IMPLEMENTATION OF PHYSICS-INFORMED NEURAL NETWORKS USING SPIRAL OPTIMIZATION IN DETERMINING SOLUTION FOR BLACK-SCHOLES EQUATION
All dynamic states that exist in the universe can be formed into a partial differential equation. However, this does not guarantee that the partial differential equation has a simple numerical solution. Physics-informed neural networks (PINN), introduced by Raissi, is a method that can be used to...
Saved in:
| Main Author: | |
|---|---|
| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/71789 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | All dynamic states that exist in the universe can be formed into a partial differential
equation. However, this does not guarantee that the partial differential equation
has a simple numerical solution. Physics-informed neural networks (PINN), introduced
by Raissi, is a method that can be used to find approximate solutions for
partial differential equations related to laws of pyhsics such as the Burger equation
or Schrodinger equations. In general, in carrying out the training process, PINN
and standard neural networks use derivative-based optimization tools. However, in
this research, another approach is used where PINN is combined with a metaheuristic
method, namely the spiral algorithm. To support the analysis of the PINN
method and the spiral algorithm, the Black-Scholes partial differential equation will
be used as the main object of research. The effect of parameters on the results in
PINN and the spiral algorithm will be examined more deeply in this study. |
|---|