Related papers: ODEN: A Framework to Solve Ordinary Differential E…

In this study, we present and validate the predictive capability of the Physics-Informed Neural Networks (PINNs) methodology for solving a variety of engineering and biological dynamical systems governed by ordinary differential equations…

A feedforward neural network, including hidden layers, motivated by nonlinear functions (such as Tanh, ReLU, and Sigmoid functions), exhibits uniform approximation properties in Sobolev space, and discontinuous neural networks can reduce…

Learned iterative reconstruction algorithms for inverse problems offer the flexibility to combine analytical knowledge about the problem with modules learned from data. This way, they achieve high reconstruction performance while ensuring…

Artificial neural networks, widely recognised for their role in machine learning, are now transforming the study of ordinary differential equations (ODEs), bridging data-driven modelling with classical dynamical systems and enabling the…

Deep neural networks have become invaluable tools for supervised machine learning, e.g., classification of text or images. While often offering superior results over traditional techniques and successfully expressing complicated patterns in…

The existing Neural ODE formulation relies on an explicit knowledge of the termination time. We extend Neural ODEs to implicitly defined termination criteria modeled by neural event functions, which can be chained together and…

Finding model parameters from data is an essential task in science and engineering, from weather and climate forecasts to plasma control. Previous works have employed neural networks to greatly accelerate finding solutions to inverse…

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…

Neuroscientists fit morphologically and biophysically detailed neuron simulations to physiological data, often using evolutionary algorithms. However, such gradient-free approaches are computationally expensive, making convergence slow when…

Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…

The neural Ordinary Differential Equation (ODE) model has shown success in learning complex continuous-time processes from observations on discrete time stamps. In this work, we consider the modeling and forecasting of time series data that…

Residual networks are an Euler discretization of solutions to Ordinary Differential Equations (ODE). This paper explores a deeper relationship between Transformer and numerical ODE methods. We first show that a residual block of layers in…

To understand the fundamental trade-offs between training stability, temporal dynamics and architectural complexity of recurrent neural networks~(RNNs), we directly analyze RNN architectures using numerical methods of ordinary differential…

In this work, we propose a new deep learning-based scheme for solving high dimensional nonlinear backward stochastic differential equations (BSDEs). The idea is to reformulate the problem as a global optimization, where the local loss…

In this paper, feedforward neural networks are presented that have nonlinear weight functions based on look--up tables, that are specially smoothed in a regularization called the diffusion. The idea of such a type of networks is based on…

Learning large scale nonlinear ordinary differential equation (ODE) systems from data is known to be computationally and statistically challenging. We present a framework together with the adaptive integral matching (AIM) algorithm for…

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.…

Neural Ordinary Differential Equations (NODEs) use a neural network to model the instantaneous rate of change in the state of a system. However, despite their apparent suitability for dynamics-governed time-series, NODEs present a few…

Neural Ordinary Differential Equations model dynamical systems with ODEs learned by neural networks. However, ODEs are fundamentally inadequate to model systems with long-range dependencies or discontinuities, which are common in…

We propose new machine learning schemes for solving high dimensional nonlinear partial differential equations (PDEs). Relying on the classical backward stochastic differential equation (BSDE) representation of PDEs, our algorithms estimate…