Symbolic Regression is the study of algorithms that automate the search for analytic expressions that fit data. While recent advances in deep learning have generated renewed interest in such approaches, efforts have not been focused on physics, where we have important additional constraints due to the units associated with our data. Here we present $\Phi$-SO, a Physical Symbolic Optimization framework for recovering analytical symbolic expressions from physics data using deep reinforcement learning techniques by learning units constraints. Our system is built, from the ground up, to propose solutions where the physical units are consistent by construction. This is useful not only in eliminating physically impossible solutions, but because it restricts enormously the freedom of the equation generator, thus vastly improving performance. The algorithm can be used to fit noiseless data, which can be useful for instance when attempting to derive an analytical property of a physical model, and it can also be used to obtain analytical approximations to noisy data. We showcase our machinery on a panel of examples from astrophysics.
翻译:符号回归是研究算法,使搜索分析表达式的工作自动化,这种分析表达式符合数据要求。虽然最近深层次学习的进展使人们对这种方法产生了新的兴趣,但努力并没有集中在物理学上,因为与我们的数据相关的单位还存在重要的额外限制。这里我们展示了一个物理符号优化框架,用学习单位的制约,从物理数据中利用深强化学习技术恢复分析符号表达式。我们的系统是从基层建立起来的,目的是在物理单位通过构造保持一致的情况下提出解决方案。这不仅有助于消除物理上不可能的解决方案,而且因为它极大地限制了等式生成器的自由,从而极大地改进了性能。这一算法可用于匹配无噪音数据,在试图从物理模型中获取分析属性时,可以使用这些数据作为实例,也可以用来获取分析近似,以获取噪音数据。我们从天体物理学中提取的示例小组展示了我们的机器。</s>