AI Feynman: a Physics-Inspired Method for Symbolic Regression

Udrescu, Silviu-Marian; Tegmark, Max

doi:10.48550/arxiv.1905.11481

Cited by 16 publications

(14 citation statements)

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“…While symbolic regression has a long history of evolutionary strategies, especially GP (Koza, 1992;Bäck et al, 2018;Uy et al, 2011), several recent approaches leverage deep learning for symbolic regression. The AI Feynman algorithm (Udrescu & Tegmark, 2019) is a multi-staged approach that uses neural networks to identify simplifying properties in a dataset (e.g. multiplicative separability or translational symmetry), which they exploit to recursively define simplified subproblems that are eventually solved using simple techniques like a polynomial fit.…”

Section: Related Workmentioning

confidence: 99%

Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients

Petersen¹,

Landajuela²,

Mundhenk³

et al. 2019

Preprint

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Discovering the underlying mathematical expressions describing a dataset is a core challenge for artificial intelligence. This is the problem of symbolic regression. Despite recent advances in training neural networks to solve complex tasks, deep learning approaches to symbolic regression are underexplored. We propose a framework that combines deep learning with symbolic regression via a simple idea: use a large model to search the space of small models. More specifically, we use a recurrent neural network to emit a distribution over tractable mathematical expressions, and employ reinforcement learning to train the network to generate better-fitting expressions. Our algorithm significantly outperforms standard genetic programming-based symbolic regression in its ability to exactly recover symbolic expressions on a series of benchmark problems, both with and without added noise. More broadly, our contributions include a framework that can be applied to optimize hierarchical, variable-length objects under a black-box performance metric, with the ability to incorporate a priori constraints in situ, and a risk-seeking policy gradient formulation that optimizes for best-case performance instead of expected performance.

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Section: Related Workmentioning

confidence: 99%

Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients

Petersen¹,

Landajuela²,

Mundhenk³

et al. 2019

Preprint

View full text Add to dashboard Cite

show abstract

“…It has been shown that a good design of the search space is essential in discrete structure optimization problems, e.g., neural architecture search [10][11][12], molecule optimization [13], composite design [14] and symbolic regression [15,16]. Since the QAOA is a well-recognized ansatz for combinatorial problems, we have designed the search space for G A based on gradual modifications of the QAOA ansatz.…”

Section: Optimizing the Ansatzmentioning

confidence: 99%

Quantum optimization with a novel Gibbs objective function and ansatz architecture search

Fan

Coram

et al. 2020

Phys. Rev. Research

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The Quantum Approximate Optimization Algorithm (QAOA) is a standard method for combinatorial optimization with a gate-based quantum computer. The QAOA consists of a particular ansatz for the quantum circuit architecture, together with a prescription for choosing the variational parameters of the circuit. We propose modifications to both. First, we define the Gibbs objective function and show that it is superior to the energy expectation value for use as an objective function in tuning the variational parameters. Second, we describe an Ansatz Architecture Search (AAS) algorithm for searching the discrete space of quantum circuit architectures near the QAOA to find a better ansatz. Through the AAS we find quantum circuits with the same number of variational parameters as the QAOA but which have improved performance on certain Ising-type problems. This opens a new research field of quantum circuit architecture design for quantum optimization algorithms.arXiv:1909.07621v1 [quant-ph]

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“…Other applications of the GA have been used for particle physics [60][61][62], astronomy and astrophysics [63][64][65]. Finally, other symbolic regression methods implemented in physics and cosmology can be found at [66][67][68][69][70][71][72][73].…”

Section: Genetic Algorithmsmentioning

confidence: 99%

Testing the $Λ$CDM paradigm with growth rate data and machine learning

Arjona,

Melchiorri,

Nesseris

2021

Preprint

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The cosmological constant Λ and cold dark matter (CDM) model (ΛCDM) is one of the pillars of modern cosmology and is widely used as the de facto theoretical model by current and forthcoming surveys. As the nature of dark energy is very elusive, in order to avoid the problem of model bias, here we present a novel null test at the perturbation level that uses the growth of matter perturbation data in order to assess the concordance model. We analyze how accurate this null test can be reconstructed by using data from forthcoming surveys creating mock catalogs based on ΛCDM and three models that display a different evolution of the matter perturbations, namely a dark energy model with constant equation of state w (wCDM), the Hu & Sawicki and designer f (R) models, and we reconstruct them with a machine learning technique known as the Genetic Algorithms. We show that with future LSST-like mock data our consistency test will be able to rule out these viable cosmological models at more than 5σ, help to check for tensions in the data and alleviate the existing tension of the amplitude of matter fluctuations S8 = σ8 (Ωm/0.3) 0.5 .

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AI Feynman: a Physics-Inspired Method for Symbolic Regression

Cited by 16 publications

References 0 publications

Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients

Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients

Quantum optimization with a novel Gibbs objective function and ansatz architecture search

Testing the $Λ$CDM paradigm with growth rate data and machine learning

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