Inference for Dynamical Systems
Inference for Dynamical Systems
20 January 2021 ...
Inference for Dynamical Systems ‒ A seminar series
Co-Organizers: Adam Rupe (CNLS, Los Alamos) and James P. Crutchfield (UC Davis)
Background & Goals
Many of us are interested in computational mechanics, so that will be a major focus, but these meetings are for a more general discussion of theory and algorithms for inference and dynamical systems. The meetings will be moderately informal and flexible.
Topical Areas
This seminar aims to address the following:
•Continuum computational mechanics
•Geometry in inference (e.g. diffusion maps, derivative/delay embeddings, ...)
•Neural networks for dynamical system inference
•Inference for bioacoustics signals
•Ensemble analogue forecasting
•Information measures and information processing for continuous systems
•Inference of causal mechanisms
Presentations:
1.20 January 2021: Adam Rupe (CNLS, LANL) on Ergodic Theory & Dynamical Process Modeling, Part I
2.27 January 2021: Adam Rupe (CNLS, LANL) on Ergodic Theory & Dynamical Process Modeling, Part II
Computational mechanics was originally conceived as a framework for modeling fully-discrete (i.e. symbolic) stochastic processes. To generalize computational mechanics to a continuum setting, we first need to clarify the types of continuous processes we wish to model. I will refer to these continuous processes as dynamical processes, and give a (semi) rigorous formulation using ergodic theory and the Koopman and Perron-Frobenius operators. I will also provide a brief (noncomprehensive) overview of modeling approaches for dynamical processes.
Part I Talk video: CSC host or Google host
3.3 February 2021: Nicolas Brodu (INRIA, Bordeaux) on Continuous Causal States
The associated paper is quite long and tedious to go through. Instead, I'll stick to the main concepts, give you intuition of what's going on, without entering all details. I will show applications of the method to real data sets. More importantly for me, I will also speculate on some physics connexions that I would like to have your feedback on. Make it hopefully an interactive session, even if that means not reaching to the end of what I planned to present (which may be continued later on).
4.10 February 2021: Stefan Klus (University of Surrey) on Transfer Operators
Slides (PDF)
5.17 February 2021: Nina Miolane (UC Santa Barbara) on Geometric Modeling for Dynamical Systems
GeomStats: A Python Package for Riemannian Geometry in Machine Learning
6.3 March 2021: Sam Loomis (UC Davis) on The Topology of Prediction
Topology, Measure, and Kernels in Structure Discovery (what the Wasserstein metric can do for us).
Slides (once manuscript is completed)
Talk Video (ditto)
7.17 March 2021: Sarah Marzen (Pitzer College) on Predicting Processes, Potentially Lossily
“Inference, Prediction, and Entropy-Rate Estimation of Continuous-time, Discrete-event Processes”:
https://arxiv.org/abs/2005.03750
“Probabilistic Deterministic Finite Automata and Recurrent Networks, Revisited”:
https://arxiv.org/abs/1910.07663
8.14 April 2021: Adam Rupe on Representation Learning for Dynamical Systems: Linear Modal Decompositions
9. 21 April 2021: Pablo Flores on Prediction and Explanation in Social Sciences
The current access to the public information that millions of users publish on the internet and the advancement of the computational tools that allow researchers to harvest and analyze big amounts of data have created a favorable environment for the study of social behaviors using observational data. Social sciences have a long tradition of seeking out explanations that describe causal mechanisms to understand social phenomena, a process guided by theoretical reasoning. However, the progressive irruption of computational methods in social sciences has created the need to look at the possibility of including predictions as another analytical tool to understand human and social events. The expansion of the explanatory tradition of social science research adding elements of prediction instead of ignoring it should generate a synergistic hybrid approach in which predictions might shed light about patterns that can provide the base for future theoretical advancement. In this context, this presentation is structured in two complementary parts. First, I describe the definitions of explanation and prediction applied to social sciences. Second, I introduce a set of analytical methods from causal inference, time series, and information theory that can be useful in the study of research questions of explanatory or predictive nature.
10.21 July 2021: Adam Rupe (CNLS, LANL) on Learning Implicit Models of Complex Dynamical Systems from Partial Observations
11.20 April 2022: Antonio C. Costa (ENS, Paris, https://antonioccosta.github.io) on Statistical Mechanics of Animal Behavior
Upcoming:
•Alec Boyd: Thermodynamic Machine Learning
•Sam Loomis: Observable Operator Models, a review
•Fushing Hsieh
•And others