Coarse graining

Also, fluctuation theorems

November 11, 2014 — September 9, 2024

algebra
Bayes
machine learning
networks
physics
sciml
snarks
statmech
surrogate
Figure 1

AFAICT, coarse graining describes the question “how much worse do your predictions get as you discard information in some orderly fashion?”, as framed by physicists.

Do “renormalization groups”, whatever they are, fit in here? Fast-slow systems?

The ML equivalent seems to be multi-fidelity modelling.

1 Fluctuation theorems

2 Green-Kubo relations

3 Persistent homology

What’s that? Petri et al. (2014):

Persistent homology is a recent technique in computational topology developed for shape recognition and the analysis of high-dimensional datasets.… The central idea is the construction of a sequence of successive approximations of the original dataset seen as a topological space X. This sequence of topological spaces \(X_0, X_1, \dots{}, X_N = X\) is such that \(X_i \subseteq X_j\) whenever \(i < j\) and is called the filtration.

5 Incoming

  • jkbren/einet: Uncertainty and causal emergence in complex networks

    Python code for calculating effective information in networks. This can then be used to search for macroscale representations of a network such that the coarse-grained representation has more effective information than the microscale, a phenomenon known as causal emergence. This code accompanies the recent paper: Klein and Hoel (2020)

6 References

Bar-Sinai, Hoyer, Hickey, et al. 2019. Learning Data-Driven Discretizations for Partial Differential Equations.” Proceedings of the National Academy of Sciences.
Bar-Yam. 2003. Dynamics Of Complex Systems.
Beretta. 2020. The Fourth Law of Thermodynamics: Steepest Entropy Ascent.” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.
Castiglione, and Falcioni. 2008. Chaos and Coarse Graining in Statistical Mechanics.
Cérou, and Guyader. 2016. Fluctuation Analysis of Adaptive Multilevel Splitting.” The Annals of Applied Probability.
Crooks. 1999. The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences.” Physical Review E.
Dewar. 2003. Information Theory Explanation of the Fluctuation Theorem, Maximum Entropy Production and Self-Organized Criticality in Non-Equilibrium Stationary States.” Journal of Physics A: Mathematical and General.
Doney. 2007. Fluctuation Theory for Lévy Processes: Ecole d’eté de Probabilités de Saint-Flour XXXV, 2005. Lecture Notes in Mathematics 1897.
Fodor, Nardini, Cates, et al. 2016. How Far from Equilibrium Is Active Matter? Physical Review Letters.
Hasegawa, and Van Vu. 2019. Uncertainty Relations in Stochastic Processes: An Information Inequality Approach.” Physical Review E.
Hoel. 2017. When the Map Is Better Than the Territory.” Entropy.
Hoel, Albantakis, Marshall, et al. 2016. Can the Macro Beat the Micro? Integrated Information Across Spatiotemporal Scales.” Neuroscience of Consciousness.
Hoel, Albantakis, and Tononi. 2013. Quantifying Causal Emergence Shows That Macro Can Beat Micro.” Proceedings of the National Academy of Sciences.
Kelly, and Melbourne. 2014. Deterministic Homogenization for Fast-Slow Systems with Chaotic Noise.”
Klein, and Hoel. 2020. The Emergence of Informative Higher Scales in Complex Networks.” Complexity.
Komorowski, Landim, and Olla. 2012. Fluctuations in Markov Processes: Time Symmetry and Martingale Approximation. Grundlehren Der Mathematischen Wissenschaften : A Series of Comprehensive Studies in Mathematics 345.
Lecomte, Appert-Rolland, and Wijland. 2007. Thermodynamic Formalism for Systems with Markov Dynamics.” Journal of Statistical Physics.
Marsland, and England. 2018. Limits of Predictions in Thermodynamic Systems: A Review.” Reports on Progress in Physics.
Messel. 1952. The Solution of the Fluctuation Problem in Nucleon Cascade Theory: Homogeneous Nuclear Matter.” Proceedings of the Physical Society. Section A.
Messel, and Potts. 1952. Note on the Fluctuation Problem in Cascade Theory.” Proceedings of the Physical Society. Section A.
Noid. 2013. “Perspective: Coarse-Grained Models for Biomolecular Systems.” The Journal of Chemical Physics.
Norton. 2013. All Shook Up: Fluctuations, Maxwell’s Demon and the Thermodynamics of Computation.” Entropy.
Onsager, and Machlup. 1953. Fluctuations and Irreversible Processes.” Physical Review.
Petri, Expert, Turkheimer, et al. 2014. Homological Scaffolds of Brain Functional Networks.” Journal of The Royal Society Interface.
Plis, Danks, and Yang. 2015. Mesochronal Structure Learning.” Uncertainty in Artificial Intelligence : Proceedings of the … Conference. Conference on Uncertainty in Artificial Intelligence.
Searles, and Evans. 2000. The Fluctuation Theorem and Green–Kubo Relations.” The Journal of Chemical Physics.
Seifert. 2012. Stochastic Thermodynamics, Fluctuation Theorems and Molecular Machines.” Reports on Progress in Physics.
Sethna. 2006. Statistical Mechanics: Entropy, Order Parameters, and Complexity.
Shalizi, and Moore. 2003. What Is a Macrostate? Subjective Observations and Objective Dynamics.”
Still, Sivak, Bell, et al. 2012. Thermodynamics of Prediction.” Physical Review Letters.
Touchette. 2011. A Basic Introduction to Large Deviations: Theory, Applications, Simulations.”
Voth. 2008. Coarse-Graining of Condensed Phase and Biomolecular Systems.
Wolpert. 2021. Fluctuation Theorems for Multiple Co-Evolving Systems.” arXiv:2003.11144 [Cond-Mat].