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Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…

Deep neural networks (DNNs) have been widely used in various video analytic tasks. These tasks demand real-time responses. Due to the limited processing power on mobile devices, a common way to support such real-time analytics is to offload…

Time series modeling has entered an era of unprecedented growth in the size and complexity of data which require new modeling approaches. While many new general purpose machine learning approaches have emerged, they remain poorly understand…

In realistic scenarios, multivariate timeseries evolve over case-by-case time-scales. This is particularly clear in medicine, where the rate of clinical events varies by ward, patient, and application. Increasingly complex models have been…

Bidirectional recurrent neural networks (RNN) are trained to predict both in the positive and negative time directions simultaneously. They have not been used commonly in unsupervised tasks, because a probabilistic interpretation of the…

Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…

Classical methods of solving spatiotemporal dynamical systems include statistical approaches such as autoregressive integrated moving average, which assume linear and stationary relationships between systems' previous outputs. Development…

Many real-world datasets are time series that are sequentially collected and contain rich temporal information. Thus, a common interest in practice is to capture dynamics of time series and predict their future evolutions. To this end, the…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of…

Increasing the layer number of on-chip photonic neural networks (PNNs) is essential to improve its model performance. However, the successively cascading of network hidden layers results in larger integrated photonic chip areas. To address…

Continuous normalizing flows (CNFs) construct invertible mappings between an arbitrary complex distribution and an isotropic Gaussian distribution using Neural Ordinary Differential Equations (neural ODEs). It has not been tractable on…

Time series forecasting has received a lot of attention, with recurrent neural networks (RNNs) being one of the widely used models due to their ability to handle sequential data. Previous studies on RNN time series forecasting, however,…

Recurrent Neural Networks (RNNs) are widely used for online regression due to their ability to generalize nonlinear temporal dependencies. As an RNN model, Long-Short-Term-Memory Networks (LSTMs) are commonly preferred in practice, as these…

Effective anomaly detection in time series is pivotal for modern industrial applications and financial systems. Due to the scarcity of anomaly labels and the high cost of manual labeling, reconstruction-based unsupervised approaches have…

Recurrent Neural Networks (RNNs) are designed to handle sequential data but suffer from vanishing or exploding gradients. Recent work on Unitary Recurrent Neural Networks (uRNNs) have been used to address this issue and in some cases,…

Recurrent neural networks have achieved great success in many NLP tasks. However, they have difficulty in parallelization because of the recurrent structure, so it takes much time to train RNNs. In this paper, we introduce sliced recurrent…

Background. Commonly, Deep Neural Networks (DNNs) generalize well on samples drawn from a distribution similar to that of the training set. However, DNNs' predictions are brittle and unreliable when the test samples are drawn from a…

Modern graph representation learning works mostly under the assumption of dealing with regularly sampled temporal graph snapshots, which is far from realistic, e.g., social networks and physical systems are characterized by continuous…

Recurrent neural networks (RNNs) are a powerful approach for time series prediction. However, their performance is strongly affected by their architecture and hyperparameter settings. The architecture optimization of RNNs is a…

By interpreting the forward dynamics of the latent representation of neural networks as an ordinary differential equation, Neural Ordinary Differential Equation (Neural ODE) emerged as an effective framework for modeling a system dynamics…