Scientific modeling has traditionally evolved through the discovery of measurement variables and their transformation to be most predictive of a physical process. But the transformation of raw measurements into meaningful variables has been mostly done manually, deep learning offers promising avenues to simultaneously discover both the variables of interest and the governing equations directly from measurement data, in both the high-dimensional or partially observation settings. In this project, we develop a family of models that advance this innovative approach to model discovery.

Machine learning and physics both strive to discover models that generalize well to unseen data. However, physics has the advantage of rigorous experimentation and mathematical modeling, ensuring that its foundational models are reliable, robust, interpretable, and generalizable. When physical models fail, there are established methods to refine them — a clarity often missing in machine learning models. This project aims to bridge this gap by integrating known physical constraints, specifically the knowledge of physical units and dimensions, into existing machine learning algorithms. By incorporating units into ML models, we improve their generalizability and ensure they align more closely with fundamental physical laws, such as conservation of energy and mass.

Granular media such as sand, powders, and even nuts are a fascinating class of materials whose behavior can range from gas-like to liquid-like to solid-like states, often transitioning phases within the same domain. Despite their ubiquitous presence (involved in more than 50% of manufacturing), many fundamental questions about them remain unanswered. For example, simple queries like “Where is the maximum normal stress beneath a sand pile?” still lack definitive answers. This project seeks to address these open problems by applying machine learning techniques to model granular materials at various scales. We aim to gain new insights into their complex behaviors and contribute to a better understanding of these intriguing materials.

Almost everything can be considered a complex system — made of smaller things whose interaction gives rise to emergent behavior. Among these, society is the one we relate to the most. Societies morph, change, evolve, and merge like living organisms, and their structures follow patterns that we strive to uncover. Simple agent-based rules often capture a wide variety of social behaviors in a statistical sense. Recently, large language models have opened exciting avenues for modeling these behaviors within an agent-based modeling (ABM) and graph-based frameworks. Additionally, the rich tradition of social modeling offers a wealth of methods to understand the unpredictable interaction of AI agents often used to enhance their intelligence. Our lab focuses on developing modeling tools for social LLMs and AI models for social modeling.