Whatever happens, there is always ‘noise’ – the random variations that confuse the bigger picture. It affects anything, from studying human impacts on climate change, through to the behaviour of countless consumers in the economy – there are always unexpected factors causing noise. Yet that noise is often missing in mathematical models of reality. With Mark Veraar's mathematical models this no longer needs to be the case – they help to incorporate noise into models to make them more realistic. He has now received a prestigious Vici grant, the largest grant of the Dutch NWO, which will help him to progress even further.
At the basis of Veraar's noise processing lies Brownian motion: the phenomenon that small particles follow, such as pollen in water, to take one example, an apparently random path, resulting from many random collisions with much smaller water molecules. The mathematical description of the phenomenon is over a hundred years old, but new properties are still being discovered, for example by Veraar. In Brownian motion models, noise remains unpredictable, but it often leads to more accurate models that better describe reality in cases such as models of climate science.
Mathematically, adding noise to a model leads to a so-called stochastic partial differential equation – and many of these equations are currently poorly understood. Numerical solution methods for these models are also often unavailable or very inefficient. Veraar wants to develop new mathematical techniques to improve understanding, and to find better and more rigorous approximation results. His Vici grant means that he is now aiming to contribute to new insights and methods on the long-term behaviour of these models.
Read more about Mark Veraar and his research in his Science Story.