The last years have seen a rapid development of machine learning-based tools, among them text-to-image generators using so-called score-based diffusion models. Abstractly, image generation is a problem in "conditional simulation": Diffusion models are trained to randomly generate or "sample" new images based on existing image databases, and the user input restricts to generate only images from a conditional distribution, e.g. constraining the image to show cats. The generation process itself creates images by gradually transforming unstructured random noise, which is simple to realize on computers.

Due to their popularity, there has been much research on improvements of diffusion models. One of them, providing high quality samples at low computational costs at generation, is the diffusion Schrödinger bridge. While Schrödinger bridges are a well-known concept in probability theory and optimal transport, it has only now become possible to use them for modern high-dimensional generative tasks. In this Gateway Fellowship project, I will develop and analyze new Schrödinger bridge samplers for so-called Bayesian inverse problems. The idea of Bayesian inverse problems is to update prior knowledge about the probability distribution of - often high-dimensional - random parameters based on indirect and noisy observations. To characterize the updated "posterior" distribution, it is necessary to generate samples of the random parameter, conditioned on the available observations, similar to the image generation task above. The aim of this project is to study properties of Schrödinger bridges in the setting of Bayesian inverse problems, and use the results to obtain more efficient sampling schemes.

To realize the project, I will collaborate with Prof. Youssef Marzouk who heads the Uncertainty Quantification Group at the Massachusetts Institute of Technology in Cambridge, MA, USA. Prof. Marzouk is a leading expert on computational aspects of Bayesian inverse problems, with a particular focus on measure transport methods, and therefore an ideal host for this Gateway Fellowship project.

A healthy brain requires steady nourishment and clearance of waste products which is assured by brain blood flow. Surprisingly, the relationships between brain blood flow and the availability of nutrients in the gut and blood remain poorly understood. Little is known about how brain blood flow changes when we shift from being satiated to fasting, or when we overconsume food during the day. Furthermore, sleep is associated with fasting and during sleep brain blood flow increases to help clear out waste. Lately, the gut microbiome has emerged as a powerful regulator of body functions. However, despite its ability to sense ingested nutrients, our understanding of the gut microbiome in helping the body regulate nutrient delivery via the blood circulation remains very limited. We will test the hypothesis that gut-brain communication helps coordinate bodily energy status and brain blood flow by releasing factors into the systemic circulation depending on nutrient availability.
For the Gateway Fellowship project, I joined the lab of Prof. Grant Gordon at the Hotchkiss Brain Institute of the University of Calgary. During the project I will employ in vivo two-photon imaging in mice during rest, activity and sleep to investigate changes in cerebral blood flow induced by fasting or microbiome disruption. The research plan will discover previously unknown fundamental relationships between energy substrate delivery and brain maintenance via nutrient sensing in the gut microbiome. During an extended stay in the lab, I will test for sex differences in the effects I describe and determine which microbiome-released factors are driving improvements in brain blood flow. Additionally, deficits in cerebral blood flow are deeply connected with several neurological conditions, including Alzheimer's disease. Given this, I will then also test if fasting-induced, microbiome-dependent improvements of cerebral blood flow will be observed in a common mouse model of Alzheimer's disease, and whether this limits disease onset and progression.