Professor Pereyra will talk about; 'Physics-informed deep generative models: Applications to computational sensing'

This talk introduces a novel mathematical and computational framework for constructing high-dimensional Bayesian inversion methods that leverage state-of-the-art generative denoising diffusion models as highly informative priors. A central innovation is the construction of physics-informed generative models using Langevin diffusion processes and Markov chain Monte Carlo (MCMC) sampling techniques to develop stochastic neural network architectures capable of near-exact sampling. The obtained networks are modular and composed of interpretable layers that are directly related to statistical image priors and data likelihoods derived from forward observation models. The layers encoding the data likelihood function are designed for flexibility, enabling scene and instrument model parameters to be specified at inference time and seamlessly integrated with pre-trained foundational generative priors. To achieve high computational efficiency, we employ adversarial model distillation, which yields excellent sampling performance with as few as four Markov chain Monte Carlo steps, even in problems exceeding one million dimensions. Our approach is validated through non-asymptotic convergence analysis and extensive numerical experiments in computational image and video restoration. We conclude by discussing unsupervised training strategies that allow the models to be fine-tuned directly from measurement data, thereby bypassing the need for clean reference data.

The talk is based on recent work in physics-informed generative AI for Bayesian imaging: https://arxiv.org/abs/2503.12615 (ICCV 2025), which uses a distilled latent Stable Diffusion XL model trained on five billion clean images as a zero-shot prior, and  https://arxiv.org/pdf/2507.02686, which integrates pixel-based diffusion models with deep unfolding and diffusion distillation (TMLR 2025). The extension to video restoration is presented in https://arxiv.org/abs/2510.01339 (ICLR 2025). Our approach to unsupervised training of diffusion models is introduced in https://arxiv.org/abs/2510.11964.

This talk is divided in three parts. First, I review structural properties and examples of geometries with parallel skew torsion. Second, I take a closer look at those geometries where the torsion is in addition closed; this equips every tangent space with the structure of a metric Lie algebra. These manifolds always locally split as a product into well understood factors, allowing a complete local classification. Third, I investigate various G-structures defining a geometry of this type, with a focus on almost Hermitian structures, extending recent results of Barbaro-Pediconi-Tardini. This is joint work with Andrei Moroianu.

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Smoothed analysis has become a central tool in computer science, often allowing for significant improvements to worst-case running times if we settle for a solution to a small random perturbation of the problem instance. This is closely related to the classical concept of backward error in numerical analysis, which allows an algorithm to return a solution to a small arbitrary perturbation of the problem.

Despite the qualitative similarity of these concepts, we show that they can exhibit large quantitative differences. Notably, we prove that, while a linear system with any n × n matrix A can be solved to backward error ε using O(log n / ε) matrix-vector products with A, any algorithm that solves a random ε-sized perturbation of A requires Ω(n) matrix-vector products.

This means that a useful perturbation for solving a linear system in backward error must be adaptive to the input. We use this as a starting point to explore the role of adaptivity and randomness in designing perturbations for solving numerical linear algebra problems in backward error.

Based on joint works with Yuji Nakatsukasa, Elizaveta Rebrova, Raphael Meyer, Michael Mahoney, and Christopher Musco.

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The apicomedial actomyosin network is crucial for generating mechanical forces in epithelial cells. Pulsatile, oscillatory behaviour of this contractile network occurs in multiple organisms and contexts, for example during mouse embryo compaction or Xenopus neurulation. However, the emergence and control of such pulsed contractions are not fully understood. Here, we study pulsed contractions of larval epithelial cells (LECs) during development of the abdomen in fruit flies. Specifically, we combine in vivo 4D microscopy and simulations of an active elastomer to investigate subcellular spatial patterns of actomyosin dynamics. Our model quantitatively matches in vivo observations and identifies cell geometry and polarity as key contributors to in vivo actomyosin dynamics. Moreover, our findings support the notion that spatiotemporal oscillatory behaviour of the actomyosin network is an emergent property, rather than driven by upstream signalling.

I will additionally give a brief overview of other dynamic phenomena in cell biology that my collaborators and I have studied, such as ultradian (i.e. faster-than-circadian) oscillations in gene expression.

Throughout, I will highlight open challenges for data-driven approaches in cell biology.

Junior Algebra & Representation Theory end of term social will happen in the Quillen Room at 12pm on Friday

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