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

TL;DR

This paper presents a novel method combining AI and Reduced Order Modeling to derive high-accuracy, closed-form gravitational wave expressions from binary black hole simulations, achieving 99% overlap with supercomputer models.

Contribution

It introduces a new approach that produces explicit, fast, and accurate closed-form gravitational wave expressions directly from ab initio models without physical approximations.

Findings

Achieved 99% overlap with supercomputer simulations.

Developed a symbolic regression method for gravitational wave expressions.

Validated approach on non-spinning black hole collisions.

Abstract

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.