Related papers: Efficient Neural Controlled Differential Equations…
The vector field of a controlled differential equation (CDE) describes the relationship between a control path and the evolution of a solution path. Neural CDEs (NCDEs) treat time series data as observations from a control path,…
Neural controlled differential equations (CDEs) are the continuous-time analogue of recurrent neural networks, as Neural ODEs are to residual networks, and offer a memory-efficient continuous-time way to model functions of potentially…
Traffic forecasting is one of the most popular spatio-temporal tasks in the field of machine learning. A prevalent approach in the field is to combine graph convolutional networks and recurrent neural networks for the spatio-temporal…
Neural controlled differential equations (NCDEs), which are continuous analogues to recurrent neural networks (RNNs), are a specialized model in (irregular) time-series processing. In comparison with similar models, e.g., neural ordinary…
Neural Controlled Differential Equations (Neural CDEs, NCDEs) are a unique branch of methods, specifically tailored for analysing temporal sequences. However, they come with drawbacks, the main one being the number of parameters, required…
Neural controlled differential equations (Neural CDEs) are a continuous-time extension of recurrent neural networks (RNNs), achieving state-of-the-art (SOTA) performance at modelling functions of irregular time series. In order to interpret…
This paper focuses on representation learning for dynamic graphs with temporal interactions. A fundamental issue is that both the graph structure and the nodes own their own dynamics, and their blending induces intractable complexity in the…
Neural networks inspired by differential equations have proliferated for the past several years. Neural ordinary differential equations (NODEs) and neural controlled differential equations (NCDEs) are two representative examples of them. In…
Dynamic graphs exhibit complex temporal dynamics due to the interplay between evolving node features and changing network structures. Recently, Graph Neural Controlled Differential Equations (Graph Neural CDEs) successfully adapted Neural…
We incorporate prior graph topology information into a Neural Controlled Differential Equation (NCDE) to predict the future states of a dynamical system defined on a graph. The informed NCDE infers the future dynamics at the vertices of…
Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…
We propose a novel framework for solving continuous-time non-Markovian stochastic control problems by means of neural rough differential equations (Neural RDEs) introduced in Morrill et al. (2021). Non-Markovianity naturally arises in…
Deep learning inspired by differential equations is a recent research trend and has marked the state of the art performance for many machine learning tasks. Among them, time-series modeling with neural controlled differential equations…
Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…
Long-term traffic flow forecasting plays a crucial role in intelligent transportation as it allows traffic managers to adjust their decisions in advance. However, the problem is challenging due to spatio-temporal correlations and complex…
Classical neural ordinary differential equations (ODEs) are powerful tools for approximating the log-density functions in high-dimensional spaces along trajectories, where neural networks parameterize the velocity fields. This paper…
Safe and efficient motion planning is of fundamental importance for autonomous vehicles. This paper investigates motion planning based on nonlinear model predictive control (NMPC) over a neural network vehicle model. We aim to overcome the…
We introduce a training-efficient framework for time-series learning that combines random features with controlled differential equations (CDEs). In this approach, large randomly parameterized CDEs act as continuous-time reservoirs, mapping…
Nonlinear model predictive control (MPC) is a flexible and increasingly popular framework used to synthesize feedback control strategies that can satisfy both state and control input constraints. In this framework, an optimization problem,…
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.…