Machine learning through geometric mechanics and thermodynamics

• Název práce v češtině: Strojové učení skrze geometrickou mechaniku a termodynamiku
• Název v anglickém jazyce: Machine learning through geometric mechanics and thermodynamics
• Klíčová slova: strojové učení, termodynamika, mechanika, GENERIC, redukce
• Klíčová slova anglicky: machine learning, thermodynamics, mechanics, GENERIC, reduction
• Akademický rok vypsání: 2019/2020
• Typ práce: disertační práce
• Jazyk práce: angličtina
• Ústav: Matematický ústav UK (32-MUUK)
• Vedoucí / školitel: doc. RNDr. Michal Pavelka, Ph.D.
• Řešitel: skrytý - zadáno a potvrzeno stud. odd.
• Datum přihlášení: 20.02.2020
• Datum zadání: 20.02.2020
• Datum potvrzení stud. oddělením: 02.03.2020
• Datum a čas obhajoby: 24.06.2024 10:00
• Datum odevzdání elektronické podoby: 06.03.2024
• Datum odevzdání tištěné podoby: 23.04.2024
• Datum proběhlé obhajoby: 24.06.2024
• Oponenti: Dr. Pierre Monmarché
• Konzultanti: RNDr. Karel Tůma, Ph.D.

Zásady pro vypracování

We shall focus on three main ideas:

1) Fluid manipulation and control learned by the means of deep reinforcement learning from simulated data:
In the last five years, there has been significant progress in the field of deep reinforcement learning [2,5,6]. One of the fields with potential utilization of the new methods and approaches is control. While there are successful methods used to predict and control the behavior of physical systems with simple and quickly solvable governing equations, these methods are not able to work with an object that is described by for example Navier-Stokes equations, such as fluid. The complex nature of fluid dynamics requires long solving times and fine geometries to calculate and predict correctly. This non-triviality of governing equations may be a suitable problem to apply machine learning methods that are known to excel in such situations. We will be trying to learn the control of the system by observing the state it is in and rewarding appropriate action leading to desired results. The desired results may be e.g. not spilling any fluid.
Since the system of fluid dynamics is likely too complex even for this kind of method, a deep understanding of the system and an appropriate model reduction will be necessary. Multiscale thermodynamics and geometric physics [3,4] should provide grounds for understanding the dimensionality reduction from a broader perspective, opening doors for further generalizations, [8,9].

2) Deep networks in simulations
With the raising popularity of machine learning and neural network, there has been increasing effort in applying their speed and simplicity in simulations of various types. The ability to learn from simulated and experimental data is particularly useful in speeding up the simulations [10] or in creating relations that more adequately describe the studied system [7].
We will try to explore the possibilities neural networks open in either the area of constitutive relations, or in the molecular dynamics.

3) Fluctuations, which are ubiquitous in Nature and thus in experimental data, are in tight relation with dissipation through the fluctuation-dissipation theorem. Therefore, they provide valuable insight into the structure of dissipation governing the measured processes. Such extra information can be used to enhance the vector field reconstruction from [1,2]. Moreover, fluctuations are essential for understanding rare events like chemical reactions [11] and for reasonable phase space sampling.

Seznam odborné literatury

1. D González, Francisco Chinesta, Elías Cueto, Consistent data-driven computational mechanics, AIP Conference Proceedings, vol. 1960, Issue 1, Pages 090005, 2018.
2. B Moya, D Gonzalez, I Alfaro, F Chinesta, E Cueto, Learning slosh dynamics by means of data, Computational Mechanics, 2019
3. H. C. Öttinger, Beyond Equilibrium Thermodynamics, Wiley 2005.
4. Michal Pavelka, Václav Klika and Miroslav Grmela. Multiscale Thermo-Dynamics, de Gruyter (Berlin), 2018
5. Francisco Chinesta, Elias Cueto, Miroslav Grmela, Beatriz Moya, Michal Pavelka, Learning Physics from Data: a Thermodynamic Interpretation, arXiv:1909.01074, submitted
6. Timothy P. Lillicrap, Jonathan J. Hunt, Alexander Pritzel, Nicolas Heess, Tom Erez, Yuval Tassa, David Silver, Daan Wierstra, Continuous control with deep reinforcement learning, arXiv:1509.02971, 2015.
7. C.Zopf, M.Kaliske, Numerical characterisation of uncured elastomers by a neural network based approach, Computers & Structures, Volume 182, 1 April 2017, Pages 504-525.
8. Sam T. Roweis and Lawrence K. Saul. Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500):2323–2326, 2000.
9. Jake VanderPlas, Python Data Science Handbook: Essential Tools for Working with Data, O'Reilly Media, Inc., 2016.
10. Mohammad M. Sultan and Vijay S. Pande, Automated design of collective variables using supervised machine learning featured, J. Chem. Phys. 149, 094106 (2018);
11. A. Mielke, M. A. Peletier & D. R. M. Renger, On the Relation between Gradient Flows and the Large-Deviation Principle, with Applications to Markov Chains and Diffusion, Potential Analysis volume 41, pages1293–1327 (2014).

Předběžná náplň práce v anglickém jazyce

Machine learning is the scientific study of algorithms and statistical models that computer systems use to perform a specific task without using explicit instructions, relying on patterns and inference instead [8,9]. Having a set of trajectories, how to see a pattern expressing the most important features? When the pattern is simple, e.g. motion of a pendulum subject to low fluctuations, autonomous algorithms can recover the evolution equations of the pendulum including the energy functional (Hamiltonian) or dissipative matrix and entropy [1]. When the pattern is complex, however, e.g. evolution in high dimensional systems such as many particle dynamics, it is a formidable task to sort out the pertinet properties from the irrelevant details, and a dimensionality reduction technique has to be employed [2]. On the other hand, it is the goal of modern non-equilibrium thermodynamics [3,4] to reduce the detailed dynamics to less detailed while still covering the relevant overall features. It seems that a point has been reached when a fruitfull marriage of machine learning and non-equilibrium thermodynamics is possible and can enrich both [5].