Understanding and Designing Complex Systems: Response to "A framework for optimal high-level descriptions in science and engineering---preliminary report"

Building compact models of nonlinear processes goes to the heart of our understanding the complex world around us--a world replete with unanticipated, emergent patterns. Via discovery mechanisms that we do not yet understand well, we eventually do come to know many of these patterns, even if we have never seen them before. Such discoveries can be substantial. At a minimum, compact models that capture such emergent "macrostates" are essential tools in harnessing complex processes to useful ends. Most ambitiously, one would hope to automate the discovery process itself, providing an especially useful tool for the era of Big Data. One key problem in the larger endeavor of pattern discovery is dimension reduction: reduce the high-dimensional state space of a stochastic dynamical system into smaller, more manageable models that nonetheless still capture the relevant dynamics. The study of complex systems always requires this.