Previous talks at the SCCS Colloquium

Atalay Yirik: Machine Learning of Stochastic Differential Equations for Infection Models using Neural Networks

SCCS Colloquium |


Mathematical models which take the observed data into account provide favourable insights for dynamical systems. In this project, we identify and model the behaviour of coarse-grained particles in dynamical crowd setting from data which we observed through number of experiments. The dynamical system we study focuses on the spread of a contagious disease. We represent the behaviour of the coarse-grained particles - which are infectious agents in this case- by stochastic differential equations (SDE). In the first place, we gather corresponding agent-based simulation data for different scenarios which the spread of the virus is probable in daily life cycle through our simulation tool ’Vadere’. We then approximate the drift and diffusivity functions of SDEs through Artificial Neural Networks (ANN) which can be considered as effective stochastic ResNets. In our ANN structure, our loss function is inspired by low order approximators , namely, Euler Maruyama and Milstein methods. We then identify the surrogate models for virus spread/coarse grained particles in a stochastic crowd dynamics setting with the learned model. The infected rate for each individual is learned through the model and used to predict the likelihood of the viral infection spreading to other individuals in the crowd. We then visualized the spread of the infection through the crowd using a network with nodes representing population in an environment. The results of this study provide valuable insights into the potential spread of a viral infection in a crowd.

Master's thesis presentation. Atalay is advised by Dr. Felix Dietrich.