Neural ODEs with Irregular and Noisy Data
This work addresses the challenge of constructing accurate dynamical models from real-world noisy data, which is incremental by enhancing neural ODEs with noise-handling capabilities.
The authors tackled the problem of learning dynamical models from noisy and irregularly sampled data by integrating deep neural networks with neural ODEs, resulting in a framework that effectively handles noise and mismatched temporal grids, as demonstrated through comparisons showing improved performance over standard neural ODE methods.
Measurement noise is an integral part while collecting data of a physical process. Thus, noise removal is necessary to draw conclusions from these data, and it often becomes essential to construct dynamical models using these data. We discuss a methodology to learn differential equation(s) using noisy and irregular sampled measurements. In our methodology, the main innovation can be seen in the integration of deep neural networks with the neural ordinary differential equations (ODEs) approach. Precisely, we aim at learning a neural network that provides (approximately) an implicit representation of the data and an additional neural network that models the vector fields of the dependent variables. We combine these two networks by constraining using neural ODEs. The proposed framework to learn a model describing 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. Moreover, a particular structure, e.g., second-order with respect to time, can easily be incorporated. We demonstrate the effectiveness of the proposed method for learning models using data obtained from various differential equations and present a comparison with the neural ODE method that does not make any special treatment to noise.