Learning collective motions in soft matter by dynamic mode decomposition

Collective motion in soft matter is ubiquitous and has far-reaching implications across various applications. Analytical models are often preferred to understand and predict these behaviors, particularly in dynamic systems. However, the inherent complexity of soft matter makes analytical modeling challenging. In contrast, the growing availability of data offers new opportunities for insight. Dynamic Mode Decomposition (DMD), a data-driven technique, has gained popularity for analyzing spatiotemporal patterns.

Here, by extracting the dynamic modes using dynamic mode decomposition, we investigate collective motions from the spatiotemporal data of soft matter ranging in different length- and time- scales: a protein from molecular dynamics simulation, mesoscopic active particles, and macroscopic vortex. We find that while original dynamic mode decomposition effectively identifies stable collective modes at a larger scale and successfully reconstructs and predicts the spatiotemporal behavior, it suffers from spurious damping due to noise at smaller scales. Improved methods, such as unbiased and noise-aware decomposition methods, are required. Ultimately, our goal is to reverse engineer the soft matter systems to achieve targeted collective motions.