模拟行星形成最早阶段的多输出随机森林回归
Multi-Output Random Forest Regression to Emulate the Earliest Stages of Planet Formation
摘要：
在目前的行星形成研究范式中，人们认为形成大质量天体（如小行星和行星）的第一步需要漂浮在太空中的小星际尘埃颗粒相互碰撞并成长为更大的尺寸。这些卵石的初始形成由被称为Smoluchowski凝结方程的积分微分方程控制，除了最简单的可能情况之外，该方程的解析解对于所有情况都是难以处理的。虽然已经开发出了近似的蛮力方法，但它们在计算上是昂贵的，目前使得模拟这个过程包括与行星形成相关的其他物理过程是不可行的，并且在它发生的非常大的尺度范围内。在本文中，我们采用机器学习方法来设计一个更快近似的系统。我们开发了一个多输出的随机森林回归模型训练的蛮力模拟数据近似分布的尘埃颗粒大小在原行星盘在不同的时间点。我们的随机森林模型的性能是针对现有的蛮力模型进行测量的，蛮力模型是现实模拟的标准。结果表明，随机森林模型可以生成相对于蛮力模拟结果的高度准确的预测，$R^{2}$为0.97，并且比蛮力方法快得多。
英文摘要：
In the current paradigm of planet formation research, it is believed that the first step to forming massive bodies (such as asteroids and planets) requires that small interstellar dust grains floating through space collide with each other and grow to larger sizes. The initial formation of these pebbles is governed by an integro-differential equation known as the Smoluchowski coagulation equation, to which analytical solutions are intractable for all but the simplest possible scenarios. While brute-force methods of approximation have been developed, they are computationally costly, currently making it infeasible to simulate this process including other physical processes relevant to planet formation, and across the very large range of scales on which it occurs. In this paper, we take a machine learning approach to designing a system for a much faster approximation. We develop a multi-output random forest regression model trained on brute-force simulation data to approximate distributions of dust particle sizes in protoplanetary disks at different points in time. The performance of our random forest model is measured against the existing brute-force models, which are the standard for realistic simulations. Results indicate that the random forest model can generate highly accurate predictions relative to the brute-force simulation results, with an $R^{2}$ of 0.97, and do so significantly faster than brute-force methods.
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