arXiv subjects

Thomas Trigo Trindade

Publications and source records attributed to Thomas Trigo Trindade.

5 recordsLinked to original sources

arXiv2026

Dynamical Low-Rank Approximations for Kalman Filtering

We propose a dynamical low rank approximation of the Kalman-Bucy process (DLR-KBP), which evolves the filtering distribution of a partially continuously observed linear SDE on a small time-varying subspace at reduced computational cost. This reduction is valid in presence of small noise and when the filtering distribution concentrates around a low dimensional subspace. We further extend this approach to a DLR-ENKF process, where particles are evolved in a low dimensional time-varying subspace at reduced cost. This allows for a significantly larger ensemble size compared to standard EnKF at equivalent cost, thereby lowering the Monte Carlo error and improving filter accuracy. Theoretical properties of the DLR-KBP and DLR-ENKF are investigated, including a propagation of chaos property. Numerical experiments demonstrate the effectiveness of the technique.

math.NA↗

arXiv2026

Dynamical Low-Rank Ensemble Kalman filter for State/Parameter estimation

We propose a Dynamical Low-Rank Ensemble Kalman Filter (DLR-ENKF) for efficient joint state-parameter estimation in high-dimensional dynamical systems. The method extends the DLR-ENKF formulation of arXiv:2509.11210 to the augmented state-parameter framework, tracking the filtering density within a dynamically evolving low-dimensional subspace. Key developments include a time-integration strategy that combines the Basis Update & Galerkin scheme with forecast/analysis discretisation, and a DEIM-based hyper-reduction technique for efficient evaluation of nonlinear terms. We demonstrate the effectiveness, robustness, and computational advantages of the proposed approach on benchmark problems. The results highlight the potential of dynamically evolving reduced bases to achieve accurate filtering and parameter estimation at reduced computational cost.

math.NA↗

arXiv2024

A hybrid tau-leap for simulating chemical kinetics with applications to parameter estimation

We consider the problem of efficiently simulating stochastic models of chemical kinetics. The Gillespie Stochastic Simulation algorithm (SSA) is often used to simulate these models, however, in many scenarios of interest, the computational cost quickly becomes prohibitive. This is further exasperated in the Bayesian inference context when estimating parameters of chemical models, as the intractability of the likelihood requires multiple simulations of the underlying system. To deal with issues of computational complexity in this paper, we propose a novel hybrid $τ$-leap algorithm for simulating well-mixed chemical systems. In particular, the algorithm uses $τ$-leap when appropriate (high population densities), and SSA when necessary (low population densities, when discrete effects become non-negligible). In the intermediate regime, a combination of the two methods, which leverages the properties of the underlying Poisson formulation, is employed. As illustrated through a number of numerical experiments the hybrid $τ$ offers significant computational savings when compared to SSA without however sacrificing the overall accuracy. This feature is particularly welcomed in the Bayesian inference context, as it allows for parameter estimation of stochastic chemical kinetics at reduced computational cost.

q-bio.MN↗

arXiv2024

Petrov-Galerkin Dynamical Low Rank Approximation:SUPG stabilisation of advection-dominated problems

We propose a novel framework of generalised Petrov-Galerkin Dynamical Low Rank Approximations (DLR) in the context of random PDEs. It builds on the standard Dynamical Low Rank Approximations in their Dynamically Orthogonal formulation. It allows to seamlessly build-in many standard and well-studied stabilisation techniques that can be framed as either generalised Galerkin methods, or Petrov-Galerkin methods. The framework is subsequently applied to the case of Streamine Upwind/Petrov Galerkin (SUPG) stabilisation of advection-dominated problems with small stochastic perturbations of the transport field. The norm-stability properties of two time discretisations are analysed. Numerical experiments confirm that the stabilising properties of the SUPG method naturally carry over to the DLR framework.

math.NA↗

arXiv2024

Error estimates for SUPG-stabilised Dynamical Low Rank Approximations

We perform an error analysis of a fully discretised Streamline Upwind Petrov Galerkin Dynamical Low Rank (SUPG-DLR) method for random time-dependent advection-dominated problems. The time integration scheme has a splitting-like nature, allowing for potentially efficient computations of the factors characterising the discretised random field. The method allows to efficiently compute a low-rank approximation of the true solution, while naturally "inbuilding" the SUPG stabilisation. Standard error rates in the L2 and SUPG-norms are recovered. Numerical experiments validate the predicted rates.

math.NA↗