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This paper considers deep out-of-distribution active learning. In practice, fully trained neural networks interact randomly with out-of-distribution (OOD) inputs and map aberrant samples randomly within the model representation space. Since…

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)…

The neural Ordinary Differential Equation (ODE) model has shown success in learning complex continuous-time processes from observations on discrete time stamps. In this work, we consider the modeling and forecasting of time series data that…

Forecasting irregularly sampled time series with missing values is a crucial task for numerous real-world applications such as healthcare, astronomy, and climate sciences. State-of-the-art approaches to this problem rely on Ordinary…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [arXiv:2104.13962], we explored the use of Neural Ordinary Differential Equations (NODE) as…

With advancements in computing and communication technologies, the Internet of Things (IoT) has seen significant growth. IoT devices typically collect data from various sensors, such as temperature, humidity, and energy meters. Much of this…

Solution of Ordinary Differential Equation (ODE) model of dynamical system may not agree with its observed values. Often this discrepancy can be attributed to unmodeled forcings in the evolution rule of the dynamical system. In this…

Irregular multivariate time series impose a trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often require sequential solvers prone to drift. To bridge…

Out-of-distribution (OOD) detection is crucial for the reliable deployment of machine learning models in real-world scenarios, enabling the identification of unknown samples or objects. A prominent approach to enhance OOD detection…

Time series are ubiquitous and occur naturally in a variety of applications -- from data recorded by sensors in manufacturing processes, over financial data streams to climate data. Different tasks arise, such as regression, classification…

Anomaly and missing data constitute a thorny problem in industrial applications. In recent years, deep learning enabled anomaly detection has emerged as a critical direction, however the improved detection accuracy is achieved with the…

Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems.…

In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the…

This study introduces a novel forecasting strategy that leverages the power of fractional differencing (FD) to capture both short- and long-term dependencies in time series data. Unlike traditional integer differencing methods, FD preserves…

Continuous normalizing flows (CNFs) and diffusion models (DMs) generate high-quality data from a noise distribution. However, their sampling process demands multiple iterations to solve an ordinary differential equation (ODE) with high…

Predictive simulations of complex systems are essential for applications ranging from weather forecasting to drug design. The veracity of these predictions hinges on their capacity to capture the effective system dynamics. Massively…

Time series prediction is challenging due to our limited understanding of the underlying dynamics. Conventional models such as ARIMA and Holt's linear trend model experience difficulty in identifying nonlinear patterns in time series. In…

Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.…

Irregularly sampled time series forecasting, characterized by non-uniform intervals, is prevalent in practical applications. However, previous research have been focused on regular time series forecasting, typically relying on transformer…

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…