相关论文: An integration-free approach for particle flow fil…

Many conservative physical systems can be described using the Hamiltonian formalism. A notable example is the Vlasov-Poisson equations, a set of partial differential equations that govern the time evolution of a phase-space density function…

Devising optimal interventions for constraining stochastic systems is a challenging endeavour that has to confront the interplay between randomness and nonlinearity. Existing methods for identifying the necessary dynamical adjustments…

We introduce a novel unit-time ordinary differential equation (ODE) flow called the preconditioned F\"{o}llmer flow, which efficiently transforms a Gaussian measure into a desired target measure at time 1. To discretize the flow, we apply…

We present a new strategy for filtering high-dimensional multiscale systems characterized by high-order non-Gaussian statistics using observations from leading-order moments. A closed stochastic-statistical modeling framework suitable for…

First, a meshless simulation method is presented for multiphase fluid-particle flows with a two-way coupled Smoothed Particle Hydrodynamics (SPH) for the fluid and the Discrete Element Method (DEM) for the solid phase. The unresolved fluid…

We present a novel particle filtering framework for continuous-time dynamical systems with continuous-time measurements. Our approach is based on the duality between estimation and optimal control, which allows reformulating the estimation…

In this article, we consider exactly divergence-free $H$(div)-conforming finite element methods for time-dependent incompressible viscous flow problems. This is an extension of previous research concerning divergence-free $H^1$-conforming…

Estimation of a dynamical system's latent state subject to sensor noise and model inaccuracies remains a critical yet difficult problem in robotics. While Kalman filters provide the optimal solution in the least squared sense for linear and…

Gaseous flows under an external force are intrinsically defined by their multi-scale nature due to the large variation of densities along the forcing direction. Devising a numerical method capable of accurately and efficiently solving…

We investigate the application of ensemble transform approaches to Bayesian inference of logistic regression problems. Our approach relies on appropriate extensions of the popular ensemble Kalman filter and the feedback particle filter to…

This paper concerns the estimation problem of attitude, position, and linear velocity of a rigid-body autonomously navigating with six degrees of freedom (6 DoF). The navigation dynamics are highly nonlinear and are modeled on the matrix…

In two and three dimensions, this study is focused on the numerical analysis of an eigenproblem associated with a fluid-structure model for sloshing and elasto-acoustic vibration. We use a displacement-Herrmann pressure formulation for the…

Motivated by the viewpoint of integrable systems, we study commuting flows of 2-component quasilinear equations, reducing to investigate the solutions of the wave equation with non-constant speed. In this paper, we apply the reduction…

It is well known that closed-form analytical solutions for AC power flow equations do not exist in general. This paper proposes a multi-dimensional holomorphic embedding method (MDHEM) to obtain an explicit approximate analytical AC…

Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give…

Ordinary differential equation (ODE) based generative models have emerged as a powerful approach for producing high-quality samples in many applications. However, the ODE-based methods either suffer the discretization error of numerical…

Novel experimental modalities acquire spatially resolved velocity measurements for steady state and transient flows which are of interest for engineering and biological applications. One of the drawbacks of such high resolution velocity…

In this work, we propose a numerical method to compute the Wasserstein Hamiltonian flow (WHF), which is a Hamiltonian system on the probability density manifold. Many well-known PDE systems can be reformulated as WHFs. We use parameterized…

This research explores the development and application of the High-Order Dynamic Integration Method for solving integro-differential equations, with a specific focus on turbulent fluid dynamics. Traditional numerical methods, such as the…

Filtering is crucial in engineering fields, providing vital state estimation for control systems. However, the nonlinear nature of complex systems and the presence of non-Gaussian noises pose significant challenges to the performance of…