Data-driven study of complex systems: from nonlinear PDEs to crumpled papers

Data-driven methods, and Machine-Learning in particular, became very popular in many diverse fields due to their unprecedented ability to identify recurring features, causal relations and complex correlation structures. For the same reasons, the application of these methods to the physical sciences has also attracted much attention, though the field is still very much in its infancy. In this talk I will discuss two applications of Machine-Learning to the study of complex systems: First, I will show how data-driven discretization of nonlinear PDEs can produce accurate low-resolution models, effectively providing a coarse-grained equation which accounts for sub-gridscale physics. Second, I will discuss crumpling of thin sheets and how Machine-Learning can be insightful in studying the emergent patterns, by augmenting the dataset with in-silico calculations of a related system - rigid origami. This also suggests a general strategy of applying data-driven methods to experimental systems where data is scarce or expensive.