From 26 to 31 July 2026, we had the pleasure of welcoming an international group of mathematicians and researchers to the Speinshart Scientific Center for the workshop “Fluid Dynamics, Singularities, and AI-Driven Discovery.”
Organised by Nicola De Nitti from the University of Pisa and Jan Giesselmann from TU Darmstadt, the workshop brought together experts working at the intersection of nonlinear partial differential equations, fluid dynamics, control theory, numerical analysis and machine learning.
A central focus of the discussions was the formation of singularities in nonlinear fluid equations. These extreme phenomena remain among the most challenging subjects in mathematical analysis and are closely connected to major open questions surrounding the Euler and Navier–Stokes equations.
At the same time, participants explored how AI-based methods can contribute to the discovery and investigation of complex mathematical structures. Particular attention was given to physics-informed neural networks and related approaches that can help detect potential singularities, approximate discontinuous solutions and generate computational evidence capable of guiding further rigorous analysis.
Rather than following the format of a traditional conference, the workshop was designed as a scientific retreat. Short, focused presentations provided the basis for extended discussions, collaborative problem-solving sessions and the joint exploration of open research questions.
The interdisciplinary character of the workshop made Speinshart an ideal setting for sustained scientific exchange: researchers at different career stages and from institutions across Europe, Asia and the United States had the opportunity to connect analytical, numerical and data-driven perspectives and to identify promising directions for future collaboration.
We would like to thank the scientific organisers and all participants for the inspiring discussions, the collaborative spirit and an intellectually stimulating week at Speinshart. It was a great pleasure to host this remarkable group and to provide a space in which new ideas, connections and research questions could emerge.
