AI-Timoshenko: Automatedly Discovering Simplified Governing Equations for Applied Mechanics Problems From Simulated Data

Huang, Z.L.; Li, Chunjiang; Huang, Zhongdong; Wang, Yong; Jiang, Hanqing

doi:10.1115/1.4051334

Cited by 5 publications

(2 citation statements)

References 20 publications

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“…Following the study, data-driven scientific discovery has been attracting attention from research communities and been applied to various domains such as Physics [13][14][15][16][17][18], Applied Mechanics [19], Climatology [20], Materials [21][22][23][24], and Chemistry [25].…”

Section: Srsd: Symbolic Regression For Scientific Discoverymentioning

confidence: 99%

“…SR has been studied in the genetic programming (GP) community [1][2][3][4][5][6], and DL-based SR has been attracting more attention from the ML/DL community [7][8][9][10][11][12]. Because of the properties, various research communities apply SR to advance research in their scientific fields e.g., Physics [13][14][15][16][17][18], Applied Mechanics [19], Climatology [20], Materials [21][22][23][24], and Chemistry [25].…”

Section: Introductionmentioning

confidence: 99%

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Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery

Matsubara¹,

Chiba²,

Igarashi³

et al. 2022

Preprint

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This paper revisits datasets and evaluation criteria for Symbolic Regression, a task of expressing given data using mathematical equations, specifically focused on its potential for scientific discovery. Focused on a set of formulas used in the existing datasets based on Feynman Lectures on Physics, we recreate 120 datasets to discuss the performance of symbolic regression for scientific discovery (SRSD). For each of the 120 SRSD datasets, we carefully review the properties of the formula and its variables to design reasonably realistic sampling range of values so that our new SRSD datasets can be used for evaluating the potential of SRSD such as whether or not an SR method con (re)discover physical laws from such datasets. As an evaluation metric, we also propose to use normalized edit distances between a predicted equation and the ground-truth equation trees. While existing metrics are either binary or errors between the target values and an SR model's predicted values for a given input, normalized edit distances evaluate a sort of similarity between the ground-truth and predicted equation trees. We have conducted experiments on our new SRSD datasets using five state-of-the-art SR methods in SRBench and a simple baseline based on a recent Transformer architecture. The results show that we provide a more realistic performance evaluation and open up a new machine learning-based approach for scientific discovery. Our datasets 2 3 4 and code repository 5 are publicly available.

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