Machine Learning and Quantum Mechanics for Many Interacting Particles
Contents
What is this talk about?
More material
Why? Basic motivation
Overview
Machine Learning and Physics
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
Selected References
What are the basic ingredients?
Neural network types
Nuclear Physics Experiments Argon-46
Why Machine Learning?
Why Machine Learning for Experimental Analysis?
More arguments
The first theoretical system: electrons in a harmonic oscillator trap in two dimensions
Quantum Monte Carlo Motivation
Quantum Monte Carlo Motivation
Quantum Monte Carlo Motivation
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
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
What are the Machine Learning calculations here based on?
Energy as function of iterations, no Physics info \( N=2 \) electrons
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