Adaptive deep density approximation for stochastic dynamical systems

arXiv:2405.02810v1 Announce Type: cross
Abstract: In this paper we consider adaptive deep neural network approximation for stochastic dynamical systems. Based on the Liouville equation associated with the stochastic dynamical systems, a new temporal KRnet (tKRnet) is proposed to approximate the probability density functions (PDFs) of the state variables. The tKRnet gives an explicit density model for the solution of the Liouville equation, which alleviates the curse of dimensionality issue that limits the application of traditional grid based numerical methods. To …

abstract approximation arxiv cs.na deep neural network equation functions math.na network neural network paper pdfs probability state stat.ml stochastic systems temporal type variables