Repository: Freie Universit├Ąt Berlin, Math Department

Less interaction with forward models in Langevin dynamics: Enrichment and Homotopy Martin , Robert , David

Eigel, Martin and Gruhlke, Robert and Sommer, David (2024) Less interaction with forward models in Langevin dynamics: Enrichment and Homotopy Martin , Robert , David. arXiv To appear in SIADS . (Submitted)

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Official URL: https://doi.org/10.48550/arXiv.2212.11528

Abstract

Ensemble methods have become ubiquitous for the solution of Bayesian inference problems. State-of-the-art Langevin samplers such as the Ensemble Kalman Sampler (EKS), Affine Invariant Langevin Dynamics (ALDI) or its extension using weighted covariance estimates rely on successive evaluations of the forward model or its gradient. A main drawback of these methods hence is their vast number of required forward calls as well as their possible lack of convergence in the case of more involved posterior measures such as multimodal distributions. The goal of this paper is to address these challenges to some extend. First, several possible adaptive ensemble enrichment strategies that successively enlarge the number of particles in the underlying Langevin dynamics are discusses that in turn lead to a significant reduction of the total number of forward calls. Second, analytical consistency guarantees of the ensemble enrichment method are provided for linear forward models. Third, to address more involved target distributions, the method is extended by applying adapted Langevin dynamics based on a homotopy formalism for which convergence is proved. Finally, numerical investigations of several benchmark problems illustrates the possible gain of the proposed method, comparing it to state-of-the-art Langevin samplers.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Deterministic and Stochastic PDEs Group
ID Code:3107
Deposited By: Ulrike Eickers
Deposited On:19 Feb 2024 15:53
Last Modified:20 Feb 2024 13:45

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