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

• URL: http://arxiv.org/abs/2512.01207v1
• Date: Mon, 01 Dec 2025 02:45:23 GMT
• Title: Physics-Constrained Neural Dynamics: A Unified Manifold Framework for Large-Scale Power Flow Computation
• Authors: Xuezhi Liu,
• Abstract summary: Power flow analysis is a fundamental tool for power system analysis, planning, and operational control.<n>Traditional Newton-Raphson methods suffer from limitations such as initial value sensitivity and low efficiency in batch computation.<n>This paper proposes a neural physics power flow solving method based on manifold geometry and gradient flow.
• Score: 0.5076419064097734
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Neural Network Optimal Power Flow via Energy Gradient Flow and Unified Dynamics [0.5076419064097734]
  This paper proposes an Optimal Power Flow solving method based on neural network dynamics and energy gradient flow computation.<n>By constructing an energy function to measure the degree of deviation from the constraint manifold, and guiding networks to learn optimal solutions that simultaneously satisfy power flow constraints and minimize costs through gradient flow.
  arXiv  Detail & Related papers  (2025-12-01T02:59:47Z)
• NeuralStagger: Accelerating Physics-constrained Neural PDE Solver with Spatial-temporal Decomposition [67.46012350241969]
  This paper proposes a general acceleration methodology called NeuralStagger. It decomposing the original learning tasks into several coarser-resolution subtasks. We demonstrate the successful application of NeuralStagger on 2D and 3D fluid dynamics simulations.
  arXiv  Detail & Related papers  (2023-02-20T19:36:52Z)
• Unsupervised Deep Learning for AC Optimal Power Flow via Lagrangian Duality [3.412750324146571]
  AC optimal power flow is a fundamental optimization problem in power system analysis. Deep learning based approaches have gained intensive attention to conduct the time-consuming training process offline. This paper proposes an end-to-end unsupervised learning based framework for AC-OPF.
  arXiv  Detail & Related papers  (2022-12-07T22:26:45Z)
• Unsupervised Optimal Power Flow Using Graph Neural Networks [172.33624307594158]
  We use a graph neural network to learn a nonlinear parametrization between the power demanded and the corresponding allocation. We show through simulations that the use of GNNs in this unsupervised learning context leads to solutions comparable to standard solvers.
  arXiv  Detail & Related papers  (2022-10-17T17:30:09Z)
• Physics Informed RNN-DCT Networks for Time-Dependent Partial Differential Equations [62.81701992551728]
  We present a physics-informed framework for solving time-dependent partial differential equations. Our model utilizes discrete cosine transforms to encode spatial and recurrent neural networks. We show experimental results on the Taylor-Green vortex solution to the Navier-Stokes equations.
  arXiv  Detail & Related papers  (2022-02-24T20:46:52Z)
• Message Passing Neural PDE Solvers [60.77761603258397]
  We build a neural message passing solver, replacing allally designed components in the graph with backprop-optimized neural function approximators. We show that neural message passing solvers representationally contain some classical methods, such as finite differences, finite volumes, and WENO schemes. We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, equation parameters, discretizations, etc., in 1D and 2D.
  arXiv  Detail & Related papers  (2022-02-07T17:47:46Z)
• Deep Learning Approximation of Diffeomorphisms via Linear-Control Systems [91.3755431537592]
  We consider a control system of the form $dot x = sum_i=1lF_i(x)u_i$, with linear dependence in the controls. We use the corresponding flow to approximate the action of a diffeomorphism on a compact ensemble of points.
  arXiv  Detail & Related papers  (2021-10-24T08:57:46Z)
• Physics informed neural networks for continuum micromechanics [68.8204255655161]
  Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. Due to the global approximation, physics informed neural networks have difficulties in displaying localized effects and strong non-linear solutions by optimization. It is shown, that the domain decomposition approach is able to accurately resolve nonlinear stress, displacement and energy fields in heterogeneous microstructures obtained from real-world $mu$CT-scans.
  arXiv  Detail & Related papers  (2021-10-14T14:05:19Z)
• Learning to Solve AC Optimal Power Flow by Differentiating through Holomorphic Embeddings [17.338923885534193]
  Alternating current optimal power flow (AC-OPF) is one of the fundamental problems in power systems operation. In this paper, we show efficient strategies that circumvent this problem by differentiating through the operations of a power flow solver. We report a 12x increase in speed and a 40% increase in robustness compared to a traditional solver.
  arXiv  Detail & Related papers  (2020-12-16T18:23:51Z)
• Physics-Guided Deep Neural Networks for Power Flow Analysis [18.761212680554863]
  We propose a physics-guided neural network to solve the power flow (PF) problem. By encoding different granularity of Kirchhoff's laws and system topology into the rebuilt PF model, our neural-network based PF solver is regularized by the auxiliary task.
  arXiv  Detail & Related papers  (2020-01-31T23:24:30Z)
• Physics Informed Deep Learning for Transport in Porous Media. Buckley Leverett Problem [0.0]
  We present a new hybrid physics-based machine-learning approach to reservoir modeling. The methodology relies on a series of deep adversarial neural network architecture with physics-based regularization. The proposed methodology is a simple and elegant way to instill physical knowledge to machine-learning algorithms.
  arXiv  Detail & Related papers  (2020-01-15T08:20:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.