Multiscale models are often used in situations where one is interested in increasing modeling detail to include the effects of phenomena that are microscopic, compared to the macroscopic scale of interest. This usually increased the dimensionality of the model to such an extent that a deterministic simulation becomes intractable and one needs to resort to stochastic (Monte Carlo) simulation methods. Then, a new challenge arises: how can we ensure that the extra accuracy that results from adding the microscopic level of modeling detail is not completely lost in the statistical noise that is inherent in a stochastic Monte Carlo simulation?
In our group, we are working on variance reduction techniques based on control variates in this setting. We either have an approximate macroscopic model available, with which we can perform coupled stochastic simulations, or we couple stochastic simulations with the same microscopic model but related initial conditions.
- A. Lejon, B. Mortier and G. Samaey, Variance-reduced simulation of stochastic agent-based models for tumor growth, 2015. Submitted.
- D. Avitabile, R. Hoyle and G. Samaey, Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in, SIAM Journal on Applied Dynamical Systems 13(4):1583–1619, 2014.
- M. Rousset and G. Samaey, Individual-based models for bacterial chemotaxis in the diffusion asymptotics, Mathematical Models and Methods in Applied Sciences 23:2005-2037, 2013.
- M. Rousset and G. Samaey, Simulating individual-based models for bacterial chemotaxis with asymptotic variance reduction, Mathematical Models and Methods in Applied Sciences 23:2155-2191, 2013.