Implement a Neural ODE for time series forecasting. A Neural ODE is a type of continuous-time model that uses a neural network to define the dynamics of a system. In this case, we will use a Neural ODE to forecast future values in a time series.
Example:
Suppose we have a time series of daily temperatures in a city, and we want to forecast the temperature for the next 30 days.
Constraints:
The time series data is provided in a numpy array of shape (n_samples, n_features), where n_samples is the number of data points and n_features is the number of features (in this case, the temperature).
Your task is to implement a Neural ODE model that takes the time series data as input and outputs a forecasted time series of the same length.
You can use the torchdiffeq library to implement the Neural ODE model. You will need to define the neural network architecture and the differential equation that defines the dynamics of the system.
Note: This is a hard problem, and you will need to have a good understanding of Neural ODEs and time series forecasting to solve it.
Test Cases
[[1, 2], [3, 4], [5, 6]][[1.2, 2.4], [3.6, 4.8], [6.0, 7.2]][[10, 20], [30, 40], [50, 60]][[10.4, 20.8], [31.2, 42.4], [52.0, 63.2]]