ClaireGyn / pySIP

Stochastic state-space Inference and Prediction

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Stochastic State-Space Inference and Prediction in Python (pySIP)

Ordinary differential equations, determined from first-principles, can be used for modeling physical systems. However, the exact dynamics of such systems are uncertain and only measured at discrete-time instants through non-ideal sensors. In this case, stochastic differential equations provide a modeling framework which is more robust to these uncertainties. The stochastic part of the state-space model can accomodate for unmodeled disturbances, which do not have a significant influence on the system dynamics. Otherwise, unmeasured disturbances can be modeled as temporal Gaussian Processes with certain parametrized covariance structure. The resulting Latent Force Model is a combination of parametric grey-box model and non-parametric Gaussian process model.

pySIP provides a framework for infering continuous time linear stochastic state-space models . For that purpose, it is possible to chose between a frequentist and a Bayesian workflow. Each workflow allows to estimate the parameters, assess the inference and model reliability, and perform model selection.

pySIP is being developed in the perspective to build a library which gather models from different engineering applications. Currently, applications involving dynamic thermal models (RC network) and temporal Gaussian Processes are being prioritized. Nevertheless, any model following the formalism of pySIP can benefit from the features.

pySIP is currently under development and in beta version. Please feel free to contact us if you want to be involved in the current development process.

Getting started

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from pysip.statespace import TwTi_RoRi
from pysip.regressors import FreqRegressor as Regressor

# Load and prepare the data
df = pd.read_csv('data/armadillo/armadillo_data_H2.csv').set_index('Time')
df.drop(df.index[-1], axis=0, inplace=True)
inputs = ['T_ext', 'P_hea']
outputs = 'T_int'
sT = 3600.0 * 24.0
df.index /= sT  # Change time scale to days

# Parameter settings for second order dynamic thermal model
parameters = [
    dict(name='Ro', scale=1e-2, transform='log'),
    dict(name='Ri', scale=1e-3, transform='log'),
    dict(name='Cw', scale=1e7 / sT, transform='log'),
    dict(name='Ci', scale=1e6 / sT, transform='log'),
    dict(name='sigw_w', scale=1e-3 * sT ** 0.5, transform='log'),
    dict(name='sigw_i', value=0.0, transform='fixed'),
    dict(name='sigv', scale=1e-2, transform='log'),
    dict(name='x0_w', loc=25.0, scale=7.0, transform='none'),
    dict(name='x0_i', value=26.7, transform='fixed'),
    dict(name='sigx0_w', value=0.1, transform='fixed'),
    dict(name='sigx0_i', value=0.1, transform='fixed'),

# Instantiate the model and use the first order hold approximation
model = TwTi_RoRi(parameters, hold_order=1)
reg = Regressor(model)
fit_summary, corr_matrix, opt_summary =, inputs=inputs, outputs=outputs)

# Predict the indoor temperature each minute
dt = 60 / 3600
tnew = np.arange(df.index[0], df.index[-1], dt)
ym, ysd = reg.predict(df=df, inputs=inputs, tnew=tnew)

plt.plot(df.index, df['T_int'], color='darkred', label='data')
plt.plot(tnew, ym, color='navy')
plt.fill_between(tnew, ym - 2 * ysd, ym + 2 * ysd, color='darkblue', alpha=0.2, label=r'95% CI')
plt.xlabel('time [days]')
plt.ylabel('temperature [°C]')
plt.legend(loc='best', fancybox=True, framealpha=0.5)

Reference documentation

For details about the pySIP API, see the reference documentation.



  • Auvergne Rhône-Alpes, project HESTIA-Diag, habitat Econome avec Système Thermique Innovant Adapté pour le Diagnostic


Stochastic state-space Inference and Prediction


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