About me and my research Link to heading

I am Davide Murari. I enjoy reading, long-distance running , and explaining what I learn online. I am currently a Postdoctoral Research Associate in the Cambridge Image Analysis (CIA) group at the University of Cambridge.

My research background is in applied mathematics, with a focus on dynamical systems, numerical analysis, and machine learning. I completed my PhD in September 2024 in the Differential Equations and Numerical Analysis group at NTNU in Trondheim, Norway, under the supervision of Elena Celledoni and Brynjulf Owren. My doctoral thesis, “Neural Networks, Differential Equations, and Structure Preservation,” is available here .

I earned both my Bachelor’s and Master’s degrees in Applied Mathematics at the University of Verona, Italy. My bachelor’s thesis focused on dynamical billiards, while my master’s thesis studied the theory of integrability of non-Hamiltonian dynamical systems. During my university studies, I developed a strong interest in dynamical systems and geometric mechanics—interests that later found a natural continuation in numerical analysis and scientific computing.

My research focuses on analysing deep neural networks from the perspective of dynamical systems, as well as on data-driven modelling of dynamical systems. In particular, I am interested in interpreting deep neural networks as continuous-time dynamical systems, often modelled as non-autonomous parametric ordinary differential equations. From this viewpoint, network depth can be interpreted as a time variable, and learning corresponds to identifying a vector field whose flow transforms data in a meaningful way.

This perspective naturally connects deep learning with tools and questions from the theory of differential equations and numerical analysis, such as stability, robustness, structure preservation, and long-time behaviour. It also motivates problems in the opposite direction: using data-driven techniques to identify vector fields from observed trajectories, and developing hybrid approaches that combine classical numerical methods with machine learning for approximating solutions of ODEs and PDEs.

Alongside my academic work, I run Mathone, a mathematics outreach project I started in 2015. It began as a blog and later grew into a YouTube channel dedicated to mathematical popularisation. Until 2025, all content was produced in Italian; since 2026, I have transitioned to English to reach a broader audience.

I created this website to keep track of my research, improve my writing, and share what I learn along the way through the Blog . I am always happy to connect with researchers interested in related topics and open to potential collaborations.