The current research activities of Weizmann researchers span diverse areas of Applied and Computational Mathematics, including Mathematical Statistics, Nonlinear Mathematical Analysis of Turbulence and Geophysical Dynamics Models, Dynamical Systems Theory and its Applications, Data Assimilation, Statistical Signal Processing, Theory and Practice of Physics-Inspired AI, Sampling Theory and Algorithms, Sensing System Design, Mathematics of Communication Systems and Information Theory.

In the area of Signal Processing, Weizmann researchers are developing new technologies that extract and process signals and information more efficiently across a wide range of tasks, including medical imaging, radar, communication, scientific and optical imaging, healthcare, and biological inference. The new acquisition systems and algorithms rely on signal and information processing and model-based methods for AI that aid in obtaining increased information using minimal resources. These developments pave the way to new technologies such as wireless ultrasound, compact portable devices with better imaging quality, fast and quantitative MRI, efficient wideband sensing, high-resolution radar, efficient communication systems, joint radar and communication systems for automotive and IoT applications, super-resolution microscopy and ultrasound, model-based efficient and interpretable deep networks for medical imaging, communication systems, radar-based medical imaging and sensing, and more.

The research on applied analysis of oceanic and atmospheric dynamics models focuses on issues related to the well-posedness of (or the formation of finite-time singularity in) such models; in addition to providing rigorous justification of their derivation, and the development of data assimilation algorithms for weather and climate predictions. Notably, nonlinear Partial Differential Equations analytical and numerical tools, in particular, those associated with the investigation of the Euler and Navier-Stokes equations and their coupling to additional physical processes, such as moisture dynamics in clouds formation models, play an essential role in this exploration.

Contributions to the area of Dynamical Systems Theory and its Applications include developing tools to better understand fluid mixing processes and the influence of such processes on ocean currents. Another research direction develops theoretical tools for studying the motion of particles under various potential fields, including fields that have sharp fronts that induce impact-like behavior and their limiting systems – Hamiltonian systems with impacts. Recent results include establishing relations between such systems and directional flows on translational surfaces, quantization of such systems, and establishing the non-ergodicity of fast moving repelling particles in a box via proving KAM stability of choreographic motions.

Weizmann researchers working on Statistical Analysis of Complex Data and on Mathematical Foundations of Data Science are often motivated by the plethora of applications where complex high-dimensional data is collected and needs to be analyzed. Their research explores fundamental tasks, such as the extraction of structure from such datasets, imputation of missing entries, detection of low-dimensional structures, and denoising of high-dimensional data. It includes the mathematical foundations of data science, development of scalable data-science algorithms, derivation of supporting theoretical guarantees, as well as application to real datasets.

### Recurring seminars and meetings

- Machine Learning and Statistics seminar

### Local events and workshops

- Weizmann PDEs Day, September 2023
- Translational AI and Engineering in Health and Communication, December 2022

### Research centers