This repository contains the Python code to reproduce the results of the paper On the adaptation of recurrent neural networks for system identification by Marco Forgione, Aneri Muni, Dario Piga, and Marco Gallieri.

We introduce a transfer learning approach which enables fast and efficient adaptation of Recurrent Neural Network models.

A nominal RNN model is first identified using available measurements. The system dynamics are then assumed to change, leading to an unacceptable degradation of the nominal model performance on the perturbed system.

To cope with the mismatch, the model is augmented with an additive correction term trained on fresh data from the new dynamic regime. The correction term is learned through a Bayesian Linear Regression (BLR) method defined in terms of the features spanned by the nominal model's Jacobian with respect to its parameters.

A non-parametric view of the approach is also proposed, which extends the recent work on Gaussian Process with Neural Tangent Kernel (NTK-GP) discussed in [1] to the RNN case (RNTK-GP).

Finally, we introduce an approach to initialize the RNN state based on a context of past data, so that an estimate of the initial state is not needed on top of the parameter estimation.

• examples: examples transfer learning with
  • CSTR reactor
  • Non-linear RLC circuit
  • Wiener-Hammerstein system (not discussed in the paper)
• diffutil: computation of:
  • full parameter Jacobians matrix in jacobian.py
  • Jacobian-vector / transposed Jacobian-vector products in products.py
• torchid: system identification tools with PyTorch. Copied from https://github.com/forgi86/pytorch-ident

Simulations were performed on a Python 3.8 conda environment with

• numpy
• matplotlib
• pandas
• pytorch (version 1.8.1)

These dependencies may be installed through the commands:

conda install numpy scipy pandas matplotlib
conda install pytorch torchvision cudatoolkit=10.2 -c pytorch

If you find this project useful, we encourage you to

• Star this repository ⭐
• Cite the paper

To cite the paper, you may use the following BibTex entry:

@article{forgione2022adapt,
  title={On the adaptation of recurrent neural networks for system identification},
  author={Forgione, M. and Muni, A. and Piga, D. and Gallieri, M.},
  journal={arXiv e-prints arXiv:2201.08660},
  year={2022}
}

Using the IEEEtran bibliography style, it should look like:

M. Forgione, A. Muni, D. Piga, and M. Gallieri, "On the adaptation of recurrent neural networks for system identification," arXiv preprint arXiv:2201.08660, 2022.

[1] W. Maddox, S. Tang, P. Moreno, A. Wilson, and A. Damianou, "Fast Adaptation with Linearized Neural Networks,"
in Proc. of the International Conference on Artificial Intelligence and Statistics, 2021.