Automated Symbolic Law Discovery: A Computer Vision Approach

Abstract

One of the most exciting applications of modern artificial intelligence is to automatically discover scientific laws from experimental data. This is not a trivial problem as it involves searching for a complex mathematical relationship over a large set of explanatory variables and operators that can be combined in an infinite number of ways. Inspired by the incredible success of deep learning in computer vision, we tackle this problem by adapting various successful network architectures into the symbolic law discovery pipeline. The novelty of our approach is in (1) encoding the input data as an image with super-resolution, (2) developing an appropriate deep network pipeline, and (3) predicting the importance of each mathematical operator from the relationship image. This allows us to prior the exponentially large search with the predicted importance of the symbolic operators, which can significantly accelerate the discovery process. We apply our model to a variety of plausible relationships---both simulated and from physics and mathematics domains---involving different dimensions and constituents. We show that our model is able to identify the underlying operators from data, achieving a high accuracy and AUC (91% and 0.96 on average resp.) for systems with as many as ten independent variables. Our method significantly outperforms the current state of the art in terms of data fitting (R^2), discovery rate (recovering the true relationship), and succinctness (output formula complexity). The discovered equations can be seen as first drafts of scientific laws that can be helpful to the scientists for (1) hypothesis building, and (2) understanding the complex underlying structure of the studied phenomena. Our approach holds a real promise to help speed up the rate of scientific discovery.

A Dataset for Learning University STEM Courses at Scale and Generating Questions at a Human Level

“…Machine Learning Physics Models The AI Feynman system (Udrescu and Tegmark 2020; Udrescu et al 2020) and improvements (Xing, Salleb-Aouissi, and Verma 2021) uses machine learning to perform symbolic regression on data from physical systems. AI Feynman uses neural networks to guide automated search over symbolic expression trees.…”

Online Symbolic Regression with Informative Query

“…Symbolic regression. Symbolic regression in an offline setting has been studied for years (Koza 1994;Martius and Lampert 2016;Sahoo, Lampert, and Martius 2018;Lample and Charton 2019;La Cava et al 2021;Xing, Salleb-Aouissi, and Verma 2021;Zheng et al 2022). Traditionally, methods based on genetic evolution algorithms have been utilized to tackle offline symbolic regression (Augusto and Barbosa 2000;Schmidt and Lipson 2009;Arnaldo, Krawiec, and O'Reilly 2014;La Cava et al 2018;Virgolin et al 2021;Mundhenk et al 2021).…”