Alastair Gregory

Alastair Gregory, Colin Cotter, Sebastian Reich

This paper extends the Multilevel Monte Carlo variance reduction technique to nonlinear filtering. In particular, Multilevel Monte Carlo is applied to a certain variant of the particle filter, the Ensemble Transform Particle Filter. A key aspect is the use of optimal transport methods to re-establish correlation between coarse and fine ensembles after resampling; this controls the variance of the estimator. Numerical examples present a proof of concept of the effectiveness of the proposed method, demonstrating significant computational cost reductions (relative to the single-level ETPF counterpart) in the propagation of ensembles.

Qiqi Wang, Steven Gomez, Patrick Blonigan et al.

We present a reformulation of unsteady turbulent flow simulations. The initial condition is relaxed and information is allowed to propagate both forward and backward in time. Simulations of chaotic dynamical systems with this reformulation can be proven to be well-conditioned time domain boundary value problems. The reformulation can enable scalable parallel-in-time simulation of turbulent flows.

Alastair Gregory, Din-Houn Lau, Alex Tessier et al.

An increasing amount of civil engineering applications are utilising data acquired from infrastructure instrumented with sensing devices. This data has an important role in monitoring the response of these structures to excitation, and evaluating structural health. In this paper we seek to monitor pedestrian-events (such as a person walking) on a footbridge using strain and acceleration data. The rate of this data acquisition and the number of sensing devices make the storage and analysis of this data a computational challenge. We introduce a streaming method to compress the sensor data, whilst preserving key patterns and features (unique to different sensor types) corresponding to pedestrian-events. Numerical demonstrations of the methodology on data obtained from strain sensors and accelerometers on the pedestrian footbridge are provided to show the trade-off between compression and accuracy during and in-between periods of pedestrian-events.

Alastair Gregory, Colin Cotter

This paper presents a seamless algorithm for the application of the multilevel Monte Carlo (MLMC) method to the ensemble transform particle filter (ETPF). The algorithm uses a combination of optimal coupling transformations between coarse and fine ensembles in difference estimators within a multilevel framework, to minimise estimator variance. It differs from that of Gregory et al. (2016) in that strong coupling between the coarse and fine ensembles is seamlessly maintained during all stages of the assimilation algorithm, instead of using independent transformations to equal weights followed by recoupling with an assignment problem. This modification is found to lead to an increased rate in variance decay between coarse and fine ensembles with level in the hierarchy, a key component of MLMC. This offers the potential for greater computational cost reductions. This is shown, alongside evidence of asymptotic consistency, in numerical examples.