Réglage des hyperparamètres pour la méthode Gauss-Seidel projetée dans les simulations de corps rigides

Abstract

Physical simulation of rigid bodies is affected by the type of solver used to solve the kinematic constraints. For interactive simulations, it is recommended to use an interactive solver such as the projected Gauss-Seidel (PGS) method. In this thesis, an automatic pipeline is proposed to optimize some parameters of the algorithm, including the relaxation parameter and the regularization parameter. The hyperparameters’ optimization was performed using a covariance matrix adaptation evolution strategy (CMA-ES). Our analysis confirms through rigorous experimentation that the guideline proposed, for the choice of the relaxation parameter, in previous works is a good choice. We also show that the SOR parameter can be adjusted on a per-frame basis by a linear relationship with the conditioning of the systems for each simulation. These relationships could serve as a basis for future work to choose the relaxation parameter using a machine learning-based adjustment for a given simulation. Moreover, the work done allowed us to reduce the overall error thanks to the use of optimized hyperparameters. The reduction of the error is also accompanied by a reduction of the number of iterations. This last result could be a starting point to reduce the resolution time in a real time interactive simulations.

Date	27 Apr 2022
Original language	French
Awarding Institution	École de technologie supérieure
Supervisor	Sheldon Andrews (Supervisor)