Kati8/ICLR_2023_2025 huggingface dataset:
authors: Anna Varbella
authors: Damien Briens
authors: Giuseppe Alessio D'Inverno
authors: Blazhe Gjorgiev
authors: Giovanni Sansavini
reviews: 
Comments: This paper presents PINCO, a neural architecture for solving the AC-OPF problem. PINCO is a combination of GNN + PINNs with hard constraints. Numerical tests show the usefulness of the proposed model.
Strengths: + A new model combining the GNNs and PINNs for solving AC-OPF
+ Promising numerical performance relative to MIPS solver
Weaknesses: - Both GNNs and PINNs have been used for solving AC-OPF, and the paper directly combines the two without much novel design in the architecture.
- Insufficient comparison against other numerical solvers for AC-OPF of distribution systems including e.g., using GNNs, PINNs, SDP relaxation and SOCP relaxation, and linear-OPF initialized Newton-Raphson method in terms of performance.
Recommendation: 3
Reviewer confidence: 4
Soundness/correctness: 3
Clarity: 3
reviews: 
Comments: This paper considers a physics-informed graph neural network, PINCO, to solve the AC-OPF problem. Using standard test cases, it shows that proposed method is faster than standard nonlinear solvers. Some generalization properties are discussed.
Strengths: - ACOPF is an important problem in grid operations. 
- The paper is easy to read, and the results seem correct.
Weaknesses: - In my opinion the main weakness of the paper is that the result isn't that good. In the sense that the main goal of the paper is to find feasible solutions, and I don't think that goal is accomplished.
- In Figure 3, the violations of $P, \theta, Q,$ and $V$ are shown. But the violations can be pretty large, especially for $Q$ and $V$. One of the reasons ACOPF is ran is to handle the V/Q constraints, and having a 10% error is not great. 
- Table 2 reports the "equality constraint" violations when the input load scenarios changes. But this violation can be 16 MW, which is again not a small number. I don't think operators would be likely to accept these types of violations. Although the nonlinear solver can be slow, but the problem can be resolved when the load changes. 
- The approaches in the paper is based on generic methods, and can be applied to any constrained optimization problem. It would be good to see if there is anything special about the ACOPF when applying the method.
Recommendation: 1
Reviewer confidence: 5
Soundness/correctness: 2
Clarity: 3
reviews: 
Comments: - This paper introduces PINCO, a physics-informed graph neural network (GNN) designed to approximate solutions for the frequently employed Alternating Current Optimal Power Flow (AC-OPF) problem in power transmission networks. By leveraging existing independent tools like physics-informed NNs and GNNs, PINCO distinguishes itself from prior approaches by better adhering to the inequality constraints of the AC-OPF problem, thereby enhancing solution feasibility in a data-driven framework.
Strengths: - The paper is clear in its exposition and is well-structured that makes the contributions and methodology easy to follow.
- Prior work is clearly acknowledged, and the authors effectively situate their approach within the existing body of research
- The authors make effective use of established methodologies to tackle the AC-OPF problem through an unsupervised learning approach with a focus on ensuring feasible AC-OPF solutions
- Experimental results do highlight feasible AC-OPF solutions quantified via the Equality Loss at the expense of slightly higher cost difference (which is inevitable given the data-driven model).
- The authors also showcase the additional benefits such as faster inference times
Weaknesses: - *Novelty*: The novelty of this approach appears limited, as it primarily relies on well-established tools like GNNs and PINNs. The work could further benefit from clearer differentiation that goes beyond simply combining existing frameworks. For e.g., did the authors explore architectural modifications to the GNN tailored to the characteristics of power transmission networks, or a customized optimization technique designed for AC-OPF? This could significantly enhance the paper’s originality within the ML domain.

- *Scope*: The current approach also presents practical concerns in real-world applications. In practice, power system operators frequently adjust network topology due to maintenance, unplanned outages, and other operational needs, leading to variations in the grid adjacency matrix for a *given* power system test case. Based on the paper’s description, the proposed model would need re-training from scratch for each such new grid adjacency matrix, which presents a notable limitation. Did the authors explore methods to make their model more adaptable to changing topologies for a given test case (even if the cost of the OPF solution is relatively high)? Developing a more flexible framework that can accommodate such variations within a single model would make the approach far more practical than showcasing the performance results across multiple IEEE benchmark systems.
Recommendation: 5
Reviewer confidence: 4
Soundness/correctness: 3
Clarity: 4
reviews: 
Comments: The paper presents a GNN-based approach to address the ACOPF problem, with the primary aim of reducing the computation time required by traditional interior-point solvers to enable faster ACOPF solutions. It leverages a physics-informed loss function incorporating penalties for both equality and inequality constraints. The grid model is represented as a graph, having real and reactive power demand, along with node type as inputs. Experimental results are provided, comparing the proposed approach with the MIPS solver across both single and multiple load scenarios.
Strengths: -- Attempting to solve a very relevant problem in the form of ACOPF.
-- Idea of using PINNs and GNN together is a strength.
Weaknesses: — The authors’ claim of being the first to use a PINN for solving the ACOPF problem must be clarified against the various existing works [1]-[2]. There are several works already using PINNs, in both supervised and unsupervised learning settings. There exists a substantial body of work under end-to-end learning that relates to this area, for example: [1]-[2].

— The issue mentioned above seems to stem from an incomplete literature review. For example, [1] presents a survey on end-to-end learning methods for constrained optimization, the general class of optimization problems to which ACOPF belongs. Many works listed there use PINNs in either supervised or unsupervised fashions. Additionally, several key references such as [2]-[4] are not discussed in the paper. Furthermore, the use of GNNs for the ACOPF problem is also not a unique contribution, as noted by the authors themselves. Authors should clearly discuss the limitations of these works and highlight how their work differs from them and provide advantages. 

— Experimental studies: The results presented are limited in terms of the number of experiments and comparative analysis. No comparisons are made to existing ML methods.   Authors must compare the results with various ML methods. For example, the cost difference with the proposed method is significantly higher than that achieved by various ML methods for ACOPF.



[1] Kotary, James, Ferdinando Fioretto, Pascal van Hentenryck, and Bryan Wilder. "End-to-End Constrained Optimization Learning: A Survey." In 30th International Joint Conference on Artificial Intelligence, IJCAI 2021, pp. 4475-4482. International Joint Conferences on Artificial Intelligence, 2021.
[2] Seonho Park and Pascal Van Hentenryck. Self-supervised primal-dual learning for constrained optimization. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 37, pp. 4052–4060, 2023.
[3] Ferdinando Fioretto, Terrence WK Mak, and Pascal Van Hentenryck. Predicting ac optimal power flows: Combining deep learning and lagrangian dual methods. In Proceedings of the AAAI conference on artificial intelligence, volume 34, pp. 630–637, 2020.
[4] Priya Donti, David Rolnick, and J Zico Kolter. Dc3: A learning method for optimization with hard constraints. In International Conference on Learning Representations, 2021.
Recommendation: 3
Reviewer confidence: 4
Soundness/correctness: 1
Clarity: 1