Related papers: Neural Rough Differential Equations for Long Time …

There has been an increasing interest in modeling continuous-time dynamics of temporal graph data. Previous methods encode time-evolving relational information into a low-dimensional representation by specifying discrete layers of neural…

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.…

The interest in deep learning methods for solving traditional signal processing tasks has been steadily growing in the last years. Time delay estimation (TDE) in adverse scenarios is a challenging problem, where classical approaches based…

Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…

Neural ordinary differential equations (ODEs) are an emerging class of deep learning models for dynamical systems. They are particularly useful for learning an ODE vector field from observed trajectories (i.e., inverse problems). We here…

Signature kernels, inner products of path signatures, underpin several machine learning algorithms for multivariate time series analysis. For bounded variation paths, signature kernels were recently shown to solve a Goursat PDE. However,…

Most machine learning methods are used as a black box for modelling. We may try to extract some knowledge from physics-based training methods, such as neural ODE (ordinary differential equation). Neural ODE has advantages like a possibly…

We present a comprehensive evaluation of the robustness and explainability of ResNet-like models in the context of Unintended Radiated Emission (URE) classification and suggest a new approach leveraging Neural Stochastic Differential…

Combinations of neural ODEs with recurrent neural networks (RNN), like GRU-ODE-Bayes or ODE-RNN are well suited to model irregularly observed time series. While those models outperform existing discrete-time approaches, no theoretical…

Data-driven surrogate modeling has emerged as a promising approach for reducing computational expenses of multiscale simulations. Recurrent Neural Network (RNN) is a common choice for modeling of path-dependent behavior. However, previous…

Ability of deep networks to extract high level features and of recurrent networks to perform time-series inference have been studied. In view of universality of one hidden layer network at approximating functions under weak constraints, the…

The laws of physics have been written in the language of dif-ferential equations for centuries. Neural Ordinary Differen-tial Equations (NODEs) are a new machine learning architecture which allows these differential equations to be learned…

The high computational cost associated with solving for detailed chemistry poses a significant challenge for predictive computational fluid dynamics (CFD) simulations of turbulent reacting flows. These models often require solving a system…

To model time series accurately is important within a wide range of fields. As the world is generally too complex to be modelled exactly, it is often meaningful to assess the probability of a dynamical system to be in a specific state. This…

In this paper we propose the use of continuous residual modules for graph kernels in Graph Neural Networks. We show how both discrete and continuous residual layers allow for more robust training, being that continuous residual layers are…

Neural differential equations offer a powerful approach for learning dynamics from data. However, they do not impose known constraints that should be obeyed by the learned model. It is well-known that enforcing constraints in surrogate…

Continuous deep learning architectures have recently re-emerged as Neural Ordinary Differential Equations (Neural ODEs). This infinite-depth approach theoretically bridges the gap between deep learning and dynamical systems, offering a…

Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit…

Channel prediction is critical to address the channel aging issue in mobile scenarios. Existing channel prediction techniques are mainly designed for discrete channel prediction, which can only predict the future channel in a fixed time…

The long runtime of high-fidelity partial differential equation (PDE) solvers makes them unsuitable for time-critical applications. We propose to accelerate PDE solvers using reduced-order modeling (ROM). Whereas prior ROM approaches reduce…