In this talk I will consider a method for learning the Lagrangian and forces for mechanical systems using the discrete Lagrange d'Alembert principle. The case of manifold valued data and data on Lie groups will also be discussed if time permits.
I will also describe a number of current projects with diverse applications where the main theme is learning vector fields from data.
Graph Neural Networks (GNNs) have emerged as powerful tools for nonlinear Model Order Reduction (MOR) of time-dependent parameterized Partial Differential Equations (PDEs) [1].
However, existing methodologies struggle to combine geometric inductive biases with interpretable latent dynamics, overlooking dynamics-driven features or disregarding geometric information, respectively.
In this...
Data-driven model discovery has become a powerful approach for identifying governing equations of dynamical systems using temporal data. The Sparse Identification of Nonlinear Dynamics (SINDy) algorithm, initially developed for ordinary differential equations (ODEs), has been extended to more general classes of problems, including partial differential equations (PDEs), stochastic differential...
The Hadamard decomposition is a powerful technique for data analysis and compression. Given an $m\times n$ matrix $X$ and two ranks $r_1,r_2\ll \min(m,n)$, we look for two low-rank matrices $X_1$ and $X_2$ of the same size of $X$ and with $\text{rank}(X_i)=r_i$ such that $X\approx X_1\circ X_2$, where $\circ$ is the element-wise product. In contrast with the well-known SVD, this decomposition...
