Joi, 12 noiembrie 2026, ora 10:30,  în sala e, clădirea Mathematica, Dr. Maria Oprea (Institute of Science and Technology, Austria) va susține o prelegere cu titlul:

Learning differential equations using measure-based algorithms

în cadrul Seminarului de Operatori Neliniari și Ecuații Diferențiale.

Abstract: Suppose you observe a dynamical system, governed by an ODE or PDE,  only through the data it produces, with no direct access to its equations of motion. Classical system identification methods, such as Sparse Identification of Nonlinear Dynamics (SINDy) or Neural ODEs, assume access to a single, well-resolved trajectory. Yet many real-world settings violate this assumption: data may represent the system’s attractor without trajectory labels, trajectories may be sampled too coarsely for finite differences to be reliable, or extrinsic noise may cause deterministic approaches to break down entirely.

In this talk, I address the problem of reconstructing an underlying dynamical system when the available data takes the form of a probability distribution rather than a trajectory. I will first present an extension of classical inverse-problem and dynamical-systems machinery to the setting where the state space is the manifold of probability measures. Building on this foundation, I will then survey algorithmic strategies for identifying equations of motion from distributional data, and provide a quantitative analysis of the benefits that a measure-theoretic perspective offers over trajectory-based approaches.