Machine Learning meets Nuclear Physics
Contents
What is this talk about?
More material
Why? Basic motivation
Overview
Machine Learning and AI and Nuclear Physics
What is Machine Learning?
A new world
Lots of room for creativity
Types of Machine Learning
A simple perspective on the interface between ML and Physics
ML in Nuclear Physics, Examples
More examples
Education and Work force development
Selected References
What are the Machine Learning calculations here based on?
Some members of the ML family
A Frequentist approach to data analysis
What are the basic ingredients?
Artificial neurons
A simple perceptron model
Neural network types
The first system: electrons in a harmonic oscillator trap in two dimensions
Quantum Monte Carlo Motivation
Quantum Monte Carlo Motivation
Quantum Monte Carlo Motivation
Quantum Monte Carlo
The trial wave function
The correlation part of the wave function
Resulting ansatz
Energy derivatives
Derivatives of the local energy
How do we define our cost function?
Meet the variance and its derivatives
The variance defines the cost function
Why Boltzmann machines?
A standard BM setup
The structure of the RBM network
The network
Goals
Joint distribution
Defining different types of RBMs
Representing the wave function
Choose the cost/loss function
Running the codes
Energy as function of iterations, \( N=2 \) electrons
Energy as function of iterations, no Physics info \( N=2 \) electrons
Onebody densities \( N=6 \), \( \hbar\omega=1.0 \) a.u.
Onebody densities \( N=6 \), \( \hbar\omega=0.1 \) a.u.
Onebody densities \( N=30 \), \( \hbar\omega=1.0 \) a.u.
Onebody densities \( N=30 \), \( \hbar\omega=0.1 \) a.u.
Or using Deep Learning Neural Networks
Replacing the Jastrow factor with Neural Networks
Conclusions and where do we stand
Appendix: Mathematical details
Marginal Probability Density Functions
Conditional Probability Density Functions
Python version for the two non-interacting particles
Onebody densities \( N=6 \), \( \hbar\omega=1.0 \) a.u.
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