deepSI provides a lightweight PyTorch-based framework for data-driven learning of dynamical systems (i.e., system identification). It focuses on the SUBNET method, which robustly models many systems.
If you need to install the legacy version, you can do so with:
pip install git+https://github.com/GerbenBeintema/deepSI@legacy
and by using the legacy documentation available at https://github.com/MaartenSchoukens/deepSI/tree/legacy.
import numpy as np
import deepSI as dsi
# Generate or load data
np.random.seed(0)
ulist = np.random.randn(10_000) # Input sequence
x = [0, 0] # Initial state
ylist = [] # Output sequence
for uk in ulist:
ylist.append(x[1]*x[0]*0.1 + x[0] + np.random.randn()*1e-3) # Compute output
x = x[0]/(1.2+x[1]**2) + x[1]*0.4, \
x[1]/(1.2+x[0]**2) + x[0]*0.4 + uk*(1+x[0]**2/10) # Advance state
# Put the input and output sequence in the Input_output_data format
data = dsi.Input_output_data(u=ulist, y=np.array(ylist))
# Split dataset
train, val, test = data[:8000], data[8000:9000], data[9000:]
# Create model
nu, ny, norm = dsi.get_nu_ny_and_auto_norm(data) # Characterize data
model = dsi.SUBNET(nu, ny, norm, nx=2, nb=20, na=20) # Creates encoder, f and h as MLP
# Train model on data using Adam
train_dict = dsi.fit(model, train, val, n_its=10_000, T=20, batch_size=256, val_freq=100)
# Simulate model on the test input sequence (using the encoder to initialize the state)
test_p = model.simulate(test)
# Visualize simulation of the model
from matplotlib import pyplot as plt
plt.figure(figsize=(7,3))
plt.plot(test.y, label='Real Data')
plt.plot(test_p.y, label=f'Model Sim. (NRMS = {((test.y-test_p.y)**2).mean()**0.5/test.y.std():.2%})', linestyle='--')
plt.title('Comparison of Real Data and Model Simulation', fontsize=14, fontweight='bold')
plt.legend(); plt.xlabel('Time Index'); plt.ylabel('y'); plt.grid(); plt.tight_layout(pad=0.5)
plt.show()
pip install deepSI
- A number of popular SUBNET model structures
- SUBNET encoder structue (
deepSI.models.SUBNET
). Featuring in: [1], [2], [3], [4], [5] - Continuous time SUBNET encoder structure (
deepSI.models.SUBNET_CT
). Featuring in: [6], [7], [8] - Base class for fully custom SUBNET structures with shared parameters between
f
,h
orencoder
. (deepSI.models.Custom_SUBNET
) as used in: - CNN SUBNET (
CNN_SUBNET
). Featuring in: [9] Chapter 4, [10] - LPV SUBNET (
SUBNET_LPV
andSUBNET_LPV_ext_scheduled
). Featuring in: [11] - port HNN SUBNET (
pHNN_SUBNET
). Featuring in: [12] - Koopman SUBNET (
Koopman_SUBNET
). Featuring in: [13]
- SUBNET encoder structue (
- Connection to
nonlinear_benchmarks
to easily load and evaluate on benchmarks. - Low amount of code such that it can be easily forked and edited to add missing features.
Check out examples/1. Overview deepSI.ipynb
.
deepSI is under ongoing development, and contributions to any part of the module are welcome.
- Expand demonstration notebook with pHNN examples.
- Issue where discrete time is printed in
Input_output_data
withtorch.Tensors
, andnp.array
sample time. - General documentation improvements.
- Known issue: CT SUBNET and DT SUBNET do not produce the correct initial state when the sampling time is altered (the encoder assumes the sampling time does not change).
- Possible improvement: Improve speed by copying if sufficient memory is available. Also, consider pre-transfer to GPU and asynchronous array retrieval.
- Known issue: Using the compile function in fit may result in a memory leak.