Rethinking Neural Width for Alternating Current Optimal Power Flow Proxies

2026-06-02

AI Summary

This work addresses the lack of systematic guidelines for neural network width design in deep learning approaches to solving the alternating current optimal power flow (ACOPF) problem. Through a constructive thought experiment, the authors analyze the minimal network width required to approximate the feasible manifold of ACOPF and propose a loss-guided progressive neural densification strategy that dynamically expands network capacity only when the current architecture can no longer be optimized. By embedding physical constraints directly into the deep neural network, the method achieves solution accuracy comparable to baseline models on multiple IEEE benchmark systems while using less than one-tenth the number of neurons per layer, substantially enhancing model compactness and verifiability.

Abstract

Deep learning proxies for Alternating Current Optimal Power Flow (ACOPF) lack systematic methods for determining architectural size. This paper conducts a constructive thought experiment to answer a fundamental inquiry: how wide must a neural network be to almost accurately approximate the ACOPF manifold? We introduce a Loss-Guided Neural Densification (LG-ND) algorithm that incrementally discovers necessary capacity by expanding only when the current deep neural network topology fails to improve further. Empirical results across various IEEE systems show that LG-ND achieves performance parity with literature baselines using up to ten times fewer neurons per layer. Such architectural minimalism is critical for the formal verification required in safety-critical grid operations.

Problem

• ACOPF
• neural width
• deep learning proxy
• architectural size
• manifold approximation

Innovation

• Loss-Guided Neural Densification
• Neural Width Optimization
• ACOPF Proxy
• Architectural Minimalism
• Deep Learning for Power Systems