Glyph: Symbolic Regression Tools

Quade, Markus; Gout, Julien; Abel, Markus

doi:10.5334/jors.192

Cited by 7 publications

(6 citation statements)

References 12 publications

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“…For our purposes, we systematically investigate the results of our method starting using two coupled oscillators. The extension to many oscillators is straightforward and subject of ongoing implementation activities to include a stability analysis automatically into Glyph [41].…”

Section: Resultsmentioning

confidence: 99%

“…Our software is based on Glyph, a package developed by ourselves [41], which in turn uses other, standard python packages, e.g., constant optimization is conducted using the Levenberg-Marquardt least squares algorithm (scipy) and numerical integration using the dopri5 solver (also scipy). Random numbers are generated using the Mersenne Twister pseudo-random number generator provided by the random module [46].…”

Section: Appendixmentioning

confidence: 99%

“…Random numbers are generated using the Mersenne Twister pseudo-random number generator provided by the random module [46]. Finally, the sympy module is used for the simplification of symbolic mathematical expressions generated from the GP runs [47], for more details see [41].…”

Section: Appendixmentioning

confidence: 99%

See 2 more Smart Citations

Explainable Machine Learning Control -- robust control and stability analysis

Quade¹,

Isele²,

Abel³

2020

Preprint

Self Cite

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Recently, the term explainable AI became known as an approach to produce models from artificial intelligence which allow interpretation. Since a long time, there are models of symbolic regression in use that are perfectly explainable and mathematically tractable: in this contribution we demonstrate how to use symbolic regression methods to infer the optimal control of a dynamical system given one or several optimization criteria, or cost functions. In previous publications, network control was achieved by automatized machine learning control using genetic programming. Here, we focus on the subsequent analysis of the analytical expressions which result from the machine learning. In particular, we use AUTO to analyze the stability properties of the controlled oscillator system which served as our model. As a result, we show that there is a considerable advantage of explainable models over less accessible neural networks.

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Section: Resultsmentioning

confidence: 99%

Section: Appendixmentioning

confidence: 99%

See 1 more Smart Citation

Explainable Machine Learning Control -- robust control and stability analysis

Quade¹,

Isele²,

Abel³

2020

Preprint

Self Cite

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show abstract

“…In this work we prioritize accuracy. We used Eureqa 31 for GP-SR, although there are open source alternatives such as gplearn 32 and Glyph 33 . As a fitness criteria we used the Hybrid Correlation and the - Goodness-of-fit metric errors to fit symbolic models for amplitude and phase, respectively.…”

Section: Methodsmentioning

confidence: 99%

On ab initio-based, free and closed-form expressions for gravitational waves

Tiglio

Villanueva

2021

Sci Rep

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We introduce a new approach for finding high accuracy, free and closed-form expressions for the gravitational waves emitted by binary black hole collisions from ab initio models. More precisely, our expressions are built from numerical surrogate models based on supercomputer simulations of the Einstein equations, which have been shown to be essentially indistinguishable from each other. Distinct aspects of our approach are that: (i) representations of the gravitational waves can be explicitly written in a few lines, (ii) these representations are free-form yet still fast to search for and validate and (iii) there are no underlying physical approximations in the underlying model. The key strategy is combining techniques from Artificial Intelligence and Reduced Order Modeling for parameterized systems. Namely, symbolic regression through genetic programming combined with sparse representations in parameter space and the time domain using Reduced Basis and the Empirical Interpolation Method enabling fast free-form symbolic searches and large-scale a posteriori validations. As a proof of concept we present our results for the collision of two black holes, initially without spin, and with an initial separation corresponding to 25–31 gravitational wave cycles before merger. The minimum overlap, compared to ground truth solutions, is 99%. That is, 1% difference between our closed-form expressions and supercomputer simulations; this is considered for gravitational (GW) science more than the minimum required due to experimental numerical errors which otherwise dominate. This paper aims to contribute to the field of GWs in particular and Artificial Intelligence in general.

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“…GA, firstly proposed by Holland [16], is an adaptive and competent approach for evolutionary search. It has been successfully applied in many fields; array optimization is an example [17][18][19][20][21], and can be treated as a kind of symbolic regression [22,23].…”

Section: Introductionmentioning

confidence: 99%

Even Dispersion Design for a Compact Linear Loudspeaker Array with Adaptive Genetic Algorithm

et al. 2019

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Even dispersion is important for live sound reinforcement systems; however, it needs to be carefully designed when using a linear loudspeaker array. This is because the audience area is often large, while the loudspeakers are placed centrally in this case for convenience, and thus both the level and the frequency balance may not remain reasonably constant for all audiences. To solve this problem, the adaptive genetic algorithm is firstly introduced in the parameters optimization. Secondly, taking the radiation characteristics at different frequencies into account, a linear-phase non-uniform filter bank is proposed to decompose the broad frequency band into several sub-bands. The audio is re-synthesized with the optimized parameters in each frequency band for a linear loudspeaker array. To show the validity of the proposed method, the simulations and the experiments are conducted to demonstrate that the sound pressure level in the audience area is distributed within ± 1.33 dB, ranging from 200 Hz to 4000 Hz.

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Glyph: Symbolic Regression Tools

Cited by 7 publications

References 12 publications

Explainable Machine Learning Control -- robust control and stability analysis

Explainable Machine Learning Control -- robust control and stability analysis

On ab initio-based, free and closed-form expressions for gravitational waves

Even Dispersion Design for a Compact Linear Loudspeaker Array with Adaptive Genetic Algorithm

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