Zurich Colloquium in Applied and Computational Mathematics

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Speaker

Title

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8 May 2024
16:30-17:30

Prof. Dr. Maarten de Hoop
Rice University

Event Details

Speaker invited by

Prof. Dr. Habib Ammari

Abstract

We present results pertaining to selected inverse problems associated with seismology on Earth, Mars and Saturn. We focus on geometrical or travel time data originating from the propagation of singularities and the spectra corresponding with normal modes. For terrestrial or rocky planets we highlight recent insights with generic anisotropic elasticity, and for gas giants we reveal the accommodation of the equations of state all the way up to their boundaries. We briefly touch upon whether information on uniqueness of inverse problems is encoded in the data.

Geometric and spectral inverse problems for terrestrial planets and gas giants

HG E 1.2

15 May 2024
16:30-17:30

Dr. Leonardo Zepeda-Nunez
Google Research, USA

Event Details

Speaker invited by

Prof. Dr. Siddhartha Mishra

Abstract

The advent of generative AI has turbocharged the development of a myriad of commercial applications, and it has slowly started to permeate to scientific computing. In this talk we discussed how recasting the formulation of old and new problems within a probabilistic approach opens the door to leverage and tailor state-of-the-art generative AI tools. As such, we review recent advancements in Probabilistic SciML – including computational fluid dynamics, inverse problems, and particularly climate sciences, with an emphasis on statistical downscaling. Statistical downscaling is a crucial tool for analyzing the regional effects of climate change under different climate models: it seeks to transform low-resolution data from a (potentially biased) coarse-grained numerical scheme (which is computationally inexpensive) into high-resolution data consistent with high-fidelity models. We recast this problem in a two-stage probabilistic framework using unpaired data by combining two transformations: a debiasing step performed by an optimal transport map, followed by an upsampling step achieved through a probabilistic conditional diffusion model. Our approach characterizes conditional distribution without requiring paired data and faithfully recovers relevant physical statistics, even from biased samples. We will show that our method generates statistically correct high-resolution outputs from low-resolution ones, for different chaotic systems, including well known climate models and weather data. We show that the framework is able to upsample resolutions by 8x and 16x while accurately matching the statistics of physical quantities – even when the low-frequency content of the inputs and outputs differs. This is a crucial yet challenging requirement that existing state-of-the-art methods usually struggle with.

Recent Advances in Probabilistic Scientific Machine learning

HG E 1.2

22 May 2024
16:30-17:30

Prof. Dr. Dirk Pauly
TU Dresden

Event Details

Speaker invited by	Prof. Dr. Ralf Hiptmair
Abstract	We study a new notion of trace and extension operators for abstract Hilbert complexes.

Traces for Hilbert Complexes

HG E 1.2

29 May 2024
16:30-17:30

Prof. Dr. Ivan Trapasso
Politecnico di Torino

Event Details

Speaker invited by

Prof. Dr. Rima Alaifari

Abstract

In this talk we provide a concise overview of the fundamental principles underlying harmonic analysis in phase space. The roots of this vibrant field of modern Fourier analysis are to be found at the crossroads of signal analysis, mathematical physics, representation theory and analysis of partial differential equations. The key idea is to exploit a dictionary of oscillating wave packets (or equivalently, the combined structure of translations and modulations or dilations) to investigate properties of functions, distributions and operators in terms of suitable companion phase space representations. Addressing time and frequency/scale on the same level presents both advantages and challenges due to the uncertainty principle. In essence, time and frequency exhibit a somewhat dual nature as variables, hence the efforts to handle them concurrently are ultimately directed to keep track of the multifaceted manifestations of their entanglement. We will delve into these issues, whose origins date back to the foundations of quantum mechanics, and show how they continue to stimulate insightful research in analysis. Lastly, we will offer a taste of applications of these techniques to some problems motivated by the current challenges of data science, mostly in order to convey the message that the principles of time-frequency analysis are ubiquitous, hence adopting a phase space perspective can provide a versatile framework to explore problems from pure and applied mathematics.

Explorations in wave packet analysis

HG E 1.2

25 September 2024
16:30-17:30

Dr. Martin Averseng
Université d’Angers

Event Details

Speaker invited by	Prof. Dr. Ralf Hiptmair

Title T.B.A.

HG ? ?

9 October 2024
16:30-17:30

Prof. Dr. Cristinel Mardare
Sorbonne Université

Event Details

Speaker invited by	Prof. Dr. Stefan Sauter

Title T.B.A.

HG E 1.2

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