EAGER: Real-Time: Search for dynamical dependencies and natural time-scales of physical processes

University Of California-Irvine, Irvine CA

Investigators

Abstract

A fundamental problem in physical sciences and engineering is to identify dependencies and dynamical relations between interacting processes for understanding causal relationships and advancing predictive modeling. Indeed, historically, such dependences often formed the basis of physical laws. The abundance of large data-sets about complex natural or engineered systems in our modern technological world, has brought a sense of urgency to the need for reliable and versatile machine learning tools to detect relations between processes. The starting point of the project is the realization that often the observational time scale at which data is collected may not be the native time scale at which interactions occur and thus sampling might obfuscate the nature of such relations. Indeed, linear dynamical relations between continuous-time processes may not be readily detectable from data collected at any finite sampling rate. This project will develop methodologies that will allow to fully recover sought relations between processes at the natural time-scale from data at a (typically coarser) observational time-scale. Theory and statistical learning tools that will be developed for that purpose will be applied to geophysical processes, such as identifying relationships between climate variables using a suite of observations from ground and multi-satellite sensors at different spatio-temporal scales. When relations between variables are dynamic (i.e., the interaction relies on memory in the system), sampling hides the nature of dynamical dependencies. Specifically, in linear stochastic processes, dynamical dependencies between vector-valued processes are reflected in the nullity of the power spectral density matrix when this is estimated at the natural time-scale of the process. At the observational sampling rate, the corresponding nullity no longer relates to the structure of the dynamical relations. Yet, with proper analysis the dynamical relations can be recovered by projecting sample-models to the natural time-scale of the processes involved. In fact, for linear stochastic processes there is a fastest process time-scale that is consistent with the coarser scale observational data, and it is at that fine scale that models can be projected via solving suitable algebraic equations. At any coarser scale, dynamical dependencies cannot be readily detected. The project will focus on how to learn and recover the natural time-space scale at which dynamical dependencies must be sought. Statistical learning tools will be developed and applied to geophysical data as proof of concept. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.