Differentiable Modeling for Low-Inertia Grids: Benchmarking PINNs, NODEs, and DP for Identification and Control of SMIB System

• URL: http://arxiv.org/abs/2602.09667v1
• Date: Tue, 10 Feb 2026 11:22:59 GMT
• Title: Differentiable Modeling for Low-Inertia Grids: Benchmarking PINNs, NODEs, and DP for Identification and Control of SMIB System
• Authors: Shinhoo Kang, Sangwook Kim, Sehyun Yun,
• Abstract summary: This paper presents a comparative study of different differentiable programming paradigms for modeling, identification, and control of power system dynamics.<n>We evaluate their performance in trajectory extrapolation, parameter estimation, and Linear Quadratic Regulator (LQR) synthesis.<n>Our results highlight a fundamental trade-off between data-driven flexibility and physical structure.
• Score: 17.96236104895915
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The transition toward low-inertia power systems demands modeling frameworks that provide not only accurate state predictions but also physically consistent sensitivities for control. While scientific machine learning offers powerful nonlinear modeling tools, the control-oriented implications of different differentiable paradigms remain insufficiently understood. This paper presents a comparative study of Physics-Informed Neural Networks (PINNs), Neural Ordinary Differential Equations (NODEs), and Differentiable Programming (DP) for modeling, identification, and control of power system dynamics. Using the Single Machine Infinite Bus (SMIB) system as a benchmark, we evaluate their performance in trajectory extrapolation, parameter estimation, and Linear Quadratic Regulator (LQR) synthesis. Our results highlight a fundamental trade-off between data-driven flexibility and physical structure. NODE exhibits superior extrapolation by capturing the underlying vector field, whereas PINN shows limited generalization due to its reliance on a time-dependent solution map. In the inverse problem of parameter identification, while both DP and PINN successfully recover the unknown parameters, DP achieves significantly faster convergence by enforcing governing equations as hard constraints. Most importantly, for control synthesis, the DP framework yields closed-loop stability comparable to the theoretical optimum. Furthermore, we demonstrate that NODE serves as a viable data-driven surrogate when governing equations are unavailable.

Related papers

• PINN-Obs: Physics-Informed Neural Network-Based Observer for Nonlinear Dynamical Systems [2.884893167166808]
  This paper introduces a novel Adaptive Physics-Informed Neural Network-based Observer (PINN-Obs) for accurate state estimation in nonlinear systems.<n>Unlike traditional model-based observers, which require explicit system transformations or linearization, the proposed framework directly integrates system dynamics and sensor data into a physics-informed learning process.
  arXiv  Detail & Related papers  (2025-07-09T10:09:45Z)
• Physics-Informed Neural Networks for Control of Single-Phase Flow Systems Governed by Partial Differential Equations [4.776073133338117]
  We extend the Physics-Informed Neural Nets for Control (PINC) framework to integrate neural networks with physical conservation laws.<n>The PINC model for PDEs is structured into two stages: a steady-state network, which learns equilibrium solutions for a wide range of control inputs, and a transient network, which captures dynamic responses under time-varying boundary conditions.<n>We validate our approach through numerical experiments, demonstrating that the PINC model, which is trained exclusively using physical laws, accurately represents flow dynamics and enables real-time control applications.
  arXiv  Detail & Related papers  (2025-06-06T15:50:19Z)
• Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems [49.819436680336786]
  We propose an efficient transformed Gaussian process state-space model (ETGPSSM) for scalable and flexible modeling of high-dimensional, non-stationary dynamical systems.<n>Specifically, our ETGPSSM integrates a single shared GP with input-dependent normalizing flows, yielding an expressive implicit process prior that captures complex, non-stationary transition dynamics.<n>Our ETGPSSM outperforms existing GPSSMs and neural network-based SSMs in terms of computational efficiency and accuracy.
  arXiv  Detail & Related papers  (2025-03-24T03:19:45Z)
• Response Estimation and System Identification of Dynamical Systems via Physics-Informed Neural Networks [0.0]
  This paper explores the use of Physics-Informed Neural Networks (PINNs) for the identification and estimation of dynamical systems. PINNs offer a unique advantage by embedding known physical laws directly into the neural network's loss function, allowing for simple embedding of complex phenomena. The results demonstrate that PINNs deliver an efficient tool across all aforementioned tasks, even in presence of modelling errors.
  arXiv  Detail & Related papers  (2024-10-02T08:58:30Z)
• Learning Neural Constitutive Laws From Motion Observations for Generalizable PDE Dynamics [97.38308257547186]
  Many NN approaches learn an end-to-end model that implicitly models both the governing PDE and material models. We argue that the governing PDEs are often well-known and should be explicitly enforced rather than learned. We introduce a new framework termed "Neural Constitutive Laws" (NCLaw) which utilizes a network architecture that strictly guarantees standard priors.
  arXiv  Detail & Related papers  (2023-04-27T17:42:24Z)
• LordNet: An Efficient Neural Network for Learning to Solve Parametric Partial Differential Equations without Simulated Data [47.49194807524502]
  We propose LordNet, a tunable and efficient neural network for modeling entanglements. The experiments on solving Poisson's equation and (2D and 3D) Navier-Stokes equation demonstrate that the long-range entanglements can be well modeled by the LordNet.
  arXiv  Detail & Related papers  (2022-06-19T14:41:08Z)
• Auto-PINN: Understanding and Optimizing Physics-Informed Neural Architecture [77.59766598165551]
  Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bringing together the power of deep learning to bear on scientific computation. Here, we propose Auto-PINN, which employs Neural Architecture Search (NAS) techniques to PINN design. A comprehensive set of pre-experiments using standard PDE benchmarks allows us to probe the structure-performance relationship in PINNs.
  arXiv  Detail & Related papers  (2022-05-27T03:24:31Z)
• Neural Operator with Regularity Structure for Modeling Dynamics Driven by SPDEs [70.51212431290611]
  Partial differential equations (SPDEs) are significant tools for modeling dynamics in many areas including atmospheric sciences and physics. We propose the Neural Operator with Regularity Structure (NORS) which incorporates the feature vectors for modeling dynamics driven by SPDEs. We conduct experiments on various of SPDEs including the dynamic Phi41 model and the 2d Navier-Stokes equation.
  arXiv  Detail & Related papers  (2022-04-13T08:53:41Z)
• Residual Pathway Priors for Soft Equivariance Constraints [44.19582621065543]
  We introduce Residual Pathway Priors (RPPs) as a method for converting hard architectural constraints into soft priors. RPPs are resilient to approximate or misspecified symmetries, and are as effective as fully constrained models even when symmetries are exact.
  arXiv  Detail & Related papers  (2021-12-02T16:18:17Z)
• Data-Driven Optimized Tracking Control Heuristic for MIMO Structures: A Balance System Case Study [8.035375408614776]
  The PID is illustrated on a two-input two-output balance system. It integrates a self-adjusting nonlinear threshold with a neural network to compromise between the desired transient and steady state characteristics. The neural network is trained upon optimizing a weighted-derivative like objective cost function.
  arXiv  Detail & Related papers  (2021-04-01T02:00:20Z)
• Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamics [90.81186513537777]
  We propose a novel compound kernel that captures the control-affine nature of the problem. We show that this resulting optimization problem is convex, and we call it Gaussian Process-based Control Lyapunov Function Second-Order Cone Program (GP-CLF-SOCP)
  arXiv  Detail & Related papers  (2020-11-14T01:27:32Z)

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.