Application of symbolic regression for constitutive modeling of plastic deformation

Kabliman, Evgeniya; Kolody, Ana Helena; Kronsteiner, Johannes; Kommenda, Michael; Kronberger, Gabriel

doi:10.1016/j.apples.2021.100052

Cited by 21 publications

(16 citation statements)

References 25 publications

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“…For example, let T = y 2 • (x + y)/z − sin(x + y) be an expression, and ([6, 7, 4], 3), ( [3,3,6], 2)} be a sample training dataset (here, input feature vector is labeled by [x, y, z]); let expression cache consist of the following key-value entries cache = {(x+y, [3,7,9,13,6]), (y 2 , [4, 16,25,49,9])}. Expression T does not need to be fully evaluated since some of its parts are inside the cache: y 2 and x + y.…”

Section: Expression Cachingmentioning

confidence: 99%

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RILS-ROLS: Robust Symbolic Regression via Iterated Local Search and Ordinary Least Squares

Kartelj

Djukanovic

2022

Preprint

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In this paper, we solve the well-known symbolic regression problem that has been intensively studied and has a wide range of applications. To solve it, we propose an efficient meta-heuristic-based approach, called RILS-ROLS. RILS-ROLS is based on the following two elements: (i) iterated local search, which is the method backbone, mainly solving combinatorial and some continuous aspects of the problem; (ii) ordinary least square method, which focuses on the continuous aspect of the search space -- it efficiently determines the best-fitting coefficients of linear combinations within solution equations. In addition, we introduce a novel fitness function that combines important model quality measures: R2 score, RMSE score, size of the model (or model complexity), and carefully designed local search, which allows systematic search in proximity to candidate solution. Experiments are conducted on the two well-known ground-truth benchmark sets called Feynman and Strogatz. RILS-ROLS was compared to 14 other competitors from the literature. Our method outperformed all 14 competitors with respect to the true symbolic model accuracy under varying levels of noise. It also proved to be the most efficient method considering the average running time of reaching the exact model. In addition to evaluation on known ground-truth datasets, we introduce a new randomly generated set of problem instances. The goal of the Random dataset was to test the scalability of our method with respect to incremental equation sizes and number of variables, under different levels of noise. The statistical analysis of obtained experimental results confirmed that RILS-ROLS can be considered as a new state-of-the-art method for solving the problem of symbolic regression when ground-truth equations are known.

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Section: Expression Cachingmentioning

confidence: 99%

“…The application of the SR to model analytic representations of exciton binding energy is shown in [9]. The use of SR in material science is described in [10,11,12,13]. SR application to wind speed forecasting is given in [14].…”

Section: Introductionmentioning

confidence: 99%

RILS-ROLS: Robust Symbolic Regression via Iterated Local Search and Ordinary Least Squares

Kartelj

Djukanovic

2022

Preprint

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“…Unlike most ML methods where models are formulated numerically, symbolic regression outputs the resulting model in the symbolic form. Recently, there is emerging interest in the development of symbolic regression methods for physical science problems (46)(47)(48)(49)(50)(51)(52)(53)(54)(55)(56). We illustrate our framework in Fig.…”

Section: Introductionmentioning

confidence: 99%

Evolving symbolic density functionals

Narayanaswamy

Riley

et al. 2022

Sci. Adv.

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Systematic development of accurate density functionals has been a decades-long challenge for scientists. Despite emerging applications of machine learning (ML) in approximating functionals, the resulting ML functionals usually contain more than tens of thousands of parameters, leading to a huge gap in the formulation with the conventional human-designed symbolic functionals. We propose a new framework, Symbolic Functional Evolutionary Search (SyFES), that automatically constructs accurate functionals in the symbolic form, which is more explainable to humans, cheaper to evaluate, and easier to integrate to existing codes than other ML functionals. We first show that, without prior knowledge, SyFES reconstructed a known functional from scratch. We then demonstrate that evolving from an existing functional ωB97M-V, SyFES found a new functional, GAS22 (Google Accelerated Science 22), that performs better for most of the molecular types in the test set of Main Group Chemistry Database (MGCDB84). Our framework opens a new direction in leveraging computing power for the systematic development of symbolic density functionals.

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“…Recently, there is emerging interest in development of symbolic regression methods for physical science problems. [46][47][48][49][50][51][52][53] We illustrate our framework in Fig. S1 and denote it as Symbolic Functional Evolutionary Search (SyFES).…”

Section: Introductionmentioning

confidence: 99%

Evolving symbolic density functionals

Ma,

Narayanaswamy,

Riley

et al. 2022

Preprint

View full text Add to dashboard Cite

Systematic development of accurate density functionals has been a decades-long challenge for scientists. Despite the emerging application of machine learning (ML) in approximating functionals, the resulting ML functionals usually contain more than tens of thousands parameters, which makes a huge gap in the formulation with the conventional human-designed symbolic functionals. We propose a new framework, Symbolic Functional Evolutionary Search (SyFES), that automatically constructs accurate functionals in the symbolic form, which is more explainable to humans, cheaper to evaluate, and easier to integrate to existing density functional theory codes than other ML functionals. We first show that without prior knowledge, SyFES reconstructed a known functional from scratch. We then demonstrate that evolving from an existing functional ωB97M-V, SyFES found a new functional, GAS22 (Google Accelerated Science 22), that performs better on main-group chemistry. Our framework opens a new direction in leveraging computing power for the systematic development of symbolic density functionals.

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Application of symbolic regression for constitutive modeling of plastic deformation

Cited by 21 publications

References 25 publications

RILS-ROLS: Robust Symbolic Regression via Iterated Local Search and Ordinary Least Squares

RILS-ROLS: Robust Symbolic Regression via Iterated Local Search and Ordinary Least Squares

Evolving symbolic density functionals

Evolving symbolic density functionals

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