Related papers: Symbolic Neural Ordinary Differential Equations

Galactic systems are inherently multiphase, and understanding the roles and interactions of the various phases is key towards a more complete picture of galaxy formation and evolution. For instance, these interactions play a pivotal role in…

We propose a novel framework for Network Stochastic Differential Equations (N-SDE), where each node in a network is governed by an SDE influenced by interactions with its neighbors. The evolution of each node is driven by the interplay of…

We propose Characteristic-Neural Ordinary Differential Equations (C-NODEs), a framework for extending Neural Ordinary Differential Equations (NODEs) beyond ODEs. While NODEs model the evolution of a latent variables as the solution to an…

Understanding and modeling nonlinear dynamical systems is a fundamental challenge across science and engineering. Deep learning has shown remarkable potential for capturing complex system behavior, yet achieving models that are both…

We present a numerical framework for deep neural network (DNN) modeling of unknown time-dependent partial differential equations (PDE) using their trajectory data. Unlike the recent work of [Wu and Xiu, J. Comput. Phys. 2020], where the…

Accurate modeling of spatiotemporal dynamics is crucial to understanding complex phenomena across science and engineering. However, this task faces a fundamental challenge when the governing equations are unknown and observational data are…

Semantic image understanding is a challenging topic in computer vision. It requires to detect all objects in an image, but also to identify all the relations between them. Detected objects, their labels and the discovered relations can be…

We propose a novel second-order optimization framework for training the emerging deep continuous-time models, specifically the Neural Ordinary Differential Equations (Neural ODEs). Since their training already involves expensive gradient…

Measurement noise is an integral part while collecting data of a physical process. Thus, noise removal is necessary to draw conclusions from these data, and it often becomes essential to construct dynamical models using these data. We…

Modeling dynamical systems is crucial for a wide range of tasks, but it remains challenging due to complex nonlinear dynamics, limited observations, or lack of prior knowledge. Recently, data-driven approaches such as Neural Ordinary…

We propose a unified framework for delay differential equations (DDEs) based on deep neural networks (DNNs) - the neural delay differential equations (NDDEs), aimed at solving the forward and inverse problems of delay differential…

Neural differential equations are a promising new member in the neural network family. They show the potential of differential equations for time series data analysis. In this paper, the strength of the ordinary differential equation (ODE)…

Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…

A novel approach for supervised classification is presented which sits at the intersection of machine learning and dynamical systems theory. At variance with other methodologies that employ ordinary differential equations for classification…

Neural ordinary differential equations (neural ODEs) have emerged as a novel network architecture that bridges dynamical systems and deep learning. However, the gradient obtained with the continuous adjoint method in the vanilla neural ODE…

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…

Longitudinal analysis in medical imaging is crucial to investigate the progressive changes in anatomical structures or disease progression over time. In recent years, a novel class of algorithms has emerged with the goal of learning disease…

Modeling sequential patterns from data is at the core of various time series forecasting tasks. Deep learning models have greatly outperformed many traditional models, but these black-box models generally lack explainability in prediction…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of…

Neural ordinary differential equations (neural ODEs) can effectively learn dynamical systems from time series data, but their behavior on graph-structured data remains poorly understood, especially when applied to graphs with different size…