Related papers: Neural ODEs with Irregular and Noisy Data
Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…
We investigate the use of neural networks (NNs) for the estimation of hidden model parameters and uncertainty quantification from noisy observational data for inverse parameter estimation problems. We formulate the parameter estimation as a…
Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches…
Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…
Neural differential equations are a promising new member in the neural network family. They show the potential of differential equations for time series data analysis. In this paper, the strength of the ordinary differential equation (ODE)…
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…
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…
Equation learning aims to infer differential equation models from data. While a number of studies have shown that differential equation models can be successfully identified when the data are sufficiently detailed and corrupted with…
The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…
Falsely annotated samples, also known as noisy labels, can significantly harm the performance of deep learning models. Two main approaches for learning with noisy labels are global noise estimation and data filtering. Global noise…
Neural ordinary differential equations (ODEs) are an emerging class of deep learning models for dynamical systems. They are particularly useful for learning an ODE vector field from observed trajectories (i.e., inverse problems). We here…
We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…
To derive the hidden dynamics from observed data is one of the fundamental but also challenging problems in many different fields. In this study, we propose a new type of interpretable network called the ordinary differential equation…
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.…
Learning models of dynamical systems with external inputs, which may be, for example, nonsmooth or piecewise, is crucial for studying complex phenomena and predicting future state evolution, which is essential for applications such as…
Data-driven discovery of partial differential equations (PDEs) has attracted increasing attention in recent years. Although significant progress has been made, certain unresolved issues remain. For example, for PDEs with high-order…
In data-driven modeling of spatiotemporal phenomena careful consideration often needs to be made in capturing the dynamics of the high wavenumbers. This problem becomes especially challenging when the system of interest exhibits shocks or…
Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…
We present a computational technique for modeling the evolution of dynamical systems in a reduced basis, with a focus on the challenging problem of modeling partially-observed partial differential equations (PDEs) on high-dimensional…
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…