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While exogenous variables have a major impact on performance improvement in time series analysis, inter-series correlation and time dependence among them are rarely considered in the present continuous methods. The dynamical systems of…

Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity…

In the field of cardiac electrophysiology (EP), effectively reducing noise in intra-cardiac signals is crucial for the accurate diagnosis and treatment of arrhythmias and cardiomyopathies. However, traditional noise reduction techniques…

Vision Transformers achieve impressive accuracy across a range of visual recognition tasks. Unfortunately, their accuracy frequently comes with high computational costs. This is a particular issue in video recognition, where models are…

The variational autoencoder (VAE) is a popular deep latent variable model used to analyse high-dimensional datasets by learning a low-dimensional latent representation of the data. It simultaneously learns a generative model and an…

An innovations sequence of a time series is a sequence of independent and identically distributed random variables with which the original time series has a causal representation. The innovation at a time is statistically independent of the…

Irregularly sampled time series commonly occur in several domains where they present a significant challenge to standard deep learning models. In this paper, we propose a new deep learning framework for probabilistic interpolation of…

Medical time series are often irregular and face significant missingness, posing challenges for data analysis and clinical decision-making. Existing methods typically adopt a single modeling perspective, either treating series data as…

Simulators based on neural networks offer a path to orders-of-magnitude faster electromagnetic wave simulations. Existing models, however, only address narrowly tailored classes of problems and only scale to systems of a few dozen degrees…

The Variation Evolving Method (VEM) that originates from the continuous-time dynamics stability theory seeks the optimal solutions with variation evolution principle. After establishing the first and the second evolution equations within…

Neural Ordinary Differential Equations (NODEs) use a neural network to model the instantaneous rate of change in the state of a system. However, despite their apparent suitability for dynamics-governed time-series, NODEs present a few…

Devising efficient algorithms that track the optimizers of continuously varying convex optimization problems is key in many applications. A possible strategy is to sample the time-varying problem at constant rate and solve the resulting…

In this paper we use a Variational Quantum Algorithm to solve Initial Value Problems with the Implicit Crank-Nicolson and the Method of Lines (MoL) evolution schemes. The unknown functions use a spectral decomposition with the Fourier…

The ability to record activities from hundreds of neurons simultaneously in the brain has placed an increasing demand for developing appropriate statistical techniques to analyze such data. Recently, deep generative models have been…

Cardiovascular diseases (CVDs) are disorders impacting the heart and circulatory system. These disorders are the foremost and continuously escalating cause of mortality worldwide. One of the main tasks when working with CVDs is analyzing…

Variational autoencoder-based voice conversion (VAE-VC) has the advantage of requiring only pairs of speeches and speaker labels for training. Unlike the majority of the research in VAE-VC which focuses on utilizing auxiliary losses or…

Neural ODEs are increasingly used as continuous-time models for scientific and sensor data, but unconstrained neural ODEs can drift and violate domain invariants (e.g., conservation laws), yielding physically implausible solutions. In turn,…

Predictive linear and nonlinear models based on kernel machines or deep neural networks have been used to discover dependencies among time series. This paper proposes an efficient nonlinear modeling approach for multiple time series, with a…

In this paper, we address the well-known challenge in the numerical solution of time-fractional partial differential equations (TFPDEs), namely, that the dependence on all previous time levels leads to storage requirements that grow…

Transformer models are increasingly used for solving Partial Differential Equations (PDEs). Several adaptations have been proposed, all of which suffer from the typical problems of Transformers, such as quadratic memory and time complexity.…