Phd in adaptive data assimilation in subsurface systems with ensemble transport

Challenge. Advancing the energy transition requires understanding complex subsurface processes.

Change. Developing an innovative nonlinear data assimilation strategy that can adapt itself to different natural systems.

Impact. This method will permit better forecasting of safer operations and their consequences in the subsurface and beyond.

Context
The subsurface plays a critical role in tackling the challenges of changing climate. It provides drinking water amidst increasingly frequent droughts and serves as a keystone of the energy transition by providing geothermal energy and storage space for hydrogen. Despite its importance, our insights into the subsurface's properties and processes are incomplete, limiting our ability to fully characterize this environment.
The resulting uncertainties require careful analysis to inform societally responsible subsurface operations:

• How can we sustainably heat as many homes as possible?
• Where shall we establish the next hydrogen storage reservoir?
• What can we do to mitigate our operation's environmental and economic risks?

The Problem
To answer such questions, we use numerical models to explore different simulations of what the subsurface might look like. Data assimilation is a statistical framework that combines such simulations with observations from the real system, inferring unobserved properties from quantities we can measure via the model's physical relationships. However, its implementation remains a challenge in complex systems. Most contemporary data assimilation methods either over-simplify or are prohibitively inefficient, compromising our statistical insights and thus our decision-making capabilities. A data assimilation method that adjusts its own complexity to the properties of the system could permit better, more reliable subsurface characterisations.

The Project
This project is a collaboration between TU Delft and the Norwegian energy company Equinor and focuses on co-developing an adaptive nonlinear data assimilation strategy using triangular ensemble transport. This method permits powerful ensemble-based statistical inference and shares similarities with machine learning / AI techniques such as normalizing flows and diffusion models. In particular, it can exploit two important features:

• Conditional independence: which variables affect each other directly, and which affect each other only indirectly?
• Adaptivity: How complex and nonlinear must we make our triangular map functions to capture the most important features while limiting computational demand?

By leveraging these features, we aim to create a powerful data assimilation framework that adapts itself to the system and remains always as simple as possible and as complex as necessary. This will improve subsurface characterizations and enable better, more reliable decision-making. You can learn more about the method we are using in the video tutorial here or the articles here or here. Mind that we do not expect familiarity with these methods at the time of application.

Your Role and Responsibilities
Your work will play a central role in advancing the adaptation part of our proposed data assimilation framework, in collaboration with a colleague PhD working on Conditional Independence. Your main tasks will include:

• Familiarize yourself with the theoretical and practical aspects of triangular measure transport, data assimilation, and subsurface applications.
• Explore strategies to adapt triangular maps to different environmental systems. This will involve concepts from information theory, hypothesis testing, and monotone functions.
• Co-develop a scalable, adaptive algorithm for nonlinear data assimilation based on triangular transport.
• Apply the algorithm as part of the proposed data assimilation framework to analyze the properties and uncertainties of a real geothermal operation.

Collaboration and Environment
This four-year project is part of a collaboration between TU Delft and data assimilation research at Equinor in Bergen, Norway. You will join the reservoir engineering section at TU Delft's Department of Geoscience & Engineering, where you will find a vibrant and collaborative environment in which you will have the opportunity to interact with experts in data assimilation, geothermal energy, and numerical simulation. You will be encouraged to learn new skills and develop your own ideas, and you will share your findings at conferences and in peer-reviewed journals. These experiences will pave the way for diverse career paths in industry, consultancy, governmental agencies, or academia.

• You hold a Masters degree in geoscience, geophysics, applied mathematics/statistics, or a similar field.
• You thrive on systematic, code-based research, and have an aptitude for abstract or mathematical thinking. We do not expect prior familiarity with triangular transport.
• You have a keen interest in data assimilation and machine learning, and are excited to explore their applications to geoscience problems.
• You have experience with Python or a similar programming language.
• You are a highly motivated and self-driven researcher, capable of working both independently and as part of a team.
• You have an excellent command of written and spoken English.

Delft University of Technology is built on strong foundations. As creators of the world-famous Dutch waterworks and pioneers in biotech, TU Delft is a top international university combining science, engineering and design. It delivers world class results in education, research and innovation to address challenges in the areas of energy, climate, mobility, health and digital society. For generations, our engineers have proven to be entrepreneurial problem-solvers, both in business and in a social context.

At TU Delft we embrace diversity as one of our core values and we actively engage to be a university where you feel at home and can flourish. We value different perspectives and qualities. We believe this makes our work more innovative, the TU Delft community more vibrant and the world more just. Together, we imagine, invent and create solutions using technology to have a positive impact on a global scale. That is why we invite you to apply. Your application will receive fair consideration.

28 February 2025

• A motivation letter (max. 800 words) outlining your interest in pursuing a PhD and your interest for this particular project.
• A curriculum vitae including, if available, a link to your MSc thesis.
• Academic transcript, including grades for your qualifying degrees (BSc, MSc)

Graduate Schools Admission Requirements.

After an initial selection, we plan to have a first round of online interviews in the week of 10.03.2025, and a second round of final interviews the week after. We understand that you might have other commitments and will do our best to be flexible when setting up the interviews.

Please note:

• A pre-employment screening can be part of the selection procedure.
• For the final candidates, a knowledge security check will be part of the application procedure. For more information on this check, please consult Chapter 8 of the . We carry out this check on the basis of legitimate interest.
• Please do not contact us for unsolicited services.