SYAIDec 1, 2025

Physics-Constrained Neural Dynamics: A Unified Manifold Framework for Large-Scale Power Flow Computation

arXiv:2512.01207v1
Originality Incremental advance
AI Analysis

This addresses power system analysis by providing a more efficient and physically consistent solver, though it is incremental as it builds on neural methods with a new geometric framework.

The paper tackles the inefficiency and physical inconsistency of existing power flow solvers by proposing an unsupervised neural physics method that transforms power flow equations into a dynamical system for equilibrium finding, achieving accurate solutions without labeled data.

Power flow analysis is a fundamental tool for power system analysis, planning, and operational control. Traditional Newton-Raphson methods suffer from limitations such as initial value sensitivity and low efficiency in batch computation, while existing deep learning-based power flow solvers mostly rely on supervised learning, requiring pre-solving of numerous cases and struggling to guarantee physical consistency. This paper proposes a neural physics power flow solving method based on manifold geometry and gradient flow, by describing the power flow equations as a constraint manifold, and constructing an energy function \(V(\mathbf{x}) = \frac{1}{2}\|\mathbf{F}(\mathbf{x})\|^2\) and gradient flow \(\frac{d\mathbf{x}}{dt} = -\nabla V(\mathbf{x})\), transforming power flow solving into an equilibrium point finding problem for dynamical systems. Neural networks are trained in an unsupervised manner by directly minimizing physical residuals, requiring no labeled data, achieving true "end-to-end" physics-constrained learning.

Foundations

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