CS474-574 Homework 1 Solution

Coding assignment
In the first week of the class, we saw a demo that an arbitrary neural network can learn the "law" of free falling $h=rac{1}{2}gt^2$ as a function $h=f(t)$ starting from knowning nothing about physics. It learns from simulated data that follow the $h=rac{1}{2}gt^2$ "law". Given a time elapsed, the neural network can predict the distance the free falling object travels.
Now you are expected to implement a function visualizing the groundtruth and the predictions given the same set of time points. You should obtain something like the figure blow:

Files
1. 1_intro.ipynb for those who wants to develop and run on a cloud Jupyter environment such as Google CoLab or DeepNote. This file also contains some example code that provides hints for the homework.
2. hw1.py this is where you submit your homework
Anatomy of functions
1. The time points are generated by the function generate_data that returns both the time points and groundtruth distances corresponding to those time points.
2. The function test_NN training a neural network using the data generated above, and use the same neural network to predict on the same time points used in training.
3. The function learning_curve is what you are expected to implement. It shall make two plots. One is groundtruth used in training with respect to time points. The other is the predictions with respect to time points. Both the training data and the groundtruth should have the same length.
Speficiations for the function learning_curve
Please folow the specifications carefully, such as using the right colors. Otherwise, the auotgrader will give you zero.
1. The function takes three arguements,
2. N, of type int, is the number of data points,
3. max_iter, also of type int, is the number of iterations to train the neural network 4. filename, of type str, is where the visualization is saved.
6. If you execute on DeepNote, for learning_curve(500, 300, "test.png") , the return hash shall be 4b2737555fbaabffba658659a7cd53ed. If you get the same number, then you are correct.
7. For execution on Google Colab, upgrade the version of matplotlib using !pip install matplotlib==3.6.0, restart the runtime/kernel, and after import matplotlib, reset the rcParams using matplotlib.rcParams.update(matplotlib.rcParamsDefault), you should be able to get the same hash 4b2737555fbaabffba658659a7cd53ed.
8. learning_curve shall first call generate_data to generate N data points (two parts, times Ts and heights Hs), then pass the data points to test_NN function to obtain the predictions and the score, the latter of which is not needed.
9. Finally, you visualize the ground truth and the prediction using matplotlib.pyplot.plot as shown in one cell in 1_intro.ipynb.
10. It shall plot two lines in two distinctive colors. For the groundtruth, use BLUE (color code tab:blue), and for the prediction, use ORANGE (color code tab:orange). Regarding how to change colors in line plots, see the demo in 1_intro.ipynb.
11. For every plot setting else, leave to default settings.
12. Use 4-space indentations. No tabs.
How to submit:
Please follow the instruction strictly.
Please insert your implementation to the function learning_curve into hw1.py. Do NOT modify anothing else. Code and comments left beyond the body of the function learning_curve will not be used for grading. Comments will not be used either. The grading is done automatically by code. So the TAs will not read your comments nor print outs.
Then, submit hw1.py to Canvas. Just upload it.