Non-parametric methods for learning continuous-time dynamical systems

Speaker: 
Harri Lähdesmäki

Welcome to a seminar with Harri Lähdesmäki (Aalto) on 25 October at 13.15 in room MV:L14 at Dept. Mathematical Sciences (Chalmers tvärgata 3, Gothenburg).


He will talk on:
"Non-parametric methods for learning continuous-time dynamical systems"

Abstract: Conventional differential equation models are parametric. However, for many complex/real-world systems it is practically impossible to determine parametric equations or interactions governing the underlying dynamics, rendering conventional models unpractical in many applications. To overcome this issue, we propose to use nonparametric models for differential equations by defining Gaussian process priors for the vector-field/drift and diffusion functions. We have developed statistical machine learning methods that can learn the underlying (arbitrary) ODE and SDE systems without prior knowledge. We formulate sensitivity equations for learning or use automatic differentiation with explicitly defined forward simulator for efficient model inference. Using simulated and real data, we demonstrate that our non-parametric methods can efficiently learn the underlying differential equation system, show the models' capabilities to infer unknown dynamics from sparse data, and to simulate the system forward into future. I will also highlight how our non-parametric models can learn stochastic differential equation transformations of inputs prior to a standard classification or regression function to implement state-of-the-art methods for continuous-time (infinitely) deep learning.
https://arxiv.org/abs/1803.04303
https://arxiv.org/abs/1807.05748
https://arxiv.org/abs/1810.04066

Fika and mingling with the speaker will follow at around 14.15 in the lunch-room.

University: 
Time of Seminar: 
2018-10-25 13:15 to 14:15
Location: 
room MV:L14 at Dept. Mathematical Sciences