Research Group:
The Chair of Renewable and Sustainable Energy Systems (ENS) at the Technical University of Munich (TUM) deals with the modeling and optimization of energy systems on different temporal and spatial scales. The Research Group Applied Optimization within the Chair focuses on challenging optimization problems that arise in energy-related applications. The student will work closely with the group.
Web: https://www.epe.ed.tum.de/en/ens/homepage/
Background:
In the fields of renewable energy and environmental management, there are numerous optimization problems where the underlying physical phenomena are described by partial differential equations (PDEs). Examples include optimizing wind and tidal turbine arrays, geothermal systems, thermal energy storages, or groundwater management. These problems fall under the category of PDE-constrained optimization (PDECO), which are challenging due to their high dimensionality and the associated high computational costs as well as their multidisciplinary nature (combination of optimization and numerical simulation). Therefore, it is crucial to employ suitable solution strategies to address these challenges and efficiently solve the associated optimization problems.
Physics-informed deep learning makes it possible to improve and accelerate the solution of PDECO problems. For example, physics-informed neural networks (PINNs) can be used as a surrogate for the expensive numerical PDE simulators. Such accurate and fast evaluable surrogates can be used in the optimization loop to significantly speed up the overall PDECO solution. Although PINNs are already used in some areas to solve PDECO problems, this field of research is still insufficiently explored, especially in the context of the recently developed physics-informed DeepONets (Deep Operator Networks). DeepONets are better suited for PDECO problems compared to classical PINNs, as they learn the PDE solution operator themselves. Concrete applications from the energy sector should be used to explore these possibilities.
Topic description:
The main goal of this project is the development of physics-informed DeepONets for the simulation of shallow geothermal systems (e.g. vertical borehole heat exchangers). These ML-based surrogates should accurately simulate the underlying processes in the subsurface (heat transport, groundwater flow). In the next phase, the developed surrogates can be integrated into the optimization process in order to optimize the design and operation of the corresponding geothermal systems.
Tasks:
• Familiarization with physics-informed DeepONets and the underlying physics (PDEs) for the simulation of shallow geothermal systems
• Specifying case studies for shallow geothermal applications
• Building and training physics-informed DeepONets for the selected simulation cases
• Implementing a PDE numerical model for the evaluation of DeepONets
• Benchmarking the DeepONets for performance and robustness
• Results processing, evaluation and presentation
• Preparation of a report describing the key aspects and findings of the conducted work
• Presenting the results to a scientific audience
• Maintaining a detailed documentation of the code repository
• Participate as a full member of the research group in all team activities during your stay.
References:
• S. Wang, H. Wang, and P. Perdikaris, “Learning the solution operator of parametric partial differential equations with physics-informed DeepONets”, Science advances, vol. 7, no. 40, (2021)
• Lu, L., Jin, P. and Karniadakis, G.E., “Deeponet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators”, arXiv preprint arXiv:1910.03193. (2019)
