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

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.