Physicists learn particle interaction rules from messy real-world data without needing clean trajectories

A new mathematical method lets researchers figure out how particles interact with each other using incomplete, unlabeled data — the kind scientists actually collect in experiments. Instead of needing perfect trajectory information, the method works backward from snapshots taken at random intervals, which means it can handle real experimental data that's fragmented by privacy rules or measurement limits.

For decades, studying how particles interact has required either clean experimental data with complete trajectories or expensive computational shortcuts. This method removes that bottleneck by working with the messy snapshots researchers actually get. It means experiments that were previously unusable for this kind of analysis — either too fragmented or too private to release — can now become data sources. The method scales to high-dimensional systems, which matters for anything from fluid dynamics to material science to biological systems where trajectory tracking is expensive or impossible.