very good results and has been advantageously applied to dozens of models currently in commercial use.

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