1 code implementation • 1 May 2023 • Cheng Fang, Yubin Lu, Ting Gao, Jinqiao Duan
The prediction of stochastic dynamical systems and the capture of dynamical behaviors are profound problems.
no code implementations • 19 Jan 2023 • Yubin Lu, Zhongjian Wang, Guillaume Bal
Using small-time approximations of the Green's function of the forward diffusion, we show that the analytical mean drift function in DDPM and the score function in SGM asymptotically blow up in the final stages of the sampling process for singular data distributions such as those concentrated on lower-dimensional manifolds, and is therefore difficult to approximate by a network.
1 code implementation • 31 Jan 2022 • Cheng Fang, Yubin Lu, Ting Gao, Jinqiao Duan
Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained a lot of attention in various fields.
1 code implementation • 25 Nov 2021 • Luxuan Yang, Ting Gao, Yubin Lu, Jinqiao Duan, Tao Liu
In this article, we employ a collection of stochastic differential equations with drift and diffusion coefficients approximated by neural networks to predict the trend of chaotic time series which has big jump properties.
no code implementations • 30 Sep 2021 • Yang Li, Yubin Lu, Shengyuan Xu, Jinqiao Duan
Despite the wide applications of non-Gaussian fluctuations in numerous physical phenomena, the data-driven approaches to extract stochastic dynamical systems with (non-Gaussian) L\'evy noise are relatively few so far.
1 code implementation • 28 Aug 2021 • Yubin Lu, Yang Li, Jinqiao Duan
In this work, we propose a data-driven approach to extract stochastic governing laws with both (Gaussian) Brownian motion and (non-Gaussian) L\'evy motion, from short bursts of simulation data.
no code implementations • 29 Jul 2021 • Yubin Lu, Romit Maulik, Ting Gao, Felix Dietrich, Ioannis G. Kevrekidis, Jinqiao Duan
Specifically, the learned map is a multivariate normalizing flow that deforms the support of the reference density to the support of each and every density snapshot in time.