相关论文: Neural Stochastic Differential Equations with Chan…

This paper analyzes the training process of GANs via stochastic differential equations (SDEs). It first establishes SDE approximations for the training of GANs under stochastic gradient algorithms, with precise error bound analysis. It then…

We propose a novel Stochastic Differential Equation (SDE) framework to address the problem of learning uncertainty-aware representations for graph-structured data. While Graph Neural Ordinary Differential Equations (GNODEs) have shown…

Spatio-temporal (ST) data for urban applications, such as taxi demand, traffic flow, regional rainfall is inherently stochastic and unpredictable. Recently, deep learning based ST prediction models are proposed to learn the ST…

This article introduces a novel Bayesian method for asynchronous change-point detection in multivariate time series. This method allows for change-points to occur earlier in some (leading) series followed, after a short delay, by…

Sequential (online) change-point detection involves continuously monitoring time-series data and triggering an alarm when shifts in the data distribution are detected. We propose an algorithm for real-time identification of alterations in…

Generative adversarial networks (GANs) have shown promising results when applied on partial differential equations and financial time series generation. We investigate if GANs can also be used to approximate one-dimensional Ito stochastic…

This study examines the challenges of modeling complex and noisy data related to socioeconomic factors over time, with a focus on data from various districts in Odisha, India. Traditional time-series models struggle to capture both trends…

Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated…

Deep Neural Networks (DNNs) have been shown vulnerable to Test-Time Evasion attacks (TTEs, or adversarial examples), which, by making small changes to the input, alter the DNN's decision. We propose an unsupervised attack detector on DNN…

Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units,…

We propose a new method for inferring the governing stochastic ordinary differential equations (SODEs) by observing particle ensembles at discrete and sparse time instants, i.e., multiple "snapshots". Particle coordinates at a single time…

We consider the filtering and prediction problem for a diffusion process. The signal and observation are modeled by stochastic differential equations (SDEs) driven by correlated Wiener processes. In classical estimation theory,…

This paper proposes a novel deep generative model, called BSDE-Gen, which combines the flexibility of backward stochastic differential equations (BSDEs) with the power of deep neural networks for generating high-dimensional complex target…

Graph-based change point detection (CPD) play an irreplaceable role in discovering anomalous graphs in the time-varying network. While several techniques have been proposed to detect change points by identifying whether there is a…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

Change points in real-world systems mark significant regime shifts in system dynamics, possibly triggered by exogenous or endogenous factors. These points define regimes for the time evolution of the system and are crucial for understanding…

Anomaly detection in time series data, to identify points that deviate from normal behaviour, is a common problem in various domains such as manufacturing, medical imaging, and cybersecurity. Recently, Generative Adversarial Networks (GANs)…

We present a deep learning model for data-driven simulations of random dynamical systems without a distributional assumption. The deep learning model consists of a recurrent neural network, which aims to learn the time marching structure,…

The stochastic interpolant framework offers a powerful approach for constructing generative models based on ordinary differential equations (ODEs) or stochastic differential equations (SDEs) to transform arbitrary data distributions.…

The behavior of many dynamical systems follow complex, yet still unknown partial differential equations (PDEs). While several machine learning methods have been proposed to learn PDEs directly from data, previous methods are limited to…