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Related papers: Rediscovering Hyperelasticity by Deep Symbolic Reg…

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Symbolic Regression is the study of algorithms that automate the search for analytic expressions that fit data. While recent advances in deep learning have generated renewed interest in such approaches, the development of symbolic…

Instrumentation and Methods for Astrophysics · Physics 2023-12-27 Wassim Tenachi , Rodrigo Ibata , Foivos I. Diakogiannis

In a regression task, a function is learned from labeled data to predict the labels at new data points. The goal is to achieve small prediction errors. In symbolic regression, the goal is more ambitious, namely, to learn an interpretable…

Machine Learning · Computer Science 2025-06-25 Paul Kahlmeyer , Joachim Giesen , Michael Habeck , Henrik Voigt

Discovering interpretable physical laws from high-dimensional data is a fundamental challenge in scientific research. Traditional methods, such as symbolic regression, often produce complex, unphysical formulas when searching a vast space…

Computational Physics · Physics 2026-02-27 Yifeng Guan , Chuyi Liu , Dongzhan Zhou , Lei Bai , Wan-jian Yin , Jingyuan Li , Mao Su

Symbolic regression (SR) aims to discover explicit mathematical expressions that explain observed data and is widely used in domains where interpretability is essential. Because interpretability requires expressions to reflect meaningful…

Neural and Evolutionary Computing · Computer Science 2026-05-18 Koki Ikeda , Masahiro Nomura , Ryoki Hamano

The two approaches to analyzing the large strain behavior of rubbery networks are phenomenologically, using strain energy functions drawn from continuum mechanics, and molecular models, which apply statistical mechanics to compute the…

Soft Condensed Matter · Physics 2011-04-11 C. M. Roland

Soft materials such as rubbers, silicones, gels and biological tissues have a nonlinear response to large deformations, a phenomenon which in principle can be captured by hyperelastic models. The suitability of a candidate hyperelastic…

Soft Condensed Matter · Physics 2024-03-05 Afshin Anssari-Benam , Andrea Bucchi , Michel Destrade , Giuseppe Saccomandi

Symbolic regression is a powerful technique that can discover analytical equations that describe data, which can lead to explainable models and generalizability outside of the training data set. In contrast, neural networks have achieved…

Machine Learning · Computer Science 2022-03-10 Samuel Kim , Peter Y. Lu , Srijon Mukherjee , Michael Gilbert , Li Jing , Vladimir Čeperić , Marin Soljačić

As a surrogate for computationally intensive meso-scale simulation of woven composites, this article presents Recurrent Neural Network (RNN) models. Leveraging the power of transfer learning, the initialization challenges and sparse data…

Materials Science · Physics 2024-07-08 Ehsan Ghane , Martin Fagerström , Mohsen Mirkhalaf

We present a machine learning framework capable of consistently inferring mathematical expressions of hyperelastic energy functionals for incompressible materials from sparse experimental data and physical laws. To achieve this goal, we…

Computational Engineering, Finance, and Science · Computer Science 2024-02-13 Bahador Bahmani , WaiChing Sun

In the realm of machine and deep learning regression tasks, the role of effective feature engineering (FE) is pivotal in enhancing model performance. Traditional approaches of FE often rely on domain expertise to manually design features…

Machine Learning · Computer Science 2024-06-18 Assaf Shmuel , Oren Glickman , Teddy Lazebnik

Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays…

Methodology · Statistics 2013-10-22 Hua Zhou , Lexin Li , Hongtu Zhu

The classical continuum models used for the woven fabrics do not fully describe the whole set of phenomena that occur during the testing of those materials. This incompleteness is partially due to the absence of energy terms related to some…

Soft Condensed Matter · Physics 2016-04-18 Gabriele Barbagallo , Angela Madeo , Ismael Azehaf , Ivan Giorgio , Fabrice Morestin , Philippe Boisse

We present a Machine Learning approach based on Symbolic Regression to derive, from either numerically generated or experimentally measured spectral data, closed-form expressions that model the optical properties of biological materials. To…

Computational Physics · Physics 2025-08-26 Julian Sierra-Velez , Alexandre Vial , Marina Inchaussandague , Diana Skigin , Demetrio Macías

Symbolic regression (SR) methods attempt to learn mathematical expressions that approximate the behavior of an observed system. However, when dealing with multivariate systems, they often fail to identify the functional form that explains…

Machine Learning · Computer Science 2024-06-27 Giorgio Morales , John W. Sheppard

Discovering valid and meaningful mathematical equations from observed data plays a crucial role in scientific discovery. While this task, symbolic regression, remains challenging due to the vast search space and the trade-off between…

Machine Learning · Computer Science 2025-09-17 Xiaoxu Han , Chengzhen Ning , Jinghui Zhong , Fubiao Yang , Yu Wang , Xin Mu

As a nonlocal extension of continuum mechanics, peridynamics has been widely and effectively applied in different fields where discontinuities in the field variables arise from an initially continuous body. An important component of the…

Numerical Analysis · Mathematics 2021-09-22 Xiao Xu , Marta D'Elia , John T. Foster

Highly compressible solids, such as foams, exhibit complex responses, including pronounced tension-compression asymmetry. Capturing such behaviors within unified hyperelastic frameworks remains challenging. Invariant-based hyperelastic…

Computational Engineering, Finance, and Science · Computer Science 2026-04-17 Miguel Angel Moreno-Mateos , Simon Wiesheier , Paul Steinmann , Ellen Kuhl

The increased adoption of reinforced polymer (RP) composite materials, driven by eco-design standards, calls for a fine balance between lightness, stiffness, and effective vibration control. These materials are integral to enhancing…

Machine Learning · Computer Science 2023-10-25 Victor Hoffmann , Ilias Nahmed , Parisa Rastin , Guénaël Cabanes , Julien Boisse

Numerous models have been developed in the literature to simulate the thermomechanical behavior of amorphous polymer at large strain. These models generally show a good agreement with experimental results when the material is submitted to…

Soft Condensed Matter · Physics 2021-06-23 Ca Bernard , D George , S Ahzi , Y Rémond

The difficulty of identifying the physical model of complex systems has led to exploring methods that do not rely on such complex modeling of the systems. Deep reinforcement learning has been the pioneer for solving this problem without the…

Artificial Intelligence · Computer Science 2023-10-31 Ammar N. Abbas , Georgios C. Chasparis , John D. Kelleher