This project addressed these challenges by developing Deep Constrained Learning (DCL), a new class of machine learning methods that embed physical and engineering constraints directly into neural networks. Rather than merely predicting solutions from data, DCL models were designed to ensure that any output respects critical requirements, such as power flow limits and voltage constraints. This is accomplished by integrating by fusing fundamental optimization techniques—like Lagrangian duality, Benders decomposition, or projection methods—within the training process of the neural network. The result was a class of methods that have reimagined how to approximately solve optimization problems at a tiny fraction of the computational costs required by traditional methods. 

Intellectual Merit

The core scientific contribution of this project lies in bridging the gap between large-scale optimization and deep learning. The techniques developed have provided the first known framework to handle the nonconvex, non-linear nature of problems like the AC-OPF through deep learning models, drastically reducing the time needed to generate feasible solutions. The project also explored how to handle multistage optimization, for instance, capturing the temporal dependencies of power grid operations across multiple intervals and decompositions techniques to scale to country-scale power systems. In addition, the project explored approaches to compress large deep neural networks, and predict both the decision variables (e.g., generator dispatch) and auxiliary information (e.g., dual variables). The fundamental methodologies developed through this project have opened the door to a new generation of fast, high-fidelity optimization solvers.

Broader Impacts

The growth of renewable energy sources and new demands, such as the increasingly pervasive data centers, brings increasing uncertainty to power systems, making real-time decision-making even more essential for reliability and cost-effectiveness. The methods developed by this project can help system operators to rapidly explore different scenarios, adjust generator setpoints, and maintain stability, with the goal of providing better integration of new energy sources. Beyond power systems, the same constrained learning principles have been shown to benefit other engineering domains, such as transportation and logistics that also require respecting physics and operational limits.  

This project has also trained multiple graduate students in constrained machine learning and optimization, strengthening the workforce with skills needed for next-generation energy systems and beyond. The PIs have enriched educational camps and K–12 teacher programs with new content on AI for engineering, promoting broader literacy in data-driven engineering. The idea to merge deep learning with proven optimization methods, has, through the years, proven to be transformative to improve the efficiency and reliability of large-scale infrastructure systems.

Last Modified: 04/02/2025
Modified by: Ferdinando Fioretto