State inference in spatially-extended dynamical systems is a challenging problem with significant practical applications such as numerical weather prediction. Particle filters (PFs) while having attractive theoretical properties require infeasibly large ensemble sizes for accurate inference in high-dimensional spatial models. Localisation approaches, which exploit low dependence between state variables at spatially distant points by performing local state updates, offer a potential resolution to this issue. Naively applying the resampling step of the PF update locally can however produce implausible spatially discontinuous states. The ensemble transform PF replaces resampling with linear transformation by an optimal transport (OT) map and can be localised by computing OT maps for every spatial mesh point. The resulting scheme is however computationally intensive for dense meshes and still produces non-smooth states. In this talk I will present a new local ensemble transform PF method which computes a fixed number of OT maps independent of the mesh resolution and smoothly interpolates these maps across space, reducing the computation required while also ensuring state particles retain spatial smoothness properties. I will illustrate the performance of the proposed approach compared to alternative methods in several nonlinear spatiotemporal models, including a challenging two-dimensional stochastic Navier-Stokes example.
Joint work with Alex Thiery.