Previous seminars | MoDS Seminars

Unbiased approaches to compressive sensing and low rank matrix estimation

Marcus Carlsson
Lund University
16 December 2024

It is well known that the standard compressive sensing techniques, LASSO for the scalar case and nuclear norm minimization for the matrix case, come with a significant “shrinking bias”. I will introduce a toolbox of techniques to construct non-convex penalties with a number of desirable features, in particular that they provably do not suffer from the “shrinking bias”. The types of penalites that one may construct can be tailormade to the application at hand, and works both for vectors and matrices.

When AI goes Awry

Desmond Higham
University of Edinburgh
21 August 2024

Over the last decade, adversarial attack algorithms have revealed instabilities in deep learning tools. These algorithms raise issues regarding safety, reliability and interpretability in artificial intelligence (AI); especially in high risk settings. At the heart of this landscape are ideas from optimization, numerical analysis and high dimensional stochastic analysis playing key roles. From a practical perspective, there has been a war of escalation between those developing attack and defence strategies. At a more theoretical level, researchers have also studied bigger picture questions concerning the existence and computability of successful attacks. I will present examples of attack algorithms in image classification,...

Intelligent Physics-Driven Technologies for Inverse Problems in MRI

Mehmet Akçakaya
University of Minnesota
15 August 2024

Lengthy data acquisition remains a major bottleneck in magnetic resonance imaging (MRI), often necessitating tradeoffs in resolution and signal-to-noise ratio. Thus, reconstruction and acquisition techniques for rapid imaging, noise reduction and improved data acquisition have received great interest. Each of these directions correspond to a specific inverse problem with its own distinct forward operator dictated by the underlying imaging physics.

Enabling digital twins through modeling, data, and learning — a few examples

Jan S. Hesthaven
EFPL
17 May 2024

The ability to build efficient physics-based surrogate models with predictive accuracy is an old dream, in particular for complex engineering systems. However, realizing this remains a challenge due to the need to combine advanced computational modeling, reduced complexity models and external data for calibration, updating and uncertainty management. Nevertheless, the perspectives of using such models, often referred to as digital twins, for design, predictive maintenance, operational optimization, and risk analysis are substantial and the potential for impact significant, from safety, planning, and financial points of view. In this talk we shall first discuss the importance of efficient and accurate reduced...

Executable Digital Twins — Reimagining industrial operations through Mathematics and Scientific Machine Learning

Dirk Hartmann
Siemens
06 February 2024

In the past decade, the Digital Twin concept has emerged as a major technology trend. A Digital Twin bridges the real and digital world and allows us to reimagine industrial operations like hardly any other technology before. However, today’s approaches are quite bespoke, requiring sophisticated expertise and complex software setups. While a Digital Twin offers a unique opportunity to address the mega trends and challenges our society is facing, we need widely scalable approaches to achieve the required speed and scale of adoption. With the exponential evolution of compute hardware on the one hand, and algorithms on the other, a...

Learned model-based reconstructions for inverse problems: robustness and convergence guarantees

Andreas Hauptmann
University of Oulu
23 November 2023

In recent years, deep learning has achieved remarkable empirical success for image reconstruction. This has catalysed an ongoing quest for the precise characterization of the correctness and reliability of data-driven methods in critical use cases, for instance, in medical imaging. Notwithstanding the excellent performance and efficacy of deep learning-based methods, concerns have been raised regarding the approaches’ stability, or lack thereof, with serious practical implications. Significant advances have been made in recent years to unravel the inner workings of data-driven image recovery methods, challenging their widely perceived black-box nature.

A Role for Message Passing in Data Assimilation?

Marc Deisenroth
University College London
14 November 2023

Estimating the latent state of a dynamical system based on noisy observations is a common challenge underlying many tasks in engineering, robotics, or weather modeling. We will discuss two perspectives of state estimation: temporal inference and spatial inference. In this talk, I will provide a machine learning perspective on state estimation and discuss what role message passing can play when solving large-scale spatio-temporal inference problems as they appear in data assimilation.

New avenues in high order fluid dynamics

Esteban Ferrer
Univ. Politécnica de Madrid
16 June 2023

We present the latest developments of our High-Order Spectral Element Solver (HORSES3D), an open source high-order discontinuous Galerkin framework capable of solving a variety of flow applications, including compressible flows (with or without shocks), incompressible flows, various RANS and LES turbulence models, particle dynamics, multiphase flows, and aeroacoustics [1]. Recent developments allow us to simulate challenging multiphysics including turbulent flows, multiphase and moving bodies, using local h/p-adaptation and multigrid time advancement. In addition, we present recent work that couples Machine Learning techniques and high-order simulations.

Stochastic morphometry and sampling of conditioned stochastic shape processes

Stefan Sommer
DIKU
11 May 2023

In the talk, I will give an overview of the Stochastic morphometry project and how we in the Center for Computational Evolutionary Morphometry aim to build statistical models for morphological evolution and connected phylogenetic inference tools. I will particularly focus on sampling of conditioned stochastic shape processes, both bridges where the process is conditioned on one observation at a fixed time, and processes on a phylogenetic tree conditioned on observations of all leaves. These sampling techniques constitute the foundation of the MCMC schemes we use for inferring parameters of the morphological evolution from data.

Reduced Order Modelling in Computational Mechanics: state of the art, challenges and applications

Gianluigi Rozza
SISSA
07 March 2023

We provide the state of the art of Reduced Order Methods (ROM) for parametric Partial Differential Equations (PDEs), and we focus on some perspectives in their current trends and developments, with a special interest in parametric problems arising in offline-online Computational Fluid Dynamics (CFD). Efficient parametrisations (random inputs, geometry, physics) are very important to be able to properly address an offline-online decoupling of the computational procedures and to allow competitive computational performances. Current ROM developments in CFD include: (i) a better use of stable high fidelity methods, to enhance the quality of the reduced model too, and allowing to incorporate turbulence models...

Counterfactual Analysis in Benchmarking

Dolores Romero Morales
Copenhagen Business School
01 February 2023

Traditional benchmarking based on simple key performance indicators is widely used and easy to understand. Unfortunately, such indicators cannot fully capture the complex relationship between multiple inputs and outputs in most firms. Data Envelopment Analysis (DEA) offers an attractive alternative. It builds an activity analysis model of best practices considering the multiple inputs used and products and services produced. This allows more substantial evaluations and also offers a framework that can support many other operational, tactical and strategic planning efforts.

GitHub Copilot and techniques for improving code suggestions from large language models

Johan Rosenkilde
GitHub Next
12 January 2023

Progress in large language models (LLMs) has been very rapid the last decade and LLMs are now being used to power a growing number of real-life applications. The automatic code completion tool GitHub Copilot is one such, powered by OpenAI’s Codex model. Training an LLM from scratch is very GPU intensive, and so only a handful of companies currently dominate the state-of-the-art like Google, Meta, Amazon, and OpenAI. Academia therefore has a challenge in operating in this space. There is a neighbouring arena of research, however, which seems just as important for LLMs to be impactful, and which is much...

Physics-informed machine learning: Blending data and physics for fast predictions

George Em Karniadakis
Brown University
09 November 2022

Despite great progress in simulating multiphysics problems using the numerical discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate noisy data into existing algorithms, mesh generation remains complex, and high- dimensional problems governed by parameterized PDEs cannot be tackled. Moreover, solving inverse problems with hidden physics is often prohibitively expensive and requires different formulations and elaborate computer codes. Machine learning has emerged as a promising alternative, but training deep neural networks requires big data, not always available for scientific problems. Instead, such networks can be trained from additional information obtained by enforcing the physical laws (for example, at...