相关论文: Neural Ordinary Differential Equation Model for Ev…

Recent works on optical flow estimation use neural networks to predict the flow field that maps positions of one image to positions of the other. These networks consist of a feature extractor, a correlation volume, and finally several…

Forecasting time series and time-dependent data is a common problem in many applications. One typical example is solving ordinary differential equation (ODE) systems $\dot{x}=F(x)$. Oftentimes the right hand side function $F(x)$ is not…

We develop a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from irregularly sampled and noisy observations of a single solution trajectory. We demonstrate in…

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…

In this work, we investigate a method for simulation-free training of Neural Ordinary Differential Equations (NODEs) for learning deterministic mappings between paired data. Despite the analogy of NODEs as continuous-depth residual…

This paper presents the main characteristics of the evolutionary optimization code named EOS, Evolutionary Optimization at Sapienza, and its successful application to challenging, real-world space trajectory optimization problems. EOS is a…

Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous approximation to the ResNet architecture. Some commonly used regularization mechanisms in discrete neural networks (e.g. dropout, Gaussian noise) are…

Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…

Ordinary differential equations (ODE's) are widespread models in physics, chemistry and biology. In particular, this mathematical formalism is used for describing the evolution of complex systems and it might consist of high-dimensional…

We propose a new class of parameterizations for spatio-temporal point processes which leverage Neural ODEs as a computational method and enable flexible, high-fidelity models of discrete events that are localized in continuous time and…

Chemical kinetics mechanisms are essential for understanding, analyzing, and simulating complex combustion phenomena. In this study, a Neural Ordinary Differential Equation (Neural ODE) framework is employed to optimize kinetics parameters…

Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…

This paper proposes the use of spectral element methods \citep{canuto_spectral_1988} for fast and accurate training of Neural Ordinary Differential Equations (ODE-Nets; \citealp{Chen2018NeuralOD}) for system identification. This is achieved…

Ordinary differential equation (ODE) models are widely used to describe systems in many areas of science. To ensure these models provide accurate and interpretable representations of real-world dynamics, it is often necessary to infer…

We explore in detail a method to solve ordinary differential equations using feedforward neural networks. We prove a specific loss function, which does not require knowledge of the exact solution, to be a suitable standard metric to…

A novel way of using neural networks to learn the dynamics of time delay systems from sequential data is proposed. A neural network with trainable delays is used to approximate the right hand side of a delay differential equation. We relate…

Ordinary differential equation (ODE) models of gradient-based optimization methods can provide insights into the dynamics of learning and inspire the design of new algorithms. Unfortunately, this thought-provoking perspective is weakened by…

End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…

Recent research in deep learning has shown that neural networks can learn differential equations governing dynamical systems. In this paper, we adapt this concept to Virtual Analog (VA) modeling to learn the ordinary differential equations…

Simple models have been used to describe ecological processes for over a century. However, the complexity of ecological systems makes simple models subject to modeling bias due to simplifying assumptions or unaccounted factors, limiting…