A New Distribution-Free Concept for Representing, Comparing, and Propagating Uncertainty in Dynamical Systems with Kernel Probabilistic Programming
This work provides a new foundational approach for handling uncertainty in dynamical systems, which could impact various fields relying on stochastic modeling.
The paper tackles the problem of representing, comparing, and propagating uncertainty in stochastic dynamical systems by introducing a distribution-free concept based on kernel mean embedding and kernel probabilistic programming, with results demonstrated through numerical examples and supported by functional analysis theory.
This work presents the concept of kernel mean embedding and kernel probabilistic programming in the context of stochastic systems. We propose formulations to represent, compare, and propagate uncertainties for fairly general stochastic dynamics in a distribution-free manner. The new tools enjoy sound theory rooted in functional analysis and wide applicability as demonstrated in distinct numerical examples. The implication of this new concept is a new mode of thinking about the statistical nature of uncertainty in dynamical systems.