Explicit and Implicit computing
Essay about the introduction of the class
2025 Fall Monte Carlo Methods and their Applications (lecturer: Prof. Hwang) Lee Seonggyu
In the first lecture of the class operated by Prof. Hwang, he explained what scientific computing is and classified the approaches of scientific computing. I had thought that scientific computing differs from numerical analysis (or numerical methods), but he informed that scientific computing contains numerical analysis, it is interesting. And he said that numerical methods are roughly divided to explicit programming and implicit programming. In my opinion about his explanation, explicit programming depends on an algorithm and a theory designed by humans, therefore the mechanisms of explicit programming can be explained by the developer of the methods. The performance of implicit programming may depend more on datasets than methods designed by humans. There are different advantages and disadvantages of two programming methods. However, I think that the two approaches are combined. I have researched speech enhancement and published one paper with deep learning models based on ordinary differential equations (ODEs). In the paper, I introduced flow matching which trains continuous normalizing flow (CNF) which transforms a simple probability distribution into a desired distribution. CNF is described by an ODE. In the work, I trained CNF with deep learning models, which means that I utilized implicit methods. And I used Euler method which is a traditional numerical method. Furthermore, I proved that my proposed method described by an ODE can be described by a stochastic differential equation (SDE). As I said, I utilized explicit programming, implicit programming and proved a mathematical property. From my experience and my opinion, it is important to combine mathematical theories and explicit/implicit programming.