Many phenomena in physics, chemistry, astronomy, and biology can be modelled by differential equations, but their exact form is often unknown. A main ongoing scientific challenge is discovering such equations based on a combination of physical insight and data-driven techniques. Neural differential equations provide a promising hybrid framework in which physics and neural networks can be combined, however they struggle to model chaotic problems such as turbulence. We propose to add stochastic terms and employ neural stochastic differential equations to perform probabilistic turbulence simulations. We develop a new method for discovering such equations by exploiting recent generative machine learning approaches.

In veel gebieden van wetenschap en technologie kunnen we niet direct waarnemen wat we willen weten, en er zijn slimme meetmethoden en informatieverwerking nodig om ons te helpen. Zo willen we in de medische beeldvorming weten wat er zich in een patiënt afspeelt, met zo min mogelijk verstoring. Evenzo probeert men bij niet-destructief onderzoek onvolkomenheden in materialen op te sporen die van buitenaf niet zichtbaar zijn, op basis van hoe het object als geheel reageert. Het interdisciplinaire vakgebied van inverse problemen richt zich op het ontwerpen van dergelijke procedures. Deze bijeenkomst brengt onderzoekers samen om hierover samen te werken.

Computed Tomography (CT) is a widely used method in science, industry, and health care to reveal the interior of objects using X-rays. For dynamical processes, such as bubbling fluids, a CT scan yields a long time sequence of 3D images, similar to a video. Our research shows that artificial intelligence (AI) improves these CT images by learning motion, and that this is already possible during the scan. New software was developed for the necessary fast computations, and our concepts were demonstrated on experimental data from laboratories at TU Delft and CWI.

This project is a major part of the 1-year sabbatical leave of Dr. Wouter Hoff. It will involve (1) the continuation of an ongoing collaboration on the genetic code and tRNA sets, and will (2) provide the opportunity to explore two novel collaborative projects at the intersection of the computational expertise at the CWI and expertise in biophysics and molecular evolution of Dr. Hoff. The two novel directions are combining biology and evolutionary questions with quantum computing and with computational learning theory. The three projects we plan to work on are: 1) Properties of tRNA sets. 2) Implications of quantum computing for biomolecular quantum simulations. 3) Artificial intelligence for accelerating evolution. The first project is a continuation of ongoing projects with CWI and prof. Hoff. Project 2 and 3 are entirely new research directions that become possible due to prof. Hoffs expertise and the research groups in Amsterdam (CWI/UvA/VU & QuSoft)

We propose to initiate a new research direction on the mathematics of dynamic 3D imaging problems, within the CWI Computational Imaging group. While classical 3D scanning techniques (CT, MRI, ultrasound, etc.) are mainly designed for scanning static objects, there is a growing interest in capturing the 4D (3D space + time) evolution of dynamic processes. Mathematics forms the key to making this possible. The fundamental scientific challenge of dynamic 3D imaging is the lack of sufficient image data in each individual time frame, making it impossible to solve the 3D inverse problem separately for each point in time. Instead, we need to link the 3D images by a dynamical system model of the object’s evolution, creating a complex new type of inverse problem that involves estimating both the 4D image data and the parameters governing the dynamical system simultaneously. Current mathematical and computational techniques are insufficient for dealing with these challenging problems. The proposed Tenure Track position is situated at the interface of the NDNS+ and DIAMANT clusters: - Dynamical systems theory, modeling, and simulation form the scientific context for describing the evolution of the scanned object. - Discrete inversion techniques and convex optimization methods form the scientific context for solving the inverse problems relating the measurement to the scanned object. We envision that the appointed Tenure Track candidate will play a key role in establishing cross-domain relationships between these clusters, while at the same time performing research in an important emerging field.