Surrogate Models

Remember the HPC post? Simulating a portfolio of financial instruments across scenarios might take days on single processors. What you have to do is solving many millions of complex differential or integro-differential equations. Mathematica helps us to exploit multi-core environments, but to get results in real-time, you need more. In certain cases (VaR), we gain enormous speed-up by principle component application, or, if Montecarlo simulation is required, we put valuations on GPU co-processors.

But we are also studying the possibility to use Surrogate Models (SuM). SuMs are easy-to-compute compact models that mimic the complex behaviour of the models in special ranges used in a simulation. Surrogate models are constructed using data-driven approaches as we know from machine learning in our mlf . Simplified: run the simulation with the "original" models, trying to cover the whole working-space, sample the results and extract the SUMs from them.

The finding process is time consuming, because you need to do massive model and cross-model testing.

In Mathematica's declarative environment it is easy to define higher level tasks, as in mlf, where one can define such machine learning tasks, which then run automatically.

In UnRisk this is an ongoing project, but if we think of principle component analysis, GPU co-processing, SuM and grid computing, we might gain gigantic speed-ups. With the indispensable support of Mathematica .