Learning Dynamics from Noisy Measurements using Deep Learning with a Runge-Kutta Constraint

09/23/2021
by   Pawan Goyal, et al.
79

Measurement noise is an integral part while collecting data of a physical process. Thus, noise removal is a necessary step to draw conclusions from these data, and it often becomes quite essential to construct dynamical models using these data. We discuss a methodology to learn differential equation(s) using noisy and sparsely sampled measurements. In our methodology, the main innovation can be seen in of integration of deep neural networks with a classical numerical integration method. Precisely, we aim at learning a neural network that implicitly represents the data and an additional neural network that models the vector fields of the dependent variables. We combine these two networks by enforcing the constraint that the data at the next time-steps can be given by following a numerical integration scheme such as the fourth-order Runge-Kutta scheme. The proposed framework to learn a model predicting the vector field is highly effective under noisy measurements. The approach can handle scenarios where dependent variables are not available at the same temporal grid. We demonstrate the effectiveness of the proposed method to learning models using data obtained from various differential equations. The proposed approach provides a promising methodology to learn dynamic models, where the first-principle understanding remains opaque.

READ FULL TEXT

page 8

page 10

page 11

page 12

research
05/19/2022

Neural ODEs with Irregular and Noisy Data

Measurement noise is an integral part while collecting data of a physica...
research
05/11/2021

Discovery of Nonlinear Dynamical Systems using a Runge-Kutta Inspired Dictionary-based Sparse Regression Approach

Discovering dynamical models to describe underlying dynamical behavior i...
research
12/06/2020

Estimating Vector Fields from Noisy Time Series

While there has been a surge of recent interest in learning differential...
research
09/13/2023

A Robust SINDy Approach by Combining Neural Networks and an Integral Form

The discovery of governing equations from data has been an active field ...
research
12/09/2022

A PINN Approach to Symbolic Differential Operator Discovery with Sparse Data

Given ample experimental data from a system governed by differential equ...
research
04/13/2020

Emergent spaces for coupled oscillators

In this paper we present a systematic, data-driven approach to discoveri...
research
07/04/2021

Learning ODEs via Diffeomorphisms for Fast and Robust Integration

Advances in differentiable numerical integrators have enabled the use of...

Please sign up or login with your details

Forgot password? Click here to reset