Imply-field neural networks: studying mappings on Wasserstein area
Authors: Huyên Pham, Xavier Warin
Summary: We examine the machine studying job for fashions with operators mapping between the Wasserstein area of chance measures and an area of capabilities, like e.g. in mean-field video games/management issues. Two courses of neural networks, primarily based on bin density and on cylindrical approximation, are proposed to be taught these so-called mean-field capabilities, and are theoretically supported by common approximation theorems. We carry out a number of numerical experiments for coaching these two mean-field neural networks, and present their accuracy and effectivity within the generalization error with numerous take a look at distributions. Lastly, we current completely different algorithms counting on mean-field neural networks for fixing time-dependent mean-field issues, and illustrate our outcomes with numerical assessments for the instance of a semi-linear partial differential equation within the Wasserstein area of chance measures.