README

Introduction

Theory and general introduction

• Refer to this Alex Honchar's article or NeuralODE_Alex_Honchar.htlm

Tutorial

• Refer to NeuralODE_tutorial.ipynb

Installation

Jupyter notebook

• Install jupyter notebook: pip install jupyter
• Run jupyter notebook: jupyter notebook

Pytorch and torchdyn with a GPU

1. Create new env: conda create --name py38torch python=3.8
2. Active env: conda activate py38torch
4. Install torchdyn: pip install torchdyn==1.0.3
5. Install torch: conda install pytorch==1.13.1 torchvision==0.14.1 torchaudio==0.13.1 pytorch-cuda=11.7 -c pytorch -c nvidia
==> Install 4, 5 in the end to avoid packages overwritten

Note

• Recommend to use conda to install packages for convenience

• If you dont have GPU, please refer to Torch website for more details

Recommendations for further reading

NeuralODEs and its applications

• [Journal paper] Neural Ordinary Differential Equations
• [Presentation video] Neural Ordinary Differential Equations
• [Github] Tutorials and NeuralODE variants
• [Journal paper] Neural Controlled Differential Equations for Irregular Time Series
• [Presentation video] Neural Controlled Differential Equations for Irregular Time Series

Other Time series forecasting models

• [Article] The Best Deep Learning Models for Time Series Forecasting
• [Article] DeepAR: Mastering Time-Series Forecasting with Deep Learning
• [Article] DeepAR: Mastering Time-Series Forecasting with Deep Learning
• [Python library] PyTorch Forecasting
• [Article] Time Series Forecasting with Neural Ordinary Differential Equations

Marine vehicles hydrodynamics and related machine learning applications

• [Book chapter] Autonomous Underwater Vehicle Dynamics: Top priority
• [Book] HANDBOOK OF MARINE CRAFT HYDRODYNAMICS AND MOTION CONTROL
• [Book] Modelling and Control of Dynamic Systems Using Gaussian Process Model
• [Journal paper] Nonparametric modeling of ship maneuvering motion based on self-designed fully connected neural network
• [Journal paper] Identification and Prediction of Ship Maneuvering Motion Based on a Gaussian Process with Uncertainty Propagation
• [Journal paper] System identification of ship dynamic model based on Gaussian process regression with input noise

Tips for reading articles on Medium or towardsdatascience without subscription

• Clear the cookies of your tab browser when you reach the limit of reading articles

When using venv in WSL2 or Linux

• [issue] Expected numpy array as input but given PyTorchTensors causing error

plot_2D_space_depth이 텐서를 받아들이지만 int 함수를 적용하려고 하여 발생하는것 같습니다. 따라서 아래 수식으로 lib의 torchdyn/utils.py 코드를 변경하였습니다.

Usage

Here is how to use the plot_2D_space_depth function to plot 2D trajectories in a 3D space:

import numpy as np
import torch
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt

def plot_2D_space_depth(s_span, trajectory, yn, n_lines):
    "Plots 2D trajectories in a 3D space (2 dimensions of the system + time)."
    # Convert the Tensors to numpy arrays if necessary
    s_span = s_span.detach().cpu().numpy() if torch.is_tensor(s_span) else s_span
    trajectory = trajectory.detach().cpu().numpy() if torch.is_tensor(trajectory) else trajectory
    yn = yn.detach().cpu().numpy() if torch.is_tensor(yn) else yn

    colors = ['orange', 'blue']
    fig = plt.figure(figsize=(6,3))
    ax = Axes3D(fig, auto_add_to_figure=False)
    fig.add_axes(ax)
    for i in range(n_lines):
        ax.plot(s_span, trajectory[:,i,0], trajectory[:,i,1], color=colors[yn[i].astype(int)], alpha = .1)
        ax.view_init(30, -110)

    ax.set_xlabel(r"$s$ [Depth]")
    ax.set_ylabel(r"$h_0$")
    ax.set_zlabel(r"$h_1$")
    ax.set_title("Flows in the space-depth")
    ax.xaxis._axinfo["grid"]['color'] =  (1,1,1,0)
    ax.yaxis._axinfo["grid"]['color'] =  (1,1,1,0)
    ax.zaxis._axinfo["grid"]['color'] =  (1,1,1,0)

# Create some example data
s_span = torch.linspace(0, 10, 100)
trajectory = torch.rand((100, 5, 2))  # 100 time steps, 5 lines, 2 dimensions
yn = torch.randint(0, 2, (5,))  # 5 lines

# Call the function
plot_2D_space_depth(s_span, trajectory, yn, len(trajectory[0]))