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Clinical time series data from electronic health records and medical registries offer unprecedented opportunities to understand patient trajectories and inform medical decision-making. However, leveraging such data presents significant…

Latent variable models provide a powerful framework for incorporating and inferring unobserved factors in observational data. In causal inference, they help account for hidden factors influencing treatment or outcome, thereby addressing…

We develop a numerical method to reconstruct systems of ordinary differential equations (ODEs) from time series data without {\it a priori} knowledge of the underlying ODEs using sparse basis learning and sparse function reconstruction. We…

To address the complexity of financial time series, this paper proposes a forecasting model combining sliding window and variational mode decomposition (VMD) methods. Historical stock prices and relevant market indicators are used to…

While deep learning succeeds in a wide range of tasks, it highly depends on the massive collection of annotated data which is expensive and time-consuming. To lower the cost of data annotation, active learning has been proposed to…

Computational fluid dynamics (CFD) is a powerful tool for modeling turbulent flow and is commonly used for urban microclimate simulations. However, traditional CFD methods are computationally intensive, requiring substantial hardware…

The fast simulation of dynamical systems is a key challenge in many scientific and engineering applications, such as weather forecasting, disease control, and drug discovery. With the recent success of deep learning, there is increasing…

This paper presents a novel First Order Plus Fractional Diffusive Delay (FOPFDD) model, capable of modeling delay dominant systems with high accuracy. The novelty of the FOPFDD is the Fractional Diffusive Delay (FDD) term, an exponential…

Computational Fluid Dynamics (CFD) is the main approach to analyzing flow field. However, the convergence and accuracy depend largely on mathematical models of flow, numerical methods, and time consumption. Deep learning-based analysis of…

Scientific Machine Learning (ML) is gaining momentum as a cost-effective alternative to physics-based numerical solvers in many engineering applications. In fact, scientific ML is currently being used to build accurate and efficient…

We study the problem of out-of-distribution dynamics (OODD) detection, which involves detecting when the dynamics of a temporal process change compared to the training-distribution dynamics. This is relevant to applications in control,…

The past few years have seen impressive progress in the development of deep generative models capable of producing high-dimensional, complex, and photo-realistic data. However, current methods for evaluating such models remain incomplete:…

Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an active research field. However, current methods are…

We investigate neural ordinary and stochastic differential equations (neural ODEs and SDEs) to model stochastic dynamics in fully and partially observed environments within a model-based reinforcement learning (RL) framework. Through a…

Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…

We consider several non-local models for traffic flow, including both microscopic ODE models and macroscopic PDE models. The ODE models describe the movement of individual cars, where each driver adjusts the speed according to the road…

Current time series foundation models (TSFMs) primarily focus on learning prevalent and regular patterns within a predefined time or frequency domain to enable supervised downstream tasks (e.g., forecasting). Consequently, they are often…

Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…

Ordinary differential equations (ODEs) are central to scientific modelling, but inferring their vector fields from noisy trajectories remains challenging. Current approaches such as symbolic regression, Gaussian process (GP) regression, and…

Spatio-temporal forecasting is essential for real-world applications such as traffic management and urban computing. Although recent methods have shown improved accuracy, they often fail to account for dynamic deviations between current…