Part II
Applications to Physics
The second part describes the application of machine learning to theoretical physics,
which has recently begun, with examples and history. Because machine learning
is one of the new techniques in science, its involvement in physics is diverse.
From the standard viewpoints in physics: “inverse problems”, “phases”, “differential
equations”, “quantum many systems”, and “spacetime”, we will look at possible
standpoints of machine learning, historical development of it, and some of the
recent developments. This understanding of machine learning from the perspective
of physics will provide readers’ perspectives on the relationship between machine
learning and physics so far and in the future, and will be helpful for study and
research.
Chapter 7: Inverse Problems in Physics First, we consider inverse problems in
physics. In fact, inverse problems are at the heart of revolutionary development
in physics. What does it mean to solve an inverse problem? What is the meaning
of the phrase “machine learning is good at solving inverse problems”? You will
gain a comprehensive perspective and significance in applying machine learning
to theoretical physics.
Chapter 8: Detection of Phase Transition by Machines As an approach to the
important question of whether machines can learn the discovery of physics,
this chapter examines the question “Can phase transitions be found by deep
learning?” Understanding phases is one of the most important subjects in physics.
Can machine learning really discover the thermal phase transition in the basic
physical system: the Ising model?
Chapter 9: Dynamical Systems and Neural Networks Neural networks are a way
of expressing a variety of nonlinear functions, but can also be thought of as waves
of information propagating between layers. In this chapter, we show that such
multi-layer propagation can be interpreted as the time evolution of dynamical
systems, and hence of Hamiltonian systems, and look at the close relationship
between the fundamental concept of “time evolution” in physics and deep neural
networks.
Applications to Physics
The second part describes the application of machine learning to theoretical physics,
which has recently begun, with examples and history. Because machine learning
is one of the new techniques in science, its involvement in physics is diverse.
From the standard viewpoints in physics: “inverse problems”, “phases”, “differential
equations”, “quantum many systems”, and “spacetime”, we will look at possible
standpoints of machine learning, historical development of it, and some of the
recent developments. This understanding of machine learning from the perspective
of physics will provide readers’ perspectives on the relationship between machine
learning and physics so far and in the future, and will be helpful for study and
research.
Chapter 7: Inverse Problems in Physics First, we consider inverse problems in
physics. In fact, inverse problems are at the heart of revolutionary development
in physics. What does it mean to solve an inverse problem? What is the meaning
of the phrase “machine learning is good at solving inverse problems”? You will
gain a comprehensive perspective and significance in applying machine learning
to theoretical physics.
Chapter 8: Detection of Phase Transition by Machines As an approach to the
important question of whether machines can learn the discovery of physics,
this chapter examines the question “Can phase transitions be found by deep
learning?” Understanding phases is one of the most important subjects in physics.
Can machine learning really discover the thermal phase transition in the basic
physical system: the Ising model?
Chapter 9: Dynamical Systems and Neural Networks Neural networks are a way
of expressing a variety of nonlinear functions, but can also be thought of as waves
of information propagating between layers. In this chapter, we show that such
multi-layer propagation can be interpreted as the time evolution of dynamical
systems, and hence of Hamiltonian systems, and look at the close relationship
between the fundamental concept of “time evolution” in physics and deep neural
networks.