.png){kind=icon}
.png){kind=icon}
Return
Gradient Flow Algorithms for Density Propagation in Stochastic Systems
.png){kind=icon}
OA
AI
DOI：10.1109/TAC.2019.2951348.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
We develop a new computational framework to solve the partial differential equations (PDEs) governing the flow of the joint probability density functions (PDFs) in continuous-time stochastic nonlinear systems. The need for computing the transient joint PDFs subject to prior dynamics arises in uncertainty propagation, nonlinear filtering, and stochastic control. Our methodology breaks away from the traditional approach of spatial discretization or function approximation-both of which, in general, suffer from the curse-of-dimensionality. In the proposed framework, we discretize time but not the state space. We solve infinite dimensional proximal recursions in the manifold of joint PDFs, which in the small time-step limit, is theoretically equivalent to solving the underlying transport PDEs. The resulting computation has the geometric interpretation of gradient flow of certain free energy functional with respect to the Wasserstein metric arising from the theory of optimal mass transport. We show that dualization along with an entropic regularization, leads to a cone-preserving fixed point recursion that is proved to be contractive in Thompson metric. A block co-ordinate iteration scheme is proposed to solve the resulting nonlinear recursions with guaranteed convergence. This approach enables remarkably fast computation for nonparametric transient joint PDF propagation. Numerical examples and various extensions are provided to illustrate the scope and efficacy of the proposed approach.
Keywords:
Probability density function
Handheld computers
Measurement
Manifolds
Transient analysis
Uncertainty
Function approximation
Fokker-Planck-Kolmogorov (FPK) equation
gradient descent
optimal transport
proximal operator
uncertainty propagation
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
IF:
7
Papers:
1.3W
Citations:
6.7W
