Advanced Bayesian Computation methods for modeling and inference in complex dynamical networks
Abstract
Complex models, involving many subsystems that interact in non-trivial (sometimes hard to predict) ways, appear to be ubiquitous in some of the most active #elds of science and engineering, such as biochemistry, meteorology and climate science, or complex communication and control networks. There are many di#culties yet, however, both to understand the relevant structures and schemes (and the interconnections between research #elds that rely on very similar models to solve seemingly di#erent problems) and to implement useful and reliable algorithms (for model selection, model learning, estimation, prediction, etc.) that put complex models e#ectively to work in real-world scenarios. In this project we are addressing both issues. Our #rst goal is to investigate a class of dynamical network-like models with layered structure, where each layer of the model encodes a di#erent set of dynamical features of the real-world system, and one or more layers may be active (contributing to the system dynamics) at any time instant. We will investigate therange of applicability of this class of models. The goal is to rigorously establish the family of time series models that multilayer network structures can embed. Our preliminary results show that multilayer networks are indeed very general models (almost universal, in a certain probabilistic sense), and we aim at making this claim a rigorous, provable statement.The other class of models we intend to study includes dynamical systems which display features on very di#erent time or space resolutions. Such systems, often r"eferred to as multi-scale"", are relevant in meteorology, climate science, materials science, operations research or chemistry, to n"ame a few #elds. For example, in order to make an accurate weather prediction in a given target region (e.g., France), one has to take into account the state and dynamics ofthe atmosphere in and extended region (the North Atlantic and western and central Europe), while at the same time reckon with meteorological phenomena taking place at a much smaller space scale on or within the original target region. We will address the design of discrete-time, discrete-space models of multiscale systems that can be mathematically represented by sets of stochastic partial di#erential equations (SPDEs). The aim when constructing these discrete (computer friendly) m"odels is to make them a perfect #t"" with the estimation, prediction or learning algorithms that one may want to to run on them. We" will also seek connections between the two families of models, multilayer and multiscale. Speci#cally, we will study how multilayer network models can be used to represent multiscale complex systems.Finally, the third aim of the project is to devise algorithms for learning, estimation and prediction that run e#ciently on the models of interest. This is not straightforward because most of this model are expected to be high dimensional and most inference algorithms are subject to one form or the other of the curse of dimensionality (unless they sacri#ce per-formance for simplicity). We will explore some techniques that have been suggested in the last few years in the #eld of Bayesian computation (including space-time particle #lters, non-reversible Markov chain Monte Carlo methods, or nonlinear adaptive importance samplers). We expect that our approach, based on the joint design of the models and their associated inference algorithms, will bring improvements in accuracy and reliability for range of inference problems on complex systems.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Apr 24, 2019
- Source ID
- N000141912226
Entities
People
- Joaquín Míguez
Organizations
- Office of Naval Research
- United States Navy
- Universidad Carlos III de Madrid