2018/06/01 by Samy Wu Fung, Fung, Samy Wu, Lars Ruthotto +1 · 1 citation
Computer Science · Engineering · #FOS: Mathematics #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques #Target Tracking and Data Fusion in Sensor Networks
paper · pdf · doi:10.48550/arxiv.1806.00192
openalex publication_date 2018/06/01 · openalex created_date 2022/10/04 · openalex updated_date 2026/08/01
We consider a global variable consensus ADMM algorithm for solving\nlarge-scale PDE parameter estimation problems asynchronously and in parallel.\nTo this end, we partition the data and distribute the resulting subproblems\namong the available workers. Since each subproblem can be associated with\ndifferent forward models and right-hand-sides, this provides ample options for\ntailoring the method to different applications including multi-source and\nmulti-physics PDE parameter estimation problems. We also consider an\nasynchronous variant of consensus ADMM to reduce communication and latency.\n Our key contribution is a novel weighting scheme that empirically increases\nthe progress made in early iterations of the consensus ADMM scheme and is\nattractive when using a large number of subproblems. This makes consensus ADMM\ncompetitive for solving PDE parameter estimation, which incurs immense costs\nper iteration. The weights in our scheme are related to the uncertainty\nassociated with the solutions of each subproblem. We exemplarily show that the\nweighting scheme combined with the asynchronous implementation improves the\ntime-to-solution for a 3D single-physics and multiphysics PDE parameter\nestimation problems.\n