Machine learning to enhance numerical PDE simulations
File(s)
Author(s)
Santos Silva, Vinicius Luiz
Type
Thesis
Abstract
The solution of complex physics and engineering systems, described by partial differential equations (PDEs), often require numerical methods due to their analytical intractability. These methods, like finite difference, finite volume, and finite element, demand high computational resources. The widespread success of machine learning has created new possibilities to enhance numerical PDE simulations. In this context, we can think of three main areas where machine learning can enhance these simulations: accelerating full-order numerical simulations, developing surrogate models, and enhancing the physical representation of these simulations. This thesis addresses each of these three main areas. (i) To accelerate the full-order numerical simulation, we propose a machine learning approach to accelerate convergence of a nonlinear solver by dynamically controlling a relaxation parameter. The proposed approach reduces the number of nonlinear iterations, including models far more complex than the training case. Compared to other approaches our method is simple to implement and can learn on-the-run when applied to other simulation domains. (ii) As a surrogate model, we propose a new approach in which generative neural networks within a reduced-order model (ROM) framework are used for prediction, data assimilation and uncertainty quantification. The proposed Generative Network-Based ROM can efficiently quantify uncertainty and accurately match the observed data, using only few unconditional simulations of the full-order numerical PDE model. (iii) To enhance the physical representation of full-order numerical simulations, we propose a machine learning approach to replace geochemical calculations generated by an aqueous geochemical code that is coupled with a flow and transport simulator. The results provide new insights into the rapid modelling of reactive transport. We show that machine learning can be practical to replace the reaction model. However, it needs to be carefully designed, and all the limitations need to be accounted for when coupling the fast model with a flow and transport simulator.
Version
Open Access
Date Issued
2024-04-29
Date Awarded
01/01/2025
License URL
Advisor
Pain, Christopher
Jackson, Matthew
Salinas, Pablo
Heaney, Claire
Sponsor
Petrobras (Firm)
Publisher Department
Earth Science & Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)