PhD Studentship: Data-driven methods to identify geometric dynamical systems

Data-driven predictions of dynamical systems are used in many applications, ranging from the design of products and materials to weather and climate predictions. Mathematical concepts from geometry provide powerful tools to improve the quality and efficiency of data-driven models. In parallel to the development of data-driven models for dynamical systems with geometric structures such as Hamiltonian structure, variational structure, and symmetries, data-driven techniques to solve partial differential equations (pde) have emerged.

Quantifying model uncertainty of data-based predictions is crucial for their employability in applications. Additionally, machine learning methods need to be applicable to high-dimensional and to noisy data that are typically encountered in real-world applications. The aim of this project is to exploit techniques from the data-driven pde community to design new methods to identify geometric dynamical systems, while tackling the uncertainty quantification task and the high-dimensional and noisy data regime. Ideally, convergence guarantees, and posterior contraction rates can be transferred from the pde learning setting to data-driven geometric models, with the perspective of creating a more rigorous understanding of the role of geometry in machine learning.

We are looking for an enthusiastic and highly motivated graduate with relevant background in at least one of the fields of machine learning, numerical analysis, optimisation, or related fields.

Funding notes:
Funding is available through the School of Mathematics for a suitably strong candidate. The scholarship will cover tuition fees, training support, and a stipend at standard rates for 3-3.5 years;

Candidates are encouraged to make an informal inquiry with Dr Christian Offen (https://www.birmingham.ac.uk/staff/profiles/maths/offen-christian)

For application details, see https://www.birmingham.ac.uk/study/postgraduate/research/how-to-apply

References:
C. Offen, “Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification,” Mathematics of Computation, Jun. 2025, doi: 10.1090/mcom/4120, https://arxiv.org/abs/2404.19626

C. Offen, S. Ober-Blöbaum, “Learning of discrete models of variational PDEs from data”, Chaos, Jan. 2024; 34 (1): 013104, doi:10.1063/5.0172287, https://arxiv.org/abs/2308.05082

M. Pförtner, I. Steinwart, P. Hennig, J. Wenger, „Physics-Informed Gaussian Process Regression Generalizes Linear PDE Solvers“, Apr. 2024, Preprint, https://arxiv.org/abs/2212.12474

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