High performance algorithms for quantum gravity and cosmology

Cunningham, William J.

doi:10.17760/d20289557

Cited by 4 publications

(5 citation statements)

References 134 publications

(200 reference statements)

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“…Nevertheless, to get to the asymptotic regime in d = 4 will require far more extensive computational power. Recently, using new sophisticated computational techniques (Cunningham 2018b), the algorithms of Surya (2012) have been updated, so that n ∼ 300 simulations can be done in a reasonable time.…”

Section: A Continuum-inspired Dynamicsmentioning

confidence: 99%

“…( 31) in general is however non-trivial since there are caustics in a generic spacetime which complicate the calculation. On the other hand, numerical simulations suggest that again, up to boundary terms, the Benincasa-Dowker action S is the Einstein-Hilbert action (Benincasa 2013;Cunningham 2018b). We will discuss these boundary terms below.…”

Section: The Ricci Scalar and The Benincasa-dowker Actionmentioning

confidence: 99%

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The causal set approach to quantum gravity

2019

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The causal set theory (CST) approach to quantum gravity postulates that at the most fundamental level, spacetime is discrete, with the spacetime continuum replaced by locally finite posets or "causal sets". The partial order on a causal set represents a proto-causality relation while local finiteness encodes an intrinsic discreteness. In the continuum approximation the former corresponds to the spacetime causality relation and the latter to a fundamental spacetime atomicity, so that finite volume regions in the continuum contain only a finite number of causal set elements. CST is deeply rooted in the Lorentzian character of spacetime, where a primary role is played by the causal structure poset. Importantly, the assumption of a fundamental discreteness in CST does not violate local Lorentz invariance in the continuum approximation. On the other hand, the combination of discreteness and Lorentz invariance gives rise to a characteristic non-locality which distinguishes CST from most other approaches to quantum gravity.In this review we give a broad, semi-pedagogical introduction to CST, highlighting key results as well as some of the key open questions. This review is intended both for the beginner student in quantum gravity as well as more seasoned researchers in the field.

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Section: A Continuum-inspired Dynamicsmentioning

confidence: 99%

Section: The Ricci Scalar and The Benincasa-dowker Actionmentioning

confidence: 99%

The causal set approach to quantum gravity

2019

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“…Recently, there has been a great amount of interest in applying techniques of machine learning to string theory, as pioneered in [29][30][31][32][33]. In particular, methods of machine learning have been applied to various "Big Data" problems in string compactifications, such as string vacua, the AdS/CFT correspondence, bundle cohomology and stability, cosmology and beyond, [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51] as well as the structure of mathematics. [52][53][54][55] The idea of this present work is to apply these same methods to see whether they are able to increase the accuracy and/or reduce the time and cost of numerical calculations, specifically of the Calabi-Yau metric on generic threefolds.…”

Section: Introductionmentioning

confidence: 99%

Machine Learning Calabi–Yau Metrics

Ashmore

Ovrut

2020

Fortschritte der Physik

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We apply machine learning to the problem of finding numerical Calabi–Yau metrics. Building on Donaldson's algorithm for calculating balanced metrics on Kähler manifolds, we combine conventional curve fitting and machine‐learning techniques to numerically approximate Ricci‐flat metrics. We show that machine learning is able to predict the Calabi–Yau metric and quantities associated with it, such as its determinant, having seen only a small sample of training data. Using this in conjunction with a straightforward curve fitting routine, we demonstrate that it is possible to find highly accurate numerical metrics much more quickly than by using Donaldson's algorithm alone, with our new machine‐learning algorithm decreasing the time required by between one and two orders of magnitude.

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“…in which N k (C) denotes the number of discrete spacetime order intervals containing k elements in the causal set C, and n denotes the cardinality of the causal set n = |C|. As argued by Sorkin [44], Benincasa and Dowker [46], and shown numerically by Cunningham [49] for certain restricted cases, under the assumption that the contribution to the integral from the W 2 region down the light cone vanishes, the discrete action S (4) limits (assuming zero surface terms) to the continuum Einstein-Hilbert action for the Lorentzian manifold (M, g) in the limit of infinite sprinkling density:…”

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confidence: 99%

Algorithmic Causal Sets and the Wolfram Model

Gorard

2020

Preprint

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The formal relationship between two differing approaches to the description of spacetime as an intrinsically discrete mathematical structure, namely causal set theory and the Wolfram model, is studied, and it is demonstrated that the hypergraph rewriting approach of the Wolfram model can effectively be interpreted as providing an underlying algorithmic dynamics for causal set evolution. We show how causal invariance of the hypergraph rewriting system can be used to infer conformal invariance of the induced causal partial order, in a manner that is provably compatible with the measure-theoretic arguments of Bombelli, Henson and Sorkin. We then illustrate how many of the local dimension estimation algorithms developed in the context of the Wolfram model may be reformulated as generalizations of the midpoint scaling estimator on causal sets, and are compatible with the generalized Myrheim-Meyer estimators, as well as exploring how the presence of the underlying hypergraph structure yields a significantly more robust technique for estimating spacelike distances when compared against several standard distance and predistance estimator functions in causal set theory. We finally demonstrate how the Benincasa-Dowker action on causal sets can be recovered as a special case of the discrete Einstein-Hilbert action over Wolfram model systems (with ergodicity assumptions in the hypergraph replaced by Poisson distribution assumptions in the causal set), and also how both classical and quantum sequential growth dynamics can be recovered as special cases of Wolfram model multiway evolution with an appropriate choice of discrete measure.

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High performance algorithms for quantum gravity and cosmology

Cited by 4 publications

References 134 publications

The causal set approach to quantum gravity

The causal set approach to quantum gravity

Machine Learning Calabi–Yau Metrics

Algorithmic Causal Sets and the Wolfram Model

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