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Found 7 papers, 4 papers with code
Reservoir Computing with Error Correction: Long-term Behaviors of Stochastic Dynamical Systems
The prediction of stochastic dynamical systems and the capture of dynamical behaviors are profound problems.
Mathematical analysis of singularities in the diffusion model under the submanifold assumption
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.
An end-to-end deep learning approach for extracting stochastic dynamical systems with $α$-stable Lévy noise
Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained a lot of attention in various fields.
Neural network stochastic differential equation models with applications to financial data forecasting
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.
Extracting stochastic dynamical systems with $α$-stable Lévy noise from data
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.
Extracting Stochastic Governing Laws by Nonlocal Kramers-Moyal Formulas
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.
Learning the temporal evolution of multivariate densities via normalizing flows
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.
