Related papers: Continuous Depth Recurrent Neural Differential Equ…

Recurrent neural networks (RNNs) have proved effective at one dimensional sequence learning tasks, such as speech and online handwriting recognition. Some of the properties that make RNNs suitable for such tasks, for example robustness to…

Random ordinary differential equations (RODEs), i.e. ODEs with random parameters, are often used to model complex dynamics. Most existing methods to identify unknown governing RODEs from observed data often rely on strong prior knowledge.…

Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…

Neural Ordinary Differential Equations (NODEs) have proven to be a powerful modeling tool for approximating (interpolation) and forecasting (extrapolation) irregularly sampled time series data. However, their performance degrades…

Learning continuous-time dynamics on complex networks is crucial for understanding, predicting and controlling complex systems in science and engineering. However, this task is very challenging due to the combinatorial complexities in the…

Conventional neural architectures for sequential data present important limitations. Recurrent networks suffer from exploding and vanishing gradients, small effective memory horizons, and must be trained sequentially. Convolutional networks…

Recommender systems objectives can be broadly characterized as modeling user preferences over short-or long-term time horizon. A large body of previous research studied long-term recommendation through dimensionality reduction techniques…

This paper introduces a novel algorithmic framework for a deep neural network (DNN), which in a mathematically rigorous manner, allows us to incorporate history (or memory) into the network -- it ensures all layers are connected to one…

Time series anomaly detection plays a critical role in automated monitoring systems. Most previous deep learning efforts related to time series anomaly detection were based on recurrent neural networks (RNN). In this paper, we propose a…

Recent work has introduced a simple numerical method for solving partial differential equations (PDEs) with deep neural networks (DNNs). This paper reviews and extends the method while applying it to analyze one of the most fundamental…

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…

Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…

Data-driven modeling and machine learning are widely used to model the behavior of dynamic systems. One application is the residual evaluation of technical systems where model predictions are compared with measurement data to create…

We utilize machine learning models which are based on recurrent neural networks to optimize dynamical decoupling (DD) sequences. DD is a relatively simple technique for suppressing the errors in quantum memory for certain noise models. In…

Established recurrent neural networks are well-suited to solve a wide variety of prediction tasks involving discrete sequences. However, they do not perform as well in the task of dynamical system identification, when dealing with…

Learning temporal patterns from multivariate longitudinal data is challenging especially in cases when data is sporadic, as often seen in, e.g., healthcare applications where the data can suffer from irregularity and asynchronicity as the…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

Predicting scene dynamics from visual observations is challenging. Existing methods capture dynamics only within observed boundaries failing to extrapolate far beyond the training sequence. Node-RF (Neural ODE-based NeRF) overcomes this…

We introduce \emph{Dynamical Physics-Modeled Neural Networks} (DynPMNNs), a continuous-time deep learning architecture in which each hidden layer is defined as the solution of an ordinary differential equation. Unlike classical feed-forward…

Time-series data in real-world medical settings typically exhibit long-range dependencies and are observed at non-uniform intervals. In such contexts, traditional sequence-based recurrent models struggle. To overcome this, researchers…