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SUMMARY:Learning Controlled Stochastic Differential Equations - Luc  Broga
 t-Motte (Istituto Italiano di Tecnologica (IIT))
DTSTART:20250716T140000Z
DTEND:20250716T150000Z
UID:TALK234169@talks.cam.ac.uk
DESCRIPTION:The identification of controlled nonlinear dynamical systems f
 rom data is central to tasks such as control\, prediction\, optimization\,
  and fault detection\, with applications in robotics\, finance\, and biolo
 gy. This talk presents a method for estimating both drift and diffusion in
  stochastic differential equations with control inputs. The approach appli
 es to general settings involving nonlinear\, multidimensional dynamics and
  unknown\, non-uniform diffusion\, without requiring restrictive assumptio
 ns such as linearity or known diffusion. Assuming Sobolev regularity of th
 e coefficients\, we decompose the learning problem into two stages: estima
 ting system dynamics under a finite set of controls\, and recovering the g
 overning coefficients via the Fokker&ndash\;Planck equation. We establish 
 finite-sample learning guarantees in L2\, Linf\, and risk metrics\, with l
 earning rates adaptive to the Sobolev regularity of the coefficients. The 
 method is demonstrated through numerical experiments and released as an op
 en-source Python library.\nJoint work with Luc Brogat‑Motte\, Riccardo B
 onalli\, and Alessandro Rudi.
LOCATION:Seminar Room 2\, Newton Institute
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