Inferring force laws from many-body systems in dusty plasma by machine learning Public

Abstract

In the era of big data, machine learning (ML) is a necessity. Numerous ML studies

have been conducted to analyze data within physical systems. Most of these

studies utilize data simulated by known, well-defined equations. Others attempt to

predict the future states of real experiments, rather than unraveling the governing

mechanisms (the physics) behind them. Predicting the governing mechanisms in real

experiments poses significant challenges. During my Ph.D., I have applied ML methods

to a complex many-body system, dusty plasma (DP), which is prevalent both in

the cosmos and in industrial applications, and I validated these models’ predictions

using only experimental data. DP exhibits many intriguing collective behaviors, although

the underlying mechanisms, including charging theories, are often modeled

using theories with assumptions that are difficult to test, resulting in large errors.

Throughout my six years of Ph.D. research, I initially constructed a tomography system

to track the 3D trajectories of individual particles, achieving sub-pixel accuracy

for tens of particles over several minutes. Subsequently, I analyzed the tracked ‘Brownian’

motion of one and two particles around their equilibrium positions and proposed

a linearized model for these small-amplitude motions. Applying ML, I predicted the

linear coefficients with 50% better accuracy than conventional methods, including

Fourier analysis. This prediction was corroborated by physically perturbing the particles

from their equilibrium positions. Finally, using the tracked 3D trajectories of

multiple particles, I employed ML to infer their position-dependent interaction forces,

environmental forces, and damping coefficients. Non-reciprocal interactions were observable

in these inferred forces. The charges and masses of different particles could

also be inferred. This inference was substantiated by the consistency between mass

determined from interactions and from damping coefficients. My work demonstrates

the feasibility of using ML to predict governing mechanisms, not just future dynamics,

in real experiments, confirming predictions with real experimental data alone.

My latest model holds great promise for inferring mechanisms in other many-body

systems, such as cells, colloids, and flocking behaviors in macroscopic organisms.

Table of Contents

Contents

1 Introduction 1

1.1 Predicting future vs. predicting physics: challenges in real experiments 1

1.2 Our real experiments: dusty plasma (DP) . . . . . . . . . . . . . . . 4

1.2.1 DP Basic theories and their limitations . . . . . . . . . . . . . 4

1.2.2 Particles as a tool to refine plasma basics . . . . . . . . . . . . 10

1.3 Previous work in our lab: an intermittent collective phenomenon observed

in DP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.4 Overview of thesis topics . . . . . . . . . . . . . . . . . . . . . . . . . 15

2 3D tracking of particles in a dusty plasma by laser sheet tomography 17

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.1.1 Existing DP video-processing approaches . . . . . . . . . . . . 17

2.1.2 A summary of this work . . . . . . . . . . . . . . . . . . . . . 19

2.2 Experimental design . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3 Laser divergence and parallax correction after tracking . . . . . . . . 23

2.4 Results: tracking individual 3D trajectories for tens of particles over

minutes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.5 Conclusions: benefits of simultaneous kinetic information . . . . . . . 31

3 Extracting forces from noisy 1-2 particle dynamics in DP 34

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.2 Experimental methods and particle tracking . . . . . . . . . . . . . . 36

3.3 single particle motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.3.1 The linearized model . . . . . . . . . . . . . . . . . . . . . . . 39

3.3.2 Handling random noise, parameter drift, and measurement error

in simulation . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.3.3 Features for ML . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.3.4 ML methods and performance . . . . . . . . . . . . . . . . . . 51

3.3.5 Labeling experimental data . . . . . . . . . . . . . . . . . . . 54

3.3.6 Predicting experimental data - Results . . . . . . . . . . . . . 55

3.4 Two particle potion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.4.1 The linearized model . . . . . . . . . . . . . . . . . . . . . . . 58

3.4.2 Simulation details . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.4.3 Features of two particle motion . . . . . . . . . . . . . . . . . 62

3.4.4 Predicting experimental data - results . . . . . . . . . . . . . . 63

3.5 Limitations of this approach . . . . . . . . . . . . . . . . . . . . . . . 67

4 Learning generalized force laws in many-particle DP 70

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.2 Experiments and model . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.3 Model prediction results . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.4 Inference of plasma and particle properties . . . . . . . . . . . . . . . 79

4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

4.6 Appendix for Chap. 4 . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.6.1 Model details . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.6.2 Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.6.3 Fitting of charge and mass for each particle from the model . 92

4.6.4 Dusty plasma simulations . . . . . . . . . . . . . . . . . . . . 93

5 Conclusion and future directions 100

Bibliography 106

About this Dissertation

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School	Laney Graduate School
Department	Physics
Degree	Ph.D.
Submission	Dissertation
Language	English
Research Field	Physics, Fluid and Plasma Artificial Intelligence
Mot-clé	Dusty plasma Time series processing machine learning
Committee Chair / Thesis Advisor	Justin C. Burton, Emory University
Committee Members	Ilya M. Nemenman, Emory University Eric R. Weeks, Emory University Edward Jr. Thomas, Auburn University Stefan Boettcher, Emory University

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