Hypothesis testing via AI: Generating physically interpretable models of scientific data with machine learning (Full Technical Report)

Abstract

Deep learning has demonstrated an exceptional ability to solve complex tasks (an engineering success); however, it has done so at the expense of the ability to generate new knowledge (a scientific failure). We propose an alternative framework—entitled Deep Symbolic Regression (DSR)—in which artificial neural networks (NNs) rapidly generate hypotheses about physical relationships among inputs. This framework bypasses the need to interpret an NN altogether, while still leveraging the representational power of deep learning. The resulting models are tractable mathematical expressions, which are inherently and readily human interpretable and can provide insights into underlying physical phenomena. Further, we fold this methodology into the scientific process by allowing the scientist to directly integrate a priori knowledge and beliefs to accelerate learning. We demonstrate this methodology on symbolic regression—the problem of rediscovering underlying expressions describing a dataset—and achieve state-of-the-art performance across a wide variety of symbolic regression problems. Further, we generalize our DSR framework to apply to the more general class of symbolic optimization problems, in which one seeks to optimize a sequence of symbols or “tokens” under a black-box reward function. Examples of other symbolic optimization problems include neural architecture search and computational antibody design. Our generalized tool, Deep Symbolic Optimization (DSO), has been demonstrated on the task of learning symbolic control policies for reinforcement learning environments, and has been adopted as an enabling capability for computational antibody design.