Reinforcement Learning for the Optimization of Explicit Runge-Kutta Method Parameters
(2023) In Bachelor's Theses in Mathematical Sciences NUMK11 20231Mathematics (Faculty of Engineering)
Mathematics (Faculty of Sciences)
Centre for Mathematical Sciences
- Abstract
- Reinforcement learning is one of the three main paradigms in machine learning, which is increasingly used as a method to approach scientific problems. In this thesis, we introduce and use reinforcement learning to find the optimal parameters of a numerical solver.
We first motivate that solving the linear systems can be done by solving initial value problems. These initial values problems can then be solved with an explicit, two stages Runge-Kutta solver, for which we need to find the optimal parameters for the solver, depending on the parameters of the problem.
Using reinforcement learning, and in particular policy gradient methods, we find that with some care, reinforcement learning can be used to learn the
solver parameters as... (More) - Reinforcement learning is one of the three main paradigms in machine learning, which is increasingly used as a method to approach scientific problems. In this thesis, we introduce and use reinforcement learning to find the optimal parameters of a numerical solver.
We first motivate that solving the linear systems can be done by solving initial value problems. These initial values problems can then be solved with an explicit, two stages Runge-Kutta solver, for which we need to find the optimal parameters for the solver, depending on the parameters of the problem.
Using reinforcement learning, and in particular policy gradient methods, we find that with some care, reinforcement learning can be used to learn the
solver parameters as a function of the problem parameters. These results are however tempered by some limitations, as the solver can diverge in certain cases, and convergence speed remains low in general. (Less) - Popular Abstract
- As animals, we learn about the world and how to interact with the world by trial and errors, and are "rewarded" when it goes well. This idea, applied to computer program is called reinforcement learning, and it does not take long nowadays to find applications of it, be it when interacting with a chat bot or when activating the adaptative cruise control of a car.
In this thesis, we study differential equations, which are equations that, when solved, help us understand physical phenomena, for example the trajectory of a ball when it is kicked, or how the temperature in the room changes when we turn on the AC. While solving these equations on a computer is possible, some parameters need to be chosen judiciously, as the wrong solution can... (More) - As animals, we learn about the world and how to interact with the world by trial and errors, and are "rewarded" when it goes well. This idea, applied to computer program is called reinforcement learning, and it does not take long nowadays to find applications of it, be it when interacting with a chat bot or when activating the adaptative cruise control of a car.
In this thesis, we study differential equations, which are equations that, when solved, help us understand physical phenomena, for example the trajectory of a ball when it is kicked, or how the temperature in the room changes when we turn on the AC. While solving these equations on a computer is possible, some parameters need to be chosen judiciously, as the wrong solution can be found otherwise. To mitigate this issue, we use reinforcement learning in this thesis to train a program that find these parameters automatically for some specific equations. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9132542
- author
- Fournier, Mélanie LU
- supervisor
- organization
- course
- NUMK11 20231
- year
- 2023
- type
- M2 - Bachelor Degree
- subject
- keywords
- reinforcement learning, numerical analysis, Runge-Kutta, policy gradient, REINFORCE
- publication/series
- Bachelor's Theses in Mathematical Sciences
- report number
- LUNFNA-4048-2023
- ISSN
- 1654-6229
- other publication id
- 2023:K20
- language
- English
- additional info
- Github repository with the code used to make experiment available at https://github.com/MelanieInky/ThesisBook
- id
- 9132542
- date added to LUP
- 2023-10-09 16:54:42
- date last changed
- 2023-10-09 16:54:42
@misc{9132542,
abstract = {{Reinforcement learning is one of the three main paradigms in machine learning, which is increasingly used as a method to approach scientific problems. In this thesis, we introduce and use reinforcement learning to find the optimal parameters of a numerical solver.
We first motivate that solving the linear systems can be done by solving initial value problems. These initial values problems can then be solved with an explicit, two stages Runge-Kutta solver, for which we need to find the optimal parameters for the solver, depending on the parameters of the problem.
Using reinforcement learning, and in particular policy gradient methods, we find that with some care, reinforcement learning can be used to learn the
solver parameters as a function of the problem parameters. These results are however tempered by some limitations, as the solver can diverge in certain cases, and convergence speed remains low in general.}},
author = {{Fournier, Mélanie}},
issn = {{1654-6229}},
language = {{eng}},
note = {{Student Paper}},
series = {{Bachelor's Theses in Mathematical Sciences}},
title = {{Reinforcement Learning for the Optimization of Explicit Runge-Kutta Method Parameters}},
year = {{2023}},
}