Laguerre-Volterra networks

The Laguerre-Volterra network (LVN) is a Volterra-equivalent connectionist architecture, which combines a bank of discrete Laguerre filters and a layer of polynomial activation functions. This architecture is designed to model nonlinear dynamic systems from input-output signals. In this way, the network is trained using gradient-based methods or metaheuristics.

This repository implements the LVN in a way which is independent from the possible optimization methodologies. It also implements a comparison between different strategies to train LVNs.

Those strategies are:

[Strategy 0] Optimize ALPHA and RANGE of random weights with metaheuristics
Weights are randomized and polynomial coefficients are computed as a least-squares solution

[Strategy 1] Optimize ALPHA and W with metaheuristics
Polynomial coefficients are computed as a least-squares solution

[Strategy 2] Optimize ALPHA, W and C with metaheuristics

Organization of the repository:

Third party software dependencies

• Python 3.9.13
  • NumPy 1.21.2 (vector math)
  • Matplotlib 3.5.1 (plotting)

List of modules

• base_metaheuristic.py
  • simulated_annealing.py
  • particle_swarm_optimization.py
  • ant_colony_for_continuous_domains.py
• laguerre_volterra_network.py
• optimization_utilities.py
• simulated_systems.py
• data_handling.py

Scripts and their uses

• generate_datasets.py - Uses the data_handling module to generate synthetic train and test IO signals from simulated systems.
• optimization_examples.py - Optimizes LVN using different strategies (mostly used for verification)
• strategy_comparison_collect_results.py - Runs some specified metaheuristic 30 times and stores the solutions found, along with their errors on test signals
• strategy_comparison_plot_results.py - Plots the search histories based on results from strategy_comparison_collect_results.py
• weights_ranges_collect_results.py - Evaluates ranges of the weights W on the optimization strategy 1
• weights_ranges_plots.py - Plots the NMSE associated with different ranges of W, based on results from weights_ranges_collect_results.py
• evaluate_bo_link.py - Evaluates the impact of a structural change in the network, regarding linear terms