相关论文: Learning differential equations from data

Many processes in science and engineering can be described by partial differential equations (PDEs). Traditionally, PDEs are derived by considering first principles of physics to derive the relations between the involved physical quantities…

In this article, I introduce the differential equation model and review their frequentist and Bayesian computation methods. A numerical example of the FitzHugh-Nagumo model is given.

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…

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…

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…

The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a…

In this paper, we present an initial attempt to learn evolution PDEs from data. Inspired by the latest development of neural network designs in deep learning, we propose a new feed-forward deep network, called PDE-Net, to fulfill two…

This paper is directed towards the problem of learning nonlinear ARX models based on system input--output data. In particular, our interest is in learning a conditional distribution of the current output based on a finite window of past…

Time-dependent Partial Differential Equations with given initial conditions are considered in this paper. New differentiation techniques of the unknown solution with respect to time variable are proposed. It is shown that the proposed…

Many scientific problems focus on observed patterns of change or on how to design a system to achieve particular dynamics. Those problems often require fitting differential equation models to target trajectories. Fitting such models can be…

There have been extensive studies on solving differential equations using physics-informed neural networks. While this method has proven advantageous in many cases, a major criticism lies in its lack of analytical error bounds. Therefore,…

In recent years, data-driven methods have been developed to learn dynamical systems and partial differential equations (PDE). The goal of such work is discovering unknown physics and the corresponding equations. However, prior to achieving…

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…

Obtaining dynamics models is essential for robotics to achieve accurate model-based controllers and simulators for planning. The dynamics models are typically obtained using model specification of the manufacturer or simple numerical…

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…

Modeling the traffic dynamics is essential for understanding and predicting the traffic spatiotemporal evolution. However, deriving the partial differential equation (PDE) models that capture these dynamics is challenging due to their…

Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…

To better understand and improve the behavior of neural networks, a recent line of works bridged the connection between ordinary differential equations (ODEs) and deep neural networks (DNNs). The connections are made in two folds: (1) View…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

A novel way of using neural networks to learn the dynamics of time delay systems from sequential data is proposed. A neural network with trainable delays is used to approximate the right hand side of a delay differential equation. We relate…