In-context learning for model-free system identification

This repository contains the Python code to reproduce the results of the paper In-context learning for model-free system identification by Marco Forgione, Filippo Pura and Dario Piga.

We introduce the concept of model-free in-context learning for System Identification, where a meta model is trained to describe an entire class of dynamical systems, instead of a single instance. The meta model is able to understand the underlying dynamics from a context of provided input/output samples and to perform a task such as one-step-ahead prediction or multi-step-ahead simulation, that would otherwise require a model trained on each particular dataset.

One-step-ahead model-free prediction

Decoder-only (GPT-like) Transformer architecture for model-free one-step-ahead prediction:

Multi-step-ahead model-free simulation

Encoder-decoder (machine-translation-like) Transformer architecture for model-free multi-step-ahead simulation:

Main files

The training scripts are:

• train_onestep_lin.py: Decoder-only Transformer for one-step-ahead prediction on the LTI system class
• train_onestep_wh.py: Decoder-only Transformer for one-step-ahead prediction on the WH system class
• train_sim_lin.py: Encoder-decoder Transformer for multi-step-ahead simulation on the LTI system class
• train_sim_wh.py: Encoder-decoder Transformer for multi-step-ahead simulation on the WH system class

The scripts above except train_onestep_lin.py accept command-line arguments to customize the architecture and aspects of the training. For instance, the large one-step-ahead Transformer for the WH class described in the paper may be trained with the command:

python train_onestep_wh.py --out-file ckpt_onestep_wh_large --seq-len 1024  --n-layer 12 --n-head 12 --n-embd 768 --batch-size 20

Trained weights of all the Transformers discussed in the example section of the paper are available as assets in the v0.3 Release.

Jupyter notebooks that load the trained model and make predictions/simulations on new data are also available in the repo, e.g. test_onestep_lin.ipynb for one-step prediction on the LTI class.

Software requirements

Experiments were performed on a Python 3.11 conda environment with:

• numpy
• scipy
• matplotlib
• python-control
• pytorch (v2.1.0)
• pytorch-ident

These dependencies may be installed through the commands:

conda install numpy scipy matplotlib
conda install -c conda-forge control slycot
conda install pytorch -c pytorch

For more details on pytorch installation options (e.g. support for CUDA acceleration), please refer to the official installation instructions.

The following packages are also useful:

conda install jupyter # (optional, to run the test jupyter notebooks)
pip install wandb # (optional, for experiment logging & monitoring)
pip install pytorch-ident # (optional, for the comparisons with non-linear least squares on the WH model class)

Hardware requirements

While all the scripts can run on CPU, execution may be frustratingly slow. For faster training, a GPU is highly recommended. To run the paper's examples, we used a server equipped with an nVidia RTX 3090 GPU.

Citing

If you find this project useful, we encourage you to:

• Star this repository ⭐

• Cite the paper

@article{forgione2023from,
  author={Forgione, Marco and Pura, Filippo and Piga, Dario},
  journal={IEEE Control Systems Letters}, 
  title={From System Models to Class Models:
   An In-Context Learning Paradigm}, 
  year={2023},
  volume={7},
  number={},
  pages={3513-3518},
  doi={10.1109/LCSYS.2023.3335036}
}