Year: 2024
Type: preprint
Abstract: As data-driven modeling of physical dynamical systems becomes more prevalent, a new challenge is emerging: making these models more compatible and aligned with existing human knowledge. AI-driven scientific modeling processes typically begin with identifying hidden state variables, then deriving governing equations, followed by predicting and analyzing future behaviors. The critical initial step of identification of an appropriate set of state variables remains challenging for two reasons. First, finding a compact set of meaningfully predictive variables is mathematically difficult and under-defined. A second reason is that variables found often lack physical significance, and are therefore difficult for human scientists to interpret. We propose a new general principle for distilling representations that are naturally more aligned with human intuition, without relying on prior physical knowledge. We demonstrate our approach on a number of experimental and simulated system where the variables generated by the AI closely resemble those chosen independently by human scientists. We suggest that this principle can help make human-AI collaboration more fruitful, as well as shed light on how humans make scientific modeling choices.
Source: arXiv (Cornell University)
Authors: Zhang, Kevin, Goldfeder, Judah, Lipson, Hod
Institution: Columbia University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G3791939032, Mathematical and Numerical Analysis of Asymptotically Compatible Discretization of Nonlocal Models, RTG: Research Training in Applied Mathematics at Columbia University, NRI: FND: Learning Visual Dynamics from Interaction, AI Institute in Dynamic Systems, GOALI: Collaborative Research: Model-Predictive Safety Systems for Predictive Detection of Operation Hazards
OpenAlex ID: W4403363993