 |
customer@davidpublishing.com |
 |
3275638434 |
 |
 |
| Paper Publishing WeChat |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
P. A. Belov¹ and Elliot Weiss²
Full-Text PDF
XML 158 Views
DOI:10.17265/1934-7359/2026.08.004
1. Institute of Applied Mechanics, Russian Academy of Sciences, Moscow 125040, Russia 2. Independent Researcher, USA
This study formulates the second inverse problem of genetic identification of materials as a natural generalization of the first inverse problem, in which the governing differential operator is reconstructed within a prescribed model architecture. It is shown that selecting the architecture itself constitutes an independent mathematical problem that cannot be reduced to parametric identification. The model space is represented as a discrete set of architectures defined by the smoothness class and the number of segments of the deformation curve. A theorem on the segmentation capacity of an architecture is proved, establishing a class-dependent upper bound on the maximum identifiable number of segments as a function of the experimental sample size. In contrast to the conventional approach, the sample size is treated as a characteristic of the research complex that determines the domain of potential informational observability of architectures. Mathematical admissibility, numerical identifiability, experimental admissibility, and structural optimality of models are consistently distinguished. A functional formulation of the second inverse problem is proposed on the basis of a reduced nonintegrable variational form defined over a continuous representation of the discrete architecture space. Reinsch’s principle is generalized: among all experimentally admissible models, preference is given to the architecture of minimum necessary structural complexity. The numerical methodology is based on DOE (design of experiments), interpreted not only as a means of searching for an optimal architecture but also as a tool for designing a research complex capable of providing informational observability of the model space under consideration. The proposed approach is demonstrated using experimental data for SAE 1035 steel.
Genetic
identification, inverse problem, model architecture, smoothness class, design
of experiments, operator identification.
P. A. Belov and Elliot Weiss . (2026). The Second Inverse Problem of Genetic Identification of Materials: Selection of the Optimal Model Architecture, Journal of Civil Engineering and Architecture, August 2026, Vol. 20, No. 8, 347-358
[1] Hadamard, J. 1923. Lectures on Cauchy’s Problem in Linear Partial Differential Equations. New Haven: Yale University Press. 316 pp.
[2] Tikhonov, A. N. 1963. “Solution of Incorrectly Formulated Problems and the Regularization Method.” Soviet Mathematics Doklady 4: 1035-8.
[3] Ivanov, V. K. 1963. “On Ill-Posed Problems.” Matematicheskii Sbornik 61 (103): 211-23.
[4] Lavrentiev, M. M. 1967. Some Improperly Posed Problems of Mathematical Physics. Vol. 11. Berlin-Heidelberg: Springer. doi:10.1007/978-3-642-88210-4.
[5] Engl, H. W., Hanke, M., and Neubauer, A. 1996. Regularization of Inverse Problems. Dordrecht: Kluwer Academic Publishers. 321 pp.
[6] Kabanikhin, S. I. 2008. “Definitions and Examples of Inverse and Ill-Posed Problems.” Journal of Inverse and Ill-Posed Problems 16 (4): 317-57. doi:10.1515/JIIP.2008.019.
[7] Belov, P. A. 2026. “Foundations of the Genetics of Elastoplastic Materials.” Journal of Civil Engineering and Architecture 20: 129-46. doi:10.17265/1934-7359/2026.04.001.
[8] Belov, P. A., and Golovina, N. Ya. 2026. “Structural Theory of Elastoplastic Material Models.” Journal of Civil Engineering and Architecture 20: 281-91. doi:10.17265/1934-7359/2026.07.003.
[9] Belov, P. A., and Weiss, E. 2026. “Direct and First Inverse Problems of Genetic Identification of Materials at a Fixed Smoothness Class.” Journal of Civil Engineering and Architecture. (Accepted for publication).