STAGE High Performance Generative Adversarial Network for Optimized Monte Carlo Simulations

Developments in applied mathematics must take into account the new computing hardware directions. In numerical probability, solutions based on nested Monte Carlo (MC) become both accurate and competitive because adapted to parallel architectures includin Graphics Processing Units. In our recent work, we simulate on GPU nonlinear Parabolic Partial Differential Equations (PPDEs) of dimension 100 in a much shorter execution time than any other method. Moreover, the effectiveness of MC can be further enhanced using a Neural Network (NN) for the inference of a substantial part of the result. Using pre-trained NNs should then become the mainstream practice in large MC simulations, in particular in High Performance Computing (HPC) applications. In numerical probability community, the use of NNs with MC is becoming a standard for the simulation of PPDEs and especially in Mathematical Finance. These contributions implement however NNs for their ability to provide a solution to complex problems. They miss then the genericity of NN trained on a parameterized model to be reused by other applications (automation) and for a large variety of data (scalability). In contrast, our project trains on MC-simulated values a High Performance Computing MC Generative Adversarial Network (HPC-MC-GAN) so it generates a large number of inferred values in a record execution time, in order to make it a reference building block to other larger applications