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Make a snapshot of an oscillator through its time series

Project description

Make a snapshot of an oscillator through its time series.

OscillatorSnap uses TensorFlow and Keras and provides straightforward and non-technical high-level functions meant to appeal to non-experts of artificial neural networks. It helps you train a recurrent neural network on oscillatory signals. And then from the trained network forecast the future state or probe the network for dynamical responses, e.g. estimate the phase response curve and maximal Lyapunov exponent.


Citing OscillatorSnap:

If you use OscillatorSnap in your research, please cite our publication:

Rok Cestnik and Markus Abel, Inferring the dynamics of oscillatory systems using recurrent neural networks, Chaos (2019).
@article{cestnik_inferring_2019,
author = {R. Cestnik and M. Abel},
title = {Inferring the dynamics of oscillatory systems using recurrent neural networks},
year = {2019},
journal = {Chaos},
volume = {X},
pages = {X}
}

Installing:

Install with:

sudo pip install oscillator_snap

or download the repository and execute

sudo python setup.py install

in its directory.


Simple example walkthrough:

Make sure to import oscillator_snap (it imports everything it needs):

from oscillator_snap import *

Let’s suppose we have a timeseries s(t) in the format:

data = [[s(t_1), s(t_2), s(t_3),...], [p(t_1), p(t_2), p(t_3),...]]

if one wants the signal to be generated with an ordinary differential equation this is done with:

data = generate_signal(derivatives, DATA_LENGTH, DATA_SAMPLING)

the, DATA_SAMPLING is the ratio between the integration timestep and the timestep associated with data, e.g. if the equation is integrated with dt = 0.01 and DATA_SAMPLING = 10 then the data is sampled with a timestep of 0.1.

There are some other parameters that need to be determined:

PAST = 30 # determines the number of rolls of the RNN, how many historical values are considered for the one-step prediction
NODES = 25 # number of nodes in each layer
LEARNING_RATE = 0.01
BATCH_SIZE = 100 # how many training points are fed into the network at once
EPOCHS = 10 # how many times is the data presented to the network during training
VALIDATION_POINTS = 200 # how many data points are going to be separated for the validation set

the dimensions of the input and output also have to be specified, in this example:

DIM_IN = 2
DIM_OUT = 1

Then the validation set is separated from the training data:

train_data = [data[i][:-VALIDATION_POINTS] for i in range(len(data))]
val_data = [data[i][-VALIDATION_POINTS] for i in range(len(data))]

and then the data can be parsed:

X, Y = parse_train_data(train_data, PAST, DIM_IN, DIM_OUT)
X_val, Y_val = parse_train_data(val_data, PAST, DIM_OUT, DIM_OUT)

A model needs to be created, it can be either freshly generated:

model = generate_model(DIM_IN, DIM_OUT, PAST, NODES, LEARNING_RATE, cell=LSTM, n_hidden_layers=1)

or loaded from previous use:

model = load_model_dill()

(see further down on how to save a model).

The model needs to be compiled:

model = compile_model(model, LEARNING_RATE)

and then it can be trained:

model.fit(X, Y, batch_size=BATHC_SIZE, epochs=EPOCHS, validation_data=(X_val, Y_val))

Once the model is trained it can be used for signal forecasting:

inp = [0 for i in range(PLOT_RANGE)] # input
f_starter = forecast_starter(data, PAST, DIM_IN) # initial state, to start from a different state just change 'data'
signal_forecast = forecast(model, PAST, DIM_IN, f_starter, PLOT_RANGE, inp)

estimating the natural period, phase response curve, the maximal Lyapunov exponent and the bifurcation diagram:

period = period_measure(model, PAST, DIM_IN, f_starter, constant_input_offset=0, thr=0.0)
lyapunov = lyapunov_measure(model, PAST, DIM_IN, f_starter, constant_input_offset=0)
PRC = PRC_measure(model, PAST, DIM_IN, f_starter, constant_input_offset=0.0, thr=0.0, phase_repeats=20, stimulation=1.0)
bif = bifurcation_diagram(model, PAST, DIM_IN, f_starter, ci_min=0.1, ci_max=2.0, dci=0.005, time_window=1000)

and if the true dynamical equations are known, these quantities can be determined from equations as well for comparison:

period_eq = oscillator_period(derivatives, inp=0, thr=0.0) # if the system is chaotic the average period can be computed: 'oscillator_average_period()'
lyapunov_eq = oscillator_lyapunov(derivatives, inp=0)
PRC_eq = oscillator_PRC(derivatives, inp=0, thr=0.0)
bif_eq = oscillator_bifurcation(derivatives, inp_min=0.05, inp_max=2.0, d_inp=0.01, time_window=2000)

The model as well as any objects can be saved as:

save_model_dill(model)
save_object_dill(PRC, 'PRC')
save_object_dill(bif, 'bifurcation')

To plot the signal, phase response curve, bifurcation…:

from matplotlib import pyplot

pyplot.plot(signal_forecast[:PLOT_RANGE])
pyplot.show()

pyplot.plot(PRC[0], PRC[1])
pyplot.show()

pyplot.scatter(bif[0], bif[1], s=1.5)
pyplot.show()

Other examples are found in /oscillator_snap/examples/.

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