pinn-mpc

Code to accompany the research on: "An Explicit Model Predictive Control Framework Based On Physics-Informed Neural Networks."

Table of Contents

• Overview
• Code
• How to Run Code
• Prerequisites
• License

Overview

This repository contains the Python notebooks developed as part of the research titled "An Explicit Model Predictive Control Framework Based On Physics-Informed Neural Networks." by Argyri Kardamaki, Teo Protoulis, Alex Alexandridis and Haralambos Sarimveis.

We implement Physics-Informed Neural Networks (PINNs) to approximate the explicit solution of nonlinear Model Predictive Control (MPC) problems. The controllers learn closed-loop behavior offline by training on simulated trajectories while embedding system physics directly into the loss function.

The PINN-MPC framework minimizes a composite loss consisting of:

• Physics residuals from the system dynamics,
• Tracking errors toward a set-point trajectory,
• Initial-condition consistency, and
• Soft constraints on states and control inputs.

The repository includes implementations for both:

• SISO nonlinear water-tank system used in the research study
• MIMO nonlinear quadruple water-tank system used in the research study

Both controllers are trained offline and evaluated through extensive closed-loop simulations.

Code

Two notebooks are provided:

• PINN_MPC_SISO_Github_Code.ipynb – full SISO PINN-MPC training, validation metrics, and closed-loop plots.
• PINN_MPC_MIMO_Github_Code.ipynb – full MIMO PINN-MPC training, validation, and closed-loop performance.

The code includes clearly separated sections for:

• Training using a two-phase Adam optimizer;
• Validation & metrics on test scenarios;
• Closed-loop simulations with performance plots.

The MIMO training episodes are split into three files for GitHub compatibility with size:

• mimo_training_samples_x.pt – initial states (x0_all)
• mimo_training_samples_ysp.pt – set-points (ysp_all)
• mimo_training_samples_ud.pt – inputs, disturbances, and metadata (u0_all, d0_all)

Test episodes are also included for both SISO and MIMO systems.

Users may freely adjust hyperparameters (loss weights, batch size, learning rates, prediction horizon, etc.) to explore different control behaviors.

How to Run Code

1. Open the desired notebook (PINN_MPC_SISO_Github_Code.ipynb or PINN_MPC_MIMO_Github_Code.ipynb) in Jupyter or Google Colab.
2. Upload the corresponding training and test episodes (.pt files).
3. Run all cells to:
   • Train the PINN-MPC controller,
   • Evaluate it on challenging validation scenarios,
   • Visualize closed-loop behavior.
4. Modify training or simulation parameters in the relevant sections to experiment with different configurations.

Performance Tip: Users are encouraged to run the code on a GPU to significantly reduce training time. To run your notebook on a local GPU with Google Colab, see Official Colab guidance: https://research.google.com/colaboratory/local-runtimes.html

Prerequisites

This project requires Python 3.8+ and the following packages:

• torch (PyTorch ≥ 2.0)
• numpy
• matplotlib
• scipy

License

This project is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. See the file LICENSE-CC-BY-NC-SA.txt for details.