Searching for Numerical Models of Chemical and Biological Dynamics

Modeling and simulation are central to scientific discovery. Digital twins and in silico experiments enable faster hypothesis testing, cheaper experiments, and experiments on systems that cannot be manipulated directly. Where ab initio simulation is prohibitively expensive, or the rules governing a system are too complex to formalize by hand, neural networks are commonly used in place of an explicit simulator. This removes the need to write the simulator by hand, but the result is a black box. The underlying mechanism cannot be inspected, limiting validation of scientific correctness and possible insight. We close this gap with AutoSim, a programmatic regression system in which coding agents write human-readable numerical models fitted to observed data. We evaluate it on three chemical and biological systems of increasing complexity: simulated Gray–Scott reaction–diffusion, a continuum active matter model, and real-world microscopy data of self-organizing behavior in oil droplets. On simulated systems, AutoSim-designed programs reach the lowest error among neural, symbolic, and generative baselines, while additionally providing inspection-ready code artifacts. On the oil droplets, where the fields that drive the motion are difficult to observe, no method clearly simulates accurate droplet movement. However, the AutoSim program models droplets as objects rather than pixels and shows realistic movement. We propose this automatic process for numerical simulation development as a new tool for insights into biological and chemical processes.