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, the authors tackle this problem by adapting various successful network architectures into the symbolic law discovery pipeline. The novelty of this new 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 allowed to prior the exponentially large search with the predicted importance of the symbolic operators, which can significantly accelerate the discovery process.

The model was then applied to a variety of plausible relationships—both simulated and from physics and mathematics domains—involving different dimensions and constituents. The authors show that their 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. Their 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. This novel approach holds a real promise to help speed up the rate of scientific discovery.