deepSI 0.4.4

Data-driven learning of dynamical system in the SUBNET structure and ANNs

deepSI

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.

⚠️ deepSI has been refactored without backward compatibility (5 December 2024) ⚠️

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.

Example usage

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()

Installation

pip install deepSI

Features

• 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 or encoder. (deepSI.models.Custom_SUBNET) as used in:
  • CNN SUBNET (CNN_SUBNET). Featuring in: [9] Chapter 4, [10]
  • LPV SUBNET (SUBNET_LPV and SUBNET_LPV_ext_scheduled). Featuring in: [11]
  • port HNN SUBNET (pHNN_SUBNET). Featuring in: [12]
  • Koopman SUBNET (Koopman_SUBNET). Featuring in: [13]
• 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.

Futher documentation

Check out examples/1. Overview deepSI.ipynb.

Contributing

deepSI is under ongoing development, and contributions to any part of the module are welcome.

todo list and known issues

• Expand demonstration notebook with pHNN examples.
• Issue where discrete time is printed in Input_output_data with torch.Tensors, and np.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.