A new MOX Report entitled “ParaFlow: Parareal Acceleration of Gradient-Flow Minimization” by Bellezza P.; Ciaramella G.; Macchini C.; Mazzieri I.; Verani M. has appeared in the MOX Report Collection.
Check it out here: https://www.mate.polimi.it/biblioteca/add/qmox/51-2026.pdf
Abstract: This work presents the ParaFlow class of optimization algorithms and its specific realization, the ParaFlowS algorithm. The ParaFlow framework employs the Parareal algorithm to enhance the convergence rate of gradient flows towards a minimum. The ParaFlowS method integrates the Parareal approach with (potentially stochastic) gradient descent (GD) method, resulting in a purely sequential optimization strategy. The proposed acceleration framework is assessed through extensive numerical experiments on unconstrained optimization problems associated with the training of fully connected neural networks.
