Related papers: Fractional SDE-Net: Generation of Time Series Data…

While current generative models have achieved promising performances in time-series synthesis, they either make strong assumptions on the data format (e.g., regularities) or rely on pre-processing approaches (e.g., interpolations) to…

The origin of the long-range memory in the non-equilibrium systems is still an open problem as the phenomenon can be reproduced using models based on Markov processes. In these cases a notion of spurious memory is introduced. A good example…

A body of recent work in modeling neural activity focuses on recovering low-dimensional latent features that capture the statistical structure of large-scale neural populations. Most such approaches have focused on linear generative models,…

Perception of time from sequentially acquired sensory inputs is rooted in everyday behaviors of individual organisms. Yet, most algorithms for time-series modeling fail to learn dynamics of random event timings directly from visual or audio…

Generating high-quality time series data has emerged as a critical research topic due to its broad utility in supporting downstream time series mining tasks. A major challenge lies in modeling the intrinsic stochasticity of temporal…

There has been a great deal of recent interest in learning and approximation of functions that can be expressed as expectations of a given nonlinearity with respect to its random internal parameters. Examples of such representations include…

Accurate risk assessment is essential for safety-critical autonomous and control systems under uncertainty. In many real-world settings, stochastic dynamics exhibit asymmetric jumps and long-range memory, making long-term risk probabilities…

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…

Fractional-order differential equations (FDEs) enhance traditional differential equations by extending the order of differential operators from integers to real numbers, offering greater flexibility in modeling complex dynamical systems…

Long-term time series forecasting is a vital task and has a wide range of real applications. Recent methods focus on capturing the underlying patterns from one single domain (e.g. the time domain or the frequency domain), and have not taken…

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…

The conventional deep learning approaches for solving time-series problem such as long-short term memory (LSTM) and gated recurrent unit (GRU) both consider the time-series data sequence as the input with one single unit as the output…

Long Short-Term Memory (LSTM) networks are often used to capture temporal dependency patterns. By stacking multi-layer LSTM networks, it can capture even more complex patterns. This paper explores the effectiveness of applying stacked LSTM…

Forecasting time series and time-dependent data is a common problem in many applications. One typical example is solving ordinary differential equation (ODE) systems $\dot{x}=F(x)$. Oftentimes the right hand side function $F(x)$ is not…

This work contributes to the development of neural forecasting models with novel randomization-based learning methods. These methods improve the fitting abilities of the neural model, in comparison to the standard method, by generating…

Generating forecasts for time series with multiple seasonal cycles is an important use-case for many industries nowadays. Accounting for the multi-seasonal patterns becomes necessary to generate more accurate and meaningful forecasts in…

Recurrent neural networks (RNNs) were designed for dealing with time-series data and have recently been used for creating predictive models from functional magnetic resonance imaging (fMRI) data. However, gathering large fMRI datasets for…

Neural differential equations are a promising new member in the neural network family. They show the potential of differential equations for time series data analysis. In this paper, the strength of the ordinary differential equation (ODE)…

Making the most of multispectral image time-series is a promising but still relatively under-explored research direction because of the complexity of jointly analyzing spatial, spectral and temporal information. Capturing and characterizing…

Timeseries generated from a dynamical source can often be modeled as sample paths of a stochastic differential equation (SDE). The timeseries thus reflects the motion of a particle which flows along the direction provided by a drift /…