Related papers: Modulated Neural ODEs

Since the advent of the ``Neural Ordinary Differential Equation (Neural ODE)'' paper, learning ODEs with deep learning has been applied to system identification, time-series forecasting, and related areas. Exploiting the diffeomorphic…

Learning multi-agent system dynamics has been extensively studied for various real-world applications, such as molecular dynamics in biology. Most of the existing models are built to learn single system dynamics from observed historical…

Neural ordinary differential equations (NODEs) are geometric deep learning models based on dynamical systems and flows generated by vector fields on manifolds. Despite numerous successful applications, particularly within the flow matching…

Complex systems are often decomposed into modular subsystems for engineering tractability. Although various equation based white-box modeling techniques make use of such structure, learning based methods have yet to incorporate these ideas…

Forecasting system behaviour near and across bifurcations is crucial for identifying potential shifts in dynamical systems. While machine learning has recently been used to learn critical transitions and bifurcation structures from data,…

Training dynamic models, such as neural ODEs, on long trajectories is a hard problem that requires using various tricks, such as trajectory splitting, to make model training work in practice. These methods are often heuristics with poor…

Neural Ordinary Differential Equations (NODEs) have proven successful in learning dynamical systems in terms of accurately recovering the observed trajectories. While different types of sparsity have been proposed to improve robustness, the…

The inverse problem of supervised reconstruction of depth-variable (time-dependent) parameters in a neural ordinary differential equation (NODE) is considered, that means finding the weights of a residual network with time continuous…

Neural Ordinary Differential Equations (ODEs) are elegant reinterpretations of deep networks where continuous time can replace the discrete notion of depth, ODE solvers perform forward propagation, and the adjoint method enables efficient,…

Neural Ordinary Differential Equations (Neural ODEs) represent continuous-time dynamics with neural networks, offering advancements for modeling and control tasks. However, training Neural ODEs requires solving differential equations at…

In this paper, we implement Neural Ordinary Differential Equations in a Variational Autoencoder setting for generative time series modeling. An object-oriented approach to the code was taken to allow for easier development and research and…

Identifying dynamical systems from experimental data is a notably difficult task. Prior knowledge generally helps, but the extent of this knowledge varies with the application, and customized models are often needed. Neural ordinary…

Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…

We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. In particular, given a time-series or spatio-temporal dataset, we seek to identify an accurate governing…

Neural ordinary differential equations (NODEs) are an effective approach for data-driven modeling of dynamical systems arising from simulations and experiments. One of the major shortcomings of NODEs, especially when coupled with explicit…

We introduce a novel grid-independent model for learning partial differential equations (PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a space-time continuous latent neural PDE model with an…

We propose a method to reproduce dynamic appearance textures with space-stationary but time-varying visual statistics. While most previous work decomposes dynamic textures into static appearance and motion, we focus on dynamic appearance…

We designed a new artificial neural network by modifying the neural ordinary differential equation (NODE) framework to successfully predict the time evolution of the 2D mode profile in both the linear growth and nonlinear saturated stages.…

We present a new microscopic ODE-based model for pedestrian dynamics: the Gradient Navigation Model. The model uses a superposition of gradients of distance functions to directly change the direction of the velocity vector. The velocity is…

Neural ordinary differential equations (NODEs) treat computation of intermediate feature vectors as trajectories of ordinary differential equation parameterized by a neural network. In this paper, we propose a novel model, delay…