Learning to Simulate Conditioned Diffusion Processes

PhD defence by Gefan Yang

Assessment Committee

Associate Professor Francois Lauze, Department of Computer Science, University of Copenhagen (Chairperson)
Associate Professor Karen Habermann, University of Wariwick
Professor Matti Vihola, University of Jyväskylä

Supervisors

Professor Stefan Horst Sommer

Department

Department of Computer Science

Place

Building: Observatory, Room: Seminar Room, Øster Voldgade 3, 1350 København K

Email address to gain access to the thesis: yang.gefan@outlook.com.
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Short description of the thesis

Many scientific questions ask not just how a random system evolves, but how it could have evolved given what we observe at the end. This thesis develops learning-based methods for simulating such “conditioned” stochastic processes, with a motivating application in reconstructing the evolution of biological shapes across species. The challenge is that these constrained dynamics are usually mathematically intractable, especially in high-dimensional, nonlinear, or rare-event settings. By combining ideas from stochastic analysis, machine learning, and scientific computing, this work introduces new algorithms that make these simulations more scalable and flexible, with applications to phylogenetics, shape analysis, dynamical systems, and generative modelling.