Can Li

Hao Chen, Gonzalo E. Constante-Flores, Can Li

Decision-making problems can be represented as mathematical optimization models, finding wide applications in fields such as economics, engineering and manufacturing, transportation, and health care. Optimization models are mathematical abstractions of the problem of making the best decision while satisfying a set of requirements or constraints. One of the primary barriers to deploying these models in practice is the challenge of helping practitioners understand and interpret such models, particularly when they are infeasible, meaning no decision satisfies all the constraints. Existing methods for diagnosing infeasible optimization models often rely on expert systems, necessitating significant background knowledge in optimization. In this paper, we introduce OptiChat, a first-of-its-kind natural language-based system equipped with a chatbot GUI for engaging in interactive conversations about infeasible optimization models. OptiChat can provide natural language descriptions of the optimization model itself, identify potential sources of infeasibility, and offer suggestions to make the model feasible. The implementation of OptiChat is built on GPT-4, which interfaces with an optimization solver to identify the minimal subset of constraints that render the entire optimization problem infeasible, also known as the Irreducible Infeasible Subset (IIS). We utilize few-shot learning, expert chain-of-thought, key-retrieve, and sentiment prompts to enhance OptiChat's reliability. Our experiments demonstrate that OptiChat assists both expert and non-expert users in improving their understanding of the optimization models, enabling them to quickly identify the sources of infeasibility.

Amirhossein Mollaali, Gabriel Zufferey, Gonzalo Constante-Flores et al.

This paper proposes a new data-driven methodology for predicting intervals of post-fault voltage trajectories in power systems. We begin by introducing the Quantile Attention-Fourier Deep Operator Network (QAF-DeepONet), designed to capture the complex dynamics of voltage trajectories and reliably estimate quantiles of the target trajectory without any distributional assumptions. The proposed operator regression model maps the observed portion of the voltage trajectory to its unobserved post-fault trajectory. Our methodology employs a pre-training and fine-tuning process to address the challenge of limited data availability. To ensure data privacy in learning the pre-trained model, we use merging via federated learning with data from neighboring buses, enabling the model to learn the underlying voltage dynamics from such buses without directly sharing their data. After pre-training, we fine-tune the model with data from the target bus, allowing it to adapt to unique dynamics and operating conditions. Finally, we integrate conformal prediction into the fine-tuned model to ensure coverage guarantees for the predicted intervals. We evaluated the performance of the proposed methodology using the New England 39-bus test system considering detailed models of voltage and frequency controllers. Two metrics, Prediction Interval Coverage Probability (PICP) and Prediction Interval Normalized Average Width (PINAW), are used to numerically assess the model's performance in predicting intervals. The results show that the proposed approach offers practical and reliable uncertainty quantification in predicting the interval of post-fault voltage trajectories.

Gonzalo E. Constante-Flores, Hao Chen, Can Li

Deep learning models are increasingly deployed in safety-critical tasks where predictions must satisfy hard constraints, such as physical laws, fairness requirements, or safety limits. However, standard architectures lack built-in mechanisms to enforce such constraints, and existing approaches based on regularization or projection are often limited to simple constraints, computationally expensive, or lack feasibility guarantees. This paper proposes a model-agnostic framework for enforcing input-dependent linear equality and inequality constraints on neural network outputs. The architecture combines a task network trained for prediction accuracy with a safe network trained using decision rules from the stochastic and robust optimization literature to ensure feasibility across the entire input space. The final prediction is a convex combination of the two subnetworks, guaranteeing constraint satisfaction during both training and inference without iterative procedures or runtime optimization. We prove that the architecture is a universal approximator of constrained functions and derive computationally tractable formulations based on linear decision rules. Empirical results on benchmark regression tasks show that our method consistently satisfies constraints while maintaining competitive accuracy and low inference latency.