Optscientist automates discovery of optimization laws from data
OptScientist: Automated Discovery of Optimization Laws
Artificial IntelligenceMachine LearningSymbolic Computation
Summary
Many things in science can be explained by figuring out the best way something might happen, called optimization laws. The authors created OptScientist, a tool that reads data and finds simple math rules showing these best solutions. It also uses existing science knowledge to think of new ideas and data to test. They tested it on many physics problems and real-world topics like risky choices and money policy, showing it works better than other computer methods. OptScientist helps build scientific theories by automatically uncovering the math behind observed effects.
What this means in practice
- •For data science teams: Generate simple optimization-based models directly from observational data to explain complex phenomena across various domains.
- •For economic policy analysts: Discover compact symbolic laws governing risky choices and monetary policy to improve predictive models with fewer parameters.
Authors
Ma ZhenYao, Yue Liang, Jian-Qiao Zhu
Abstract
Many scientific phenomena are best understood as outcomes of underlying optimization problems, yet automated scientific discovery has largely focused on recovering equations that describe observed input-output patterns. We introduce OptScientist, a novel automated framework for discovering compact symbolic optimization laws directly from data. OptScientist comprises (i) a model that infers symbolic optimization problems by first learning to represent data as an optimization problem and then extracting its symbolic form, and (ii) an LLM agentic system embedding the model in a discovery process that integrates theoretical priors from scientific literature, discovers candidate laws, abstracts their underlying mechanisms, and suggests new data to collect. We first evaluate OptScientist on OptFeynman, a novel benchmark of 99 physics-derived optimization problems, where OptScientist recovers ground-truth laws for over 80% of the problems and remains robust to noisy contextual information, while substantially outperforming machine-learning, symbolic, and LLM-based model-discovery baselines. On human risky choice and central-bank monetary policy, OptScientist discovers compact symbolic optimization laws that achieve held-out predictive performance competitive with leading baselines, while using few parameters and substantially fewer tokens than LLM baselines. Overall, OptScientist extends automated scientific discovery to uncovering optimization laws that generate observed phenomena, enabling automated theory building across the physical, biological, behavioral, and social sciences.