Extending a physics-based constitutive model using genetic programming

Kronberger, Gabriel; Kabliman, Evgeniya; Kronsteiner, Johannes; Kommenda, Michael

doi:10.1016/j.apples.2021.100080

Cited by 6 publications

(6 citation statements)

References 30 publications

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“…Weather forecasting models such as the weather research and forecasting have also benefited from the application of GA for the quantification of wind power density and solar irradiance [11]. In the field of physics of materials, GA have played a major role in the search for optimised photonic crystal-based structures [12] and in hot compression tests for aluminium alloys [13]. These use cases represent only a small subset of the great potential that GA have to offer to the domain of physics research.…”

Section: Gas In Physicsmentioning

confidence: 99%

Fostering scientific methods in simulations through symbolic regressions

Llorella,

Antonio Cebrián,

Corbi

et al. 2024

Phys. Educ.

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Two-dimensional computer and tablet PC physics simulations have proved to be effective in helping students understand the fundamental principles of physics and related natural processes. However, the current approach to using these simulations tends to follow a repetitive cognitive and procedural pathway, regardless of the specific physical concepts being explored or software environment being used. This approach involves manipulating the simulation interface and collecting data through interaction with controls, widgets, or other contextual elements. Students then attempt to determine how these experimental measurements align with established laws, interactions, or mechanisms, as the teacher might have previously explained. We believe that this approach, while appropriate for education, obscures scientific processes, mainly related to the hypothetico-deductive model. To address this issue, we have developed a simple and adaptable computer environment that makes use of genetic algorithms (GAs) and symbolic regression to derive many of the basic laws of nature from the data collected by students using the popular physics education technology (PhET) simulations environment. Our proposal enables learners to observe how the order and relationships of mathematical tokens are routinely refined as new data points are added to the simulation setting. This iterative distillation technique can also be augmented with the interplay of dimensional analysis. In contrast with other more sophisticated artificial intelligence patterns, GA fit into the realm of grey box machine learning models. These type of evolutionary algorithms achieve the sought results by evolving mathematical models on each stage in an understandable way, which mimics the way scientific breakthroughs are accomplished (over the course of generations of researchers and based of prior knowledge). By implementing this innovative approach, we can provide students with a more authentic empirical experience that fosters a deeper understanding of the principles of science and scientific discovery. Field tests with students supporting this claim have also been carried out.

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Section: Gas In Physicsmentioning

confidence: 99%

Fostering scientific methods in simulations through symbolic regressions

Llorella,

Antonio Cebrián,

Corbi

et al. 2024

Phys. Educ.

View full text Add to dashboard Cite

show abstract

“…The development of material properties databases in a systematic way has altered materials research, as researchers opt for ML models to extract information out of them [ 26 ]. Both material properties and their relation to processing conditions, are translated to form new computational models [ 140 ]. There are cases where constitutive models express how a material responds in different conditions, which in turn produces a stress–strain relation to generate the governing laws [ 141 ].…”

Section: Application In Science and Technologymentioning

confidence: 99%

“…Furthermore, SR has provided constitutive formulas of material behavior in aluminum alloys [ 119 ] or been incorporated into a mergent of techniques where SR estimated the calibration parameters of a physics-based model [ 188 ]. Calibration of model parameters that depend on processing conditions may pose a major obstacle [ 140 ]. These parameters are occasionally fitted, in order to reach an agreement with measurements; for that reason, the degree of importance of other parameters on the calibration parameters is not completely established [ 188 ].…”

Section: Application In Science and Technologymentioning

confidence: 99%

“…These parameters are occasionally fitted, in order to reach an agreement with measurements; for that reason, the degree of importance of other parameters on the calibration parameters is not completely established [ 188 ]. To overcome this issue, two techniques have been proposed, the explicit and implicit [ 140 ].…”

Section: Application In Science and Technologymentioning

confidence: 99%

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Artificial Intelligence in Physical Sciences: Symbolic Regression Trends and Perspectives

Angelis

Sofos

Karakasidis

2023

Arch Computat Methods Eng

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Symbolic regression (SR) is a machine learning-based regression method based on genetic programming principles that integrates techniques and processes from heterogeneous scientific fields and is capable of providing analytical equations purely from data. This remarkable characteristic diminishes the need to incorporate prior knowledge about the investigated system. SR can spot profound and elucidate ambiguous relations that can be generalizable, applicable, explainable and span over most scientific, technological, economical, and social principles. In this review, current state of the art is documented, technical and physical characteristics of SR are presented, the available programming techniques are investigated, fields of application are explored, and future perspectives are discussed.

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“…Multiple applications of symbolic regression in the field of material modeling have been proposed in recent years. The technique can be used in the field of constitutive modeling in combination with a user‐chosen material model where symbolic regression is solely responsible for finding an expression for each model parameter when the parameters are not constant (e.g., when they depend on the temperature) 16‐18 . While this hybrid application provides relatively simple solutions, it is unable to utilize symbolic regression to its full potential as the quality of the outcome is still strictly limited by the choice of the base material model.…”

Section: Introductionmentioning

confidence: 99%

Automatic generation of interpretable hyperelastic material models by symbolic regression

Abdusalamov

Hillgärtner

Itskov

2023

Numerical Meth Engineering

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In this article, 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 for example into a finite element procedure 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 to 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.

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Extending a physics-based constitutive model using genetic programming

Cited by 6 publications

References 30 publications

Fostering scientific methods in simulations through symbolic regressions

Fostering scientific methods in simulations through symbolic regressions

Artificial Intelligence in Physical Sciences: Symbolic Regression Trends and Perspectives

Automatic generation of interpretable hyperelastic material models by symbolic regression

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