Tiglio Manuel, Villanueva Aarón
Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, 5000, Córdoba, Argentina.
Sci Rep. 2021 Mar 12;11(1):5832. doi: 10.1038/s41598-021-85102-y.
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.
我们提出了一种新方法，用于从第一性原理模型中找到高精度、自由且封闭形式的表达式，以描述双黑洞碰撞所发射的引力波。更确切地说，我们的表达式是基于爱因斯坦方程的超级计算机模拟构建的数值替代模型，这些模型已被证明彼此基本无法区分。我们方法的不同之处在于：（i）引力波的表示可以用几行明确写出；（ii）这些表示是自由形式的，但搜索和验证速度仍然很快；（iii）基础模型中没有潜在的物理近似。关键策略是将人工智能技术与参数化系统的降阶建模相结合。具体而言，通过遗传编程进行符号回归，结合参数空间和时域中的稀疏表示，使用降基方法和经验插值方法，实现快速的自由形式符号搜索和大规模的后验验证。作为概念验证，我们给出了两个初始无自旋且合并前初始间距对应25 - 31个引力波周期的黑洞碰撞的结果。与真实解相比，最小重叠率为99%。也就是说，我们的封闭形式表达式与超级计算机模拟之间的差异为1%；对于引力波（GW）科学来说，考虑到实验数值误差通常占主导地位，这一差异比所需的最小值还要小。本文旨在特别为引力波领域以及一般的人工智能领域做出贡献。
