Related papers: SNODE: Spectral Discretization of Neural ODEs for …

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…

We propose a novel approach for image segmentation that combines Neural Ordinary Differential Equations (NODEs) and the Level Set method. Our approach parametrizes the evolution of an initial contour with a NODE that implicitly learns from…

We propose a simple interpolation-based method for the efficient approximation of gradients in neural ODE models. We compare it with the reverse dynamic method (known in the literature as "adjoint method") to train neural ODEs on…

The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…

Dissipative partial differential equations that exhibit chaotic dynamics tend to evolve to attractors that exist on finite-dimensional manifolds. We present a data-driven reduced order modeling method that capitalizes on this fact by…

A concept of using Neural Ordinary Differential Equations(NODE) for Transfer Learning has been introduced. In this paper we use the EfficientNets to explore transfer learning on CIFAR-10 dataset. We use NODE for fine-tuning our model. Using…

Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with some representative datasets. Recently, an augmented framework has been…

Despite the promise of scientific machine learning (SciML) in combining data-driven techniques with mechanistic modeling, existing approaches for incorporating hard constraints in neural differential equations (NDEs) face significant…

We present a comprehensive evaluation of the robustness and explainability of ResNet-like models in the context of Unintended Radiated Emission (URE) classification and suggest a new approach leveraging Neural Stochastic Differential…

We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses traditional DeepONets…

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…

This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to learn multiple dynamics specified by the input parameter…

We present a falsification framework that integrates learned surrogate dynamics with optimal control to efficiently generate counterexamples for cyber-physical systems specified in signal temporal logic (STL). The unknown system dynamics…

Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with representative datasets. Recently, an augmented framework has been…

Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…

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…

Purpose: To develop a neural ordinary differential equation (ODE) model for visualizing deep neural network (DNN) behavior during multi-parametric MRI (mp-MRI) based glioma segmentation as a method to enhance deep learning explainability.…

The connection of Taylor maps and polynomial neural networks (PNN) to solve ordinary differential equations (ODEs) numerically is considered. Having the system of ODEs, it is possible to calculate weights of PNN that simulates the dynamics…

Neural ordinary differential equations (Neural ODEs) are an effective framework for learning dynamical systems from irregularly sampled time series data. These models provide a continuous-time latent representation of the underlying…

Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated…