Machine Learning for Inverse Problems (Alberti)

The focus of this course will be the use of machine learning methods for solving inverse problems. In the first part, we will discuss the standard regularization theory for inverse problems in imaging, together with its limitations. In the second part, we will show how machine learning, and in particular deep learning, can be used to leverage prior information available through data. Possible approaches include end-to-end reconstructions and learned regularization (typically supervised), generative models (unsupervised), and untrained networks as in deep image prior. The theoretical discussions will be complemented by a lab session, mostly focusing on the comparison between traditional and deep learning methods. 

Real-Time Geological Inversion for Subsurface Decision-Making: From Theory to Practice (Alyaev)

During modern subsurface lateral drilling operations, the measurements collected down-hole are continuously streamed to the surface. Inversion of these real-time logging-while-drilling (LWD) measurements allows for the sequential and continuous update of subsurface geology around the wellbore. The extrapolation of inferences about geology can support directional drilling adjustments (called geosteering) and allow for better well placement.  

In my lectures, I will introduce the geosteering problem as a sequential inversion problem in the geological system with unknown dynamics. We will consider simple deterministic inversion algorithms and enrich them with data-driven system models. We will also look into Bayesian statistical inversion, allowing us to capture solution uncertainty. At the end of the course, the participants will be challenged to program their sequential inversion algorithm and a simple decision robot, which will compete in a setup from a past Geosteering World Cup.

Inverse problems for water waves (Kirkeby)

Studying inverse problems from physics allows you to become a natural scientist using only pen, paper and your computer. To figure out how the information you are interested in propagates through the physical system and manifests itself in the measurement, you really have to understand the mathematical model that governs the physics.  

The first lecture will be a general introduction to inverse problems, with focus on problems involving physics and partial differential equations. In the second lecture, we will derive a mathematical model for water waves and explore what the equations can tell us about the physics and propagation of information. As water waves are easily observable, we will (hopefully) conduct some simple experiments to verify the predictions coming from the model. In the third lecture we will use what we have learned to analyze an inverse problem for water waves.

Solving Inverse Problems with Julia's SciML (Rackauckas)

Solving inverse problems has a lot of theory: differentiability, adjoints, invertibility, identifiability, etc. In this workshop we will cut through the details and show how the theory translates to code in a hands-on demonstration. We will use the Julia SciML tooling to interactively discuss items such as the numerical stability of discrete and continuous adjoints, alternative loss functions for elimination of local minima, integrating neural networks for identifying missing governing equations, and performance aspects such as code optimization, choice of solvers, and GPU parallelism. The participants of this workshop will walk away with not only a better understanding of the theoretical principles of solving numerically difficult inverse problems, but also be well-versed in tools which can be used in academic and industrial environments with demanding problems.

Giovanni S. Alberti

Giovanni S. Alberti is a professor in mathematical analysis at the Department of Mathematics of the University of Genoa, and a member of MaLGa, the Machine Learning Genoa Center. He received his PhD at the University of Oxford, and held two post-doctoral positions at the École Normale Supérieure in Paris and at ETH Zürich. His research focuses on partial differential equations, applied harmonic analysis, inverse problems and machine learning. He was the recipient of the Gioacchino Iapichino prize for Mathematical Analysis in 2017, of the Eurasian Association on Inverse Problems Young Scientist Award for distinguished contributions to inverse problems in 2018, and of a ERC Starting Grant 2021.

Sergey Alyaev

Sergey Alyaev is a Senior Researcher at NORCE Energy in Bergen working on interdisciplinary research within machine learning uncertainty quantification and geosciences. He holds an MSc and a PhD in Applied and Computational Mathematics from the University of Bergen. At NORCE, he coordinates efforts in geosteering and leads a JIP, "DISTINGUISH," where the team combines generative modeling of geology, inverse problems, and decision optimization for geosteering. 

Adrian Kirkeby

Adrian Kirkeby has a PhD in applied mathematics from NTNU and the Technical University of Denmark with focus on theory and solution methods for inverse problems for problems governed by partial differential equations. He has experience from industry and the government research sector, and currently works as a postdoc at Simula Research Laboratory in Oslo.

Chris Rackauckas

Dr. Chris Rackauckas is the VP of Modeling and Simulation at JuliaHub, the Director of Scientific Research at Pumas-AI, Co-PI of the Julia Lab at MIT, and the lead developer of the SciML Open Source Software Organization. For his work in mechanistic machine learning, his work is credited for the 15,000x acceleration of NASA Launch Services simulations and recently demonstrated a 60x-570x acceleration over Modelica tools in HVAC simulation, earning Chris the US Air Force Artificial Intelligence Accelerator Scientific Excellence Award. See more here. He is the lead developer of the Pumas project and has received a top presentation award at every ACoP in the last 3 years for improving methods for uncertainty quantification, automated GPU acceleration of nonlinear mixed effects modeling (NLME), and machine learning assisted construction of NLME models with DeepNLME. For these achievements, Chris received the Emerging Scientist award from ISoP, the highest early career award in pharmacometrics. 

All lectures will take place at Dr. Holms Hotel in Geilo, Norway. Participants will receive more information by email. Exact times will also appear in the following schedule once the program is completely finalized.

Booking a train/checking the train schedule is done through Vy. The hotel is a walkable distance from the train station in Geilo.

You can subscribe to the above calendar by using this link.

See the About page for general information about the winter school.

Costs and registration

There is no registration fee for the winter school, but participants must cover their own travel costs and hotel costs at Dr. Holms. Hotel rates per person:

• 2 090 NOK/night for single room.
• 1 670 NOK/night in a double room.

Registration is now open!

Room allocation

The winter school has a limited number of rooms at Dr. Holms which will be reserved on a first come first serve basis. We have in previous years exceeded our room allocation, so please register as early as possible!

Posters

We welcome all posters to be presented, and will make space in the program for a poster session in which participants can present their work to colleagues and others. The aim of the session is to make new contacts and share your research, and it is an informal event. You need to indicate in your registration if you want to present a poster during the poster session. Please limit your poster to A0 in portrait orientation.

Organizing Committee

The organizing committee for the Geilo Winter School consists of

• Øystein Klemetsdal, Research Scientist (Department of Mathematics and Cybernetics, SINTEF).
• Torkel Andreas Haufmann, Research Manager (Department of Mathematics and Cybernetics, SINTEF). 

To get in touch with the committee, send an email .