Exercise 9.2¶

Large arrays of radio antennas can be used to measure cosmic rays by recording the electromagnetic radiation generated in the atmosphere. These radio signals are strongly contaminated by galactic noise as well as signals from human origin. Since these signals appear to be similar to the background, the discovery of cosmic-ray events can be challenging.

Identification of signals¶

In this exercise, we design an RNN to classify if the recorded radio signals contain a cosmic-ray event or only noise.

The signal-to-noise ratio (SNR) of a measured trace $S(t)$ is defined as follows:

$$\mathrm{SNR}=\frac{S^{\mathrm{signal}}(t)_\mathrm{max}}{\mathrm{RMS}[S(t)]},$$

where $S^{\mathrm{signal}}(t)_\mathrm{max}$ denotes the maximum amplitude of the (true) signal.

Typical cosmic-ray observatories enable a precise reconstruction at an SNR of roughly 3.

We choose a challenging setup in this task and try to identify cosmic-ray events in signal traces with an SNR of 2.
Training RNNs can be computationally demanding, thus, we recommend to use a GPU for this task.

In [4]:
import tensorflow as tf
from tensorflow import keras
import numpy as np
import matplotlib.pyplot as plt

layers = keras.layers
print("keras", keras.__version__)

keras 2.4.0


Load and prepare dataset¶

In this task, we use a simulation of cosmic-ray-induced air showers that are measured by radion antennas.
For more information, see https://arxiv.org/abs/1901.04079.
The task is to design an RNN which is able to identify if the measured signal traces (shortened to 500 time steps) contains a signal or not.

In [2]:
import os
import gdown
url = "https://drive.google.com/u/0/uc?export=download&confirm=HgGH&id=1R-qfxO1jVh88TC9Gnm9JGMomSRg0Zpkx"
output = 'radio_data.npz'

if os.path.exists(output) == False:
gdown.download(url, output, quiet=True)

f = np.load(output)
n_train = 40000

x_train, x_test = f["traces"][:n_train], f["traces"][n_train:]  # measured traces (signal + colored noise)
signals = f["signals"]  # signal part (only available for cosmic-ray events)

labels = (signals.std(axis=-1) != 0).astype(float)  # define training label (1=cosmic event, 0=noise)
y_train, y_test = labels[:n_train], labels[n_train:]


Plot example signal traces¶

Left: signal trace containing a cosmic-ray event. The underlying cosmic-ray signal is shown in red, the backgrounds + signal is shown in blue. Right: background noise.

In [3]:
from matplotlib import pyplot as plt
fs = 180e6  # Sampling frequency of antenna setup 180 MHz
t = np.arange(500) / fs * 1e6
idx = np.random.randint(0, labels.sum()-1)
idx2 =  np.random.randint(0, n_train - labels.sum())

plt.figure(1, (12, 4))
plt.subplot(1, 2, 1)
plt.plot(t, np.real(f["traces"][labels.astype(bool)][idx]), linewidth = 1, color="b", label="Measured trace")
plt.plot(t, np.real(signals[labels.astype(bool)][idx]), linewidth = 1, color="r", label="CR signal")
plt.ylabel('Amplitude / mV')
plt.xlabel('Time / $\mu \mathrm{s}$')
plt.legend()
plt.title("Cosmic-ray event")
plt.subplot(1, 2, 2)

plt.plot(t, np.real(x_train[~y_train.astype(bool)][idx2]), linewidth = 1, color="b", label="Measured trace")
plt.ylabel('Amplitude / mV')
plt.xlabel('Time / $\mu \mathrm{s}$')
plt.legend()
plt.title("Noise event")

plt.grid(True)
plt.tight_layout()


Define RNN model¶

In the following, design a cosmic-ray model to identify cosmic-ray events using an RNN-based classifier.

In [ ]:
model = keras.models.Sequential()
model.add(...)

model.summary()


Pre-processing of data and RNN training¶

In [ ]:
sigma = x_train.std()
x_train /= sigma
x_test /= sigma

In [ ]:
model.compile(...)

results = model.fit(x_train[...,np.newaxis], y_train, ...)

In [ ]:
model.evaluate(x_test[...,np.newaxis], y_test)


Plot loss and accuracy¶

In [ ]:
plt.figure(1, (12, 4))
plt.subplot(1, 2, 1)
plt.plot(results.history['loss'])
plt.plot(results.history['val_loss'])
plt.ylabel('loss')
plt.xlabel('epoch')
plt.legend(['train', 'val'], loc='upper right')

plt.subplot(1, 2, 2)
plt.plot(results.history['accuracy'])
plt.plot(results.history['val_accuracy'])
plt.ylabel('accuracy')
plt.xlabel('epoch')
plt.legend(['train', 'val'], loc='upper left')
plt.tight_layout()