Harmonizing Matter and Function: Automatic Design and Analysis of Computational Granular Crystals

Achieving higher gains in the density and power consumption of digital electronic processors is becoming progressively challenging due to reaching the limits of miniaturization and integration techniques. Consequently, there is a growing appreciation of unconventional computing paradigms that dismiss classic assumptions on what computation entails and leverage the intrinsic dynamics of alternate physical substrates to create special-purpose computing devices. Metamaterials hold significant promise for constructing the next generation of machines, wherein computation and function are no longer decoupled but combined in a mechanical computing system that interacts with and adapts to its environment.

Granular materials are particularly intriguing for advancing this vision because their discrete nature allows for highly tunable nonlinear dynamics that can be shaped by altering material properties, geometry, and configuration of grains. However, the absence of general mechanistic theories of computation and the daunting complexity of macro-micro relations in granular materials impede the discovery and realization of computational granular machines. This thesis is focused on devising methods that can expand the design space of such machines beyond human intuition and provide the opportunity to systematically traverse their high-dimensional parameter space to find materials with the desired functionalities.

We begin by exploring the dynamics of the granular materials and present a data-driven analysis pipeline based on the modern Koopman theory. Next, we delve into their application in the unconventional computing paradigm and establish a framework for wave-based computing in harmonically driven granular materials. Following that, we develop an optimization pipeline using Evolutionary Algorithms and utilize it in a series of experiments to demonstrate the computational capabilities of disordered granular configurations. The results indicate that granular materials have strongly nonlinear dynamics that can be exploited to polycompute universal logic functions. Further, we develop a gradient-based optimization pipeline and show that it discovers more efficient configurations with less computational effort. Lastly, the physical realization of computational granular materials is discussed, and some preliminary outcomes are presented.

Overall, the results presented in this thesis could serve as a universal tool for optimizing granular assemblies with desired temporal and spatial responses and offer insights into design principles that can guide the realization of increasingly multifunctional granular machines.