Artificial intelligence and machine learning in nuclear physics
Contents
What is this talk about?
Thanks to many
And sponsors
AI/ML and some statements you may have heard (and what do they mean?)
Types of machine learning
Main categories
The plethora of machine learning algorithms/methods
What Is Generative Modeling?
Example of generative modeling, "taken from Generative Deep Learning by David Foster":"https://www.oreilly.com/library/view/generative-deep-learning/9781098134174/ch01.html"
Generative Modeling
Generative Versus Discriminative Modeling
Example of discriminative modeling, "taken from Generative Deeep Learning by David Foster":"https://www.oreilly.com/library/view/generative-deep-learning/9781098134174/ch01.html"
Discriminative Modeling
Taxonomy of generative deep learning, "taken from Generative Deep Learning by David Foster":"https://www.oreilly.com/library/view/generative-deep-learning/9781098134174/ch01.html"
Good books with hands-on material and codes
More references
What are the basic Machine Learning ingredients?
Low-level machine learning, the family of ordinary least squares methods
Setting up the equations
The objective/cost/loss function
Training solution
Ridge and LASSO Regression
From OLS to Ridge and Lasso
Lasso regression
Selected references
Machine learning. A simple perspective on the interface between ML and Physics
ML in Nuclear Physics (or any field in physics)
Scientific Machine Learning
ML for detectors
Physics driven Machine Learning
And more
Argon-46 by Solli et al., NIMA 1010, 165461 (2021)
Many-body physics, Quantum Monte Carlo and deep learning
Quantum Monte Carlo Motivation
Quantum Monte Carlo Motivation
Energy derivatives
Derivatives of the local energy
Why Feed Forward Neural Networks (FFNN)?
Universal approximation theorem
The approximation theorem in words
More on the general approximation theorem
Class of functions we can approximate
Simple example, fitting nuclear masses
Illustration of a single perceptron model and an FFNN
Monte Carlo methods and Neural Networks
Deep learning neural networks, "Variational Monte Carlo calculations of \( A\le 4 \) nuclei with an artificial neural-network correlator ansatz by Adams et al.":"https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.022502"
"Dilute neutron star matter from neural-network quantum states by Fore et al, Physical Review Research 5, 033062 (2023)":"https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.5.033062" at density \( \rho=0.04 \) fm$^{-3}$
Pairing and Spin-singlet and triplet two-body distribution functions at \( \rho=0.01 \) fm$^{-3}$
Pairing and Spin-singlet and triplet two-body distribution functions at \( \rho=0.04 \) fm$^{-3}$
Pairing and Spin-singlet and triplet two-body distribution functions at \( \rho=0.08 \) fm$^{-3}$
The electron gas in three dimensions with \( N=14 \) electrons (Wigner-Seitz radius \( r_s=2 \) a.u.), "Gabriel Pescia, Jane Kim et al. arXiv.2305.07240,":"https://doi.org/10.48550/arXiv.2305.07240"
"Efficient solutions of fermionic systems using artificial neural networks, Nordhagen et al, Frontiers in Physics 11, 2023":"https://doi.org/10.3389/fphy.2023.1061580"
Generative models: Why Boltzmann machines?
The structure of the RBM network
The network
Goals
Joint distribution
Network Elements, the energy function
Defining different types of RBMs (Energy based models)
Gaussian binary
Representing the wave function
Define the cost function
Quantum dots and Boltzmann machines, onebody densities \( N=6 \), \( \hbar\omega=0.1 \) a.u.
Onebody densities \( N=30 \), \( \hbar\omega=1.0 \) a.u.
Expectation values as functions of the oscillator frequency
Extrapolations and model interpretability
Physics based statistical learning and data analysis
Bayes' Theorem
"Quantified limits of the nuclear landscape":"https://journals.aps.org/prc/abstract/10.1103/PhysRevC.101.044307"
Observations (or conclusions if you prefer)
More observations
Possible start to raise awareness about ML in our own field
Additional material
Our network example, simple percepetron with one input
Optimizing the parameters
Implementing the simple perceptron model
Central magic
Essential elements of generative models
Energy models
Probability model
Marginal and conditional probabilities
Change of notation
Optimization problem
Further simplifications
Optimizing the logarithm instead
Expression for the gradients
The derivative of the partition function
Explicit expression for the derivative
Final expression
Introducing the energy model
More compact notation
Binary-binary model
More references
A central paper is the one by Sohl-Dickstein et al, Deep Unsupervised Learning using Nonequilibrium Thermodynamics,
https://arxiv.org/abs/1503.03585
See also Diederik P. Kingma, Tim Salimans, Ben Poole, Jonathan Ho, Variational Diffusion Models,
https://arxiv.org/abs/2107.00630
Calvin Luo
https://calvinyluo.com/2022/08/26/diffusion-tutorial.html
An Introduction to Variational Autoencoders, by Kingma and Welling, see
https://arxiv.org/abs/1906.02691
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