# Research introduction: System dynamics

Research introduction: System dynamics

Hello. I’m Tatsuya Yokoyama, a 3rd year doctoral student at Yamada Lab.
For the purpose of elucidating the decay phenomenon of fusion plasma, I am conducting research by making full use of a data-driven approach using machine learning techniques.
In my previous blog (March), I told you about the remote experiment.
This time, I would like to introduce system dynamics as a story with a slightly different coat color.
In the lecture “Practical Exercises on Fusion” in the Department of Advanced Energy, we will work on the task of simulating the operation of a fusion reactor using system dynamics.

System dynamics is a method of displaying a model described by a differential equation in a diagram on software and executing a numerical simulation. A typical expression is called “stock & flow”, which expresses a change in state by combining the abundance (stock) and inflow / outflow (flow) of a certain object.

Let’s take a concrete example. Infectious diseases are a hot topic these days, but the spread of the infection can be mathematically modeled by differential equations.
The most basic model first divides the population into three states. The first is people who have not yet been infected or may be infected (Susceptible). The second is those who are currently infected (Infected). These people have a certain probability of transmitting the infection to others. Then, after a certain period of time, it recovers and becomes immune (Recovered). The acronym for three states (Susceptible, Infected, Recovered) is called the SIR model.

The flow of quantity (here, the number of people) is from S to I and from I to R, as shown in the above figure. This is shown in a diagram on the software, various parameters are set, and the computer automatically solves the rest. The figure below shows the actual solution, and it can be seen that the number of infected people (orange line) increases once, but then converges.

As an aside, Professor Hiroshi Nishiura of Kyoto University (Hokkaido University at that time), who became famous as “Uncle 80%”, is an expert in such mathematical models of infectious diseases. If you want to know more about the mathematical model of infectious diseases, why not read Professor Nishiura’s treatise.

Setting detailed parameters that are related to each other is quite a difficult task, but the feature of system dynamics is that it is easy to understand and connect to discussions by expressing it as a diagram.

A fusion reactor can be thought of as a complex system that circulates hydrogen isotope atoms, which are fuel. There are various elements in it, such as the generation of impurities and burning debris, the heating of plasma from the outside, and the extraction of heat to generate electricity, which are related to each other. There are many parameters for describing equations, and the same parameters appear many times in various equations. Rather than programming this one by one, using system dynamics has the advantage of being able to share work and understanding widely even if you are not an expert.

This time, we have introduced system dynamics as a method for simulating a “system” called a fusion reactor.