University of Twente Student Theses
Model-Order Reduction and Control of Partial Differential Equations using Denoising Diffusion Probabilistic Models
Sowa, Agata Marta (2024) Model-Order Reduction and Control of Partial Differential Equations using Denoising Diffusion Probabilistic Models.
Full text not available from this repository.
| Full Text Status: | Access to this publication is restricted |
| Embargo date: | 1 November 2025 |
| Abstract: | Modelling complex systems requires accurate simulations to predict behaviours under various conditions. This research explores the use of Denoising Diffusion Probabilistic Models (DDPMs) to efficiently generate solutions for parametric Partial Differential Equations (PDEs), providing an alternative to traditional computational methods. The research demonstrates that DDPMs can produce accurate and (temporally-)coherent solutions for the 1D Kuramoto-Sivashinsky equation, showing strong generalisation capabilities to scenarios involving unseen parameter values. Additionally, to enhance computational efficiency, dimensionality-reduction techniques, such as Singular Value Decomposition and Autoencoders, were employed to reduce the data's dimensionality. This approach simplifies the generation task by allowing the DDPM to operate on lower-dimensional data. Eventually, DDPMs show potential for generating controlled solutions, supporting applications where system intervention is necessary. While the models exhibited limitations in long-term prediction accuracy, the results indicate that DDPMs can generalise effectively to different instances of the PDE parameter, opening avenues for advanced simulation and control in complex systems. |
| Item Type: | Essay (Master) |
| Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |
| Subject: | 54 computer science |
| Programme: | Computer Science MSc (60300) |
| Link to this item: | https://purl.utwente.nl/essays/104575 |
| Export this item as: | BibTeX EndNote HTML Citation Reference Manager |
Show download statistics for this publication
Show download statistics for this publicationRepository Staff Only: item control page