arXiv subjects

Rasul Abdusalamov

Publications and source records attributed to Rasul Abdusalamov.

5 recordsLinked to original sources

arXiv2025

Rediscovering Hyperelasticity by Deep Symbolic Regression

The accurate modeling of the mechanical behavior of rubber-like materials under multi-axial loading constitutes a long-standing challenge in hyperelastic material modeling. This work employs deep symbolic regression as an interpretable machine learning approach to discover novel strain energy functions directly from experimental results, with a specific focus on the classical Treloar and Kawabata data sets for vulcanized rubber. The proposed approach circumvents traditional human model selection biases by exploring possible functional forms of strain energy functions, expressed in terms of both the first and second principal invariants of the right Cauchy-Green tensor. The resulting models exhibit high predictive accuracy for various deformation modes, including uniaxial tension, pure shear, equal biaxial tension, and biaxial loading. This work underscores the potential of deep symbolic regression in advancing hyperelastic material modeling and highlights the importance of considering both invariants in capturing the complex behaviors of rubber-like materials.

cs.CE↗

arXiv2025

Self-Adaptive Physics-Informed Quantum Machine Learning for Solving Differential Equations

Chebyshev polynomials have shown significant promise as an efficient tool for both classical and quantum neural networks to solve linear and nonlinear differential equations. In this work, we adapt and generalize this framework in a quantum machine learning setting for a variety of problems, including the 2D Poisson's equation, second-order linear differential equation, system of differential equations, nonlinear Duffing and Riccati equation. In particular, we propose in the quantum setting a modified Self-Adaptive Physics-Informed Neural Network (SAPINN) approach, where self-adaptive weights are applied to problems with multi-objective loss functions. We further explore capturing correlations in our loss function using a quantum-correlated measurement, resulting in improved accuracy for initial value problems. We analyse also the use of entangling layers and their impact on the solution accuracy for second-order differential equations. The results indicate a promising approach to the near-term evaluation of differential equations on quantum devices.

quant-ph↗

arXiv2024

Rediscovering the Mullins Effect With Deep Symbolic Regression

The Mullins effect represents a softening phenomenon observed in rubber-like materials and soft biological tissues. It is usually accompanied by many other inelastic effects like for example residual strain and induced anisotropy. In spite of the long term research and many material models proposed in literature, accurate modeling and prediction of this complex phenomenon still remain a challenging task. In this work, we present a novel approach using deep symbolic regression (DSR) to generate material models describing the Mullins effect in the context of nearly incompressible hyperelastic materials. The two step framework first identifies a strain energy function describing the primary loading. Subsequently, a damage function characterizing the softening behavior under cyclic loading is identified. The efficiency of the proposed approach is demonstrated through benchmark tests using the generalized the Mooney-Rivlin and the Ogden-Roxburgh model. The generalizability and robustness of the presented framework are thoroughly studied. In addition, the proposed methodology is extensively validated on a temperature-dependent data set, which demonstrates its versatile and reliable performance.

cs.CE↗

arXiv2023

Discovering Asymptotic Expansions Using Symbolic Regression

Recently, symbolic regression (SR) has demonstrated its efficiency for discovering basic governing relations in physical systems. A major impact can be potentially achieved by coupling symbolic regression with asymptotic methodology. The main advantage of asymptotic approach involves the robust approximation to the sought for solution bringing a clear idea of the effect of problem parameters. However, the analytic derivation of the asymptotic series is often highly nontrivial especially, when the exact solution is not available. In this paper, we adapt SR methodology to discover asymptotic series. As an illustration we consider three problem in mechanics, including two-mass collision, viscoelastic behavior of a Kelvin-Voigt solid and propagation of Rayleigh-Lamb waves. The training data is generated from the explicit exact solutions of these problems. The obtained SR results are compared to the benchmark asymptotic expansions of the above mentioned exact solutions. Both convergent and divergent asymptotic series are considered. A good agreement between SR expansions and analytical results is observed. It is demonstrated that the proposed approach can be used to identify material parameters, e.g. Poisson's ratio, and has high prospects for utilizing experimental and numerical data.

cs.SC↗

arXiv2022

Automatic generation of interpretable hyperelastic material models by symbolic regression

In this paper, we present a new procedure to automatically generate interpretable hyperelastic material models. This approach is based on symbolic regression which represents an evolutionary algorithm searching for a mathematical model in the form of an algebraic expression. This results in a relatively simple model with good agreement to experimental data. By expressing the strain energy function in terms of its invariants or other parameters, it is possible to interpret the resulting algebraic formulation in a physical context. In addition, a direct implementation of the obtained algebraic equation is possible. For the validation of the proposed approach, benchmark tests on the basis of the generalized Mooney-Rivlin model are presented. In all these tests, the chosen ansatz can find the predefined models. Additionally, this method is applied for the multi-axial loading data set of vulcanized rubber. Finally, a data set for a temperature-dependent thermoplastic polyester elastomer is evaluated. In latter cases, good agreement with the experimental data is obtained.

cs.CE↗