Related papers: ANODEV2: A Coupled Neural ODE Evolution Framework

This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…

We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…

There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…

We propose a continuous neural network architecture, termed Explainable Tensorized Neural Ordinary Differential Equations (ETN-ODE), for multi-step time series prediction at arbitrary time points. Unlike the existing approaches, which…

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…

Advances in differentiable numerical integrators have enabled the use of gradient descent techniques to learn ordinary differential equations (ODEs). In the context of machine learning, differentiable solvers are central for Neural ODEs…

Neural ordinary differential equations (NODEs) -- parametrizations of differential equations using neural networks -- have shown tremendous promise in learning models of unknown continuous-time dynamical systems from data. However, every…

A method for approximating sixth-order ordinary differential equations is proposed, which utilizes a deep learning feedforward artificial neural network, referred to as a neural solver. The efficacy of this unsupervised machine learning…

We address the problem of Bayesian inference for parameters in ordinary differential equation (ODE) models based on observational data. Conventional approaches in this setting typically rely on numerical solvers such as the Euler or…

Deep residual networks (ResNets) have shown state-of-the-art performance in various real-world applications. Recently, the ResNets model was reparameterized and interpreted as solutions to a continuous ordinary differential equation or…

In this paper, we present a new framework how a PDE with constraints can be formulated into a sequence of PDEs with no constraints, whose solutions are convergent to the solution of the PDE with constraints. This framework is then used to…

Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an active research field. However, current methods are…

A conventional approach to train neural ordinary differential equations (ODEs) is to fix an ODE solver and then learn the neural network's weights to optimize a target loss function. However, such an approach is tailored for a specific…

When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access to the full system state. This limits their use in partially…

Much recent interest has focused on the design of optimization algorithms from the discretization of an associated optimization flow, i.e., a system of differential equations (ODEs) whose trajectories solve an associated optimization…

Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such as Residual networks (ResNets). They provide parameter efficiency and automate the model selection…

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…

We develop a novel data-driven framework as an alternative to dynamic flux balance analysis, bypassing the demand for deep domain knowledge and manual efforts to formulate the optimization problem. The proposed framework is end-to-end,…

Neural Jump ODEs model the conditional expectation between observations by neural ODEs and jump at arrival of new observations. They have demonstrated effectiveness for fully data-driven online forecasting in settings with irregular and…

We study first-order optimization methods obtained by discretizing ordinary differential equations (ODEs) corresponding to Nesterov's accelerated gradient methods (NAGs) and Polyak's heavy-ball method. We consider three discretization…