| Description |
1 online resource (xlvii, 240 pages) |
| Contents |
Front Cover; Semi-empirical Neural Network Modeling and Digital Twins Development; Copyright; Contents; About the authors; Preface; Acknowledgments; Introduction; References; Chapter 1: Examples of problem statements and functionals; 1.1. Problems for ordinary differential equations; 1.1.1. A stiff differential equation; 1.1.2. The problem of a chemical reactor; 1.1.3. The problem of a porous catalyst; 1.1.4. Differential-algebraic problem; 1.2. Problems for partial differential equations for domains with fixed boundaries; 1.2.1. The Laplace equation on the plane and in space |
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1.2.2. The Poisson problem1.2.3. The Schrödinger equation with a piecewise potential (quantum dot); 1.2.4. The nonlinear Schrödinger equation; 1.2.5. Heat transfer in the vessel-tissue system; 1.3. Problems for partial differential equations in the case of the domain with variable borders; 1.3.1. Stefan problem; Problem formulation; 1.3.2. The problem of the alternating pressure calibrator; Problem statement; 1.4. Inverse and other ill-posed problems; 1.4.1. The inverse problem of migration flow modeling |
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1.4.2. The problem of the recovery of solutions on the measurements for the Laplace equation1.4.3. The problem for the equation of thermal conductivity with time reversal; 1.4.4. The problem of determining the boundary condition; 1.4.5. The problem of continuation of the temperature field according to the measurement data; 1.4.6. Construction of a neural network model of a temperature field according to experimental data in the case of an int ... ; 1.4.7. The problem of air pollution in the tunnel; The conclusion; References; Further reading |
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Chapter 2: The choice of the functional basis (set of bases)2.1. Multilayer perceptron; 2.1.1. Structure and activation functions of multilayer perceptron; 2.1.2. The determination of the initial values of the weights of the perceptron; 2.2. Networks with radial basis functions-RBF; 2.2.1. The architecture of RBF networks; 2.2.2. Radial basis functions; 2.2.3. Asymmetric RBF-networks; 2.3. Multilayer perceptron and RBF-networks with time delays; References; Chapter 3: Methods for the selection of parameters and structure of the neural network model; 3.1. Structural algorithms |
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3.1.1. Methods for specific tasks3.2. Methods of global non-linear optimization; 3.3. Methods in the generalized definition; 3.4. Methods of refinement of models of objects described by differential equations; References; Further reading; Chapter 4: Results of computational experiments; 4.1. Solving problems for ordinary differential equations; 4.1.1. Stiff form of differential equation; 4.1.2. Chemical reactor problem; 4.1.3. The problem of a porous catalyst; 4.1.4. Differential-algebraic problem; 4.2. Solving problems for partial differential equations in domains with constant boundaries |
| Notes |
4.2.1. Solution of the Dirichlet problem for the Laplace equation in the unit circle |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Neural networks (Computer science)
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Finite element method -- Data processing.
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Neural Networks, Computer
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Finite element method -- Data processing
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Neural networks (Computer science)
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| Form |
Electronic book
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| Author |
Lazovskaya, T. V
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Vasilyev, A. N
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Nikolayevich Vasilyev, Alexander
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| ISBN |
012815652X |
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9780128156520 |
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