Verifying Physics-Informed Neural Network Fidelity using Classical Fisher Information from Differentiable Dynamical System

• URL: http://arxiv.org/abs/2601.11638v1
• Date: Wed, 14 Jan 2026 15:20:54 GMT
• Title: Verifying Physics-Informed Neural Network Fidelity using Classical Fisher Information from Differentiable Dynamical System
• Authors: Josafat Ribeiro Leal Filho, Antônio Augusto Fröhlich,
• Abstract summary: Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving differential equations and modeling physical systems.<n>This paper proposes a novel experimental framework to address how well a PINN captures the complete dynamical behavior of the system.
• Score: 0.6445605125467574
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving differential equations and modeling physical systems by embedding physical laws into the learning process. However, rigorously quantifying how well a PINN captures the complete dynamical behavior of the system, beyond simple trajectory prediction, remains a challenge. This paper proposes a novel experimental framework to address this by employing Fisher information for differentiable dynamical systems, denoted $g_F^C$. This Fisher information, distinct from its statistical counterpart, measures inherent uncertainties in deterministic systems, such as sensitivity to initial conditions, and is related to the phase space curvature and the net stretching action of the state space evolution. We hypothesize that if a PINN accurately learns the underlying dynamics of a physical system, then the Fisher information landscape derived from the PINN's learned equations of motion will closely match that of the original analytical model. This match would signify that the PINN has achieved comprehensive fidelity capturing not only the state evolution but also crucial geometric and stability properties. We outline an experimental methodology using the dynamical model of a car to compute and compare $g_F^C$ for both the analytical model and a trained PINN. The comparison, based on the Jacobians of the respective system dynamics, provides a quantitative measure of the PINN's fidelity in representing the system's intricate dynamical characteristics.

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 Constrained Learning of Dynamics from Static Data [8.346864633675414]
  A physics-informed neural network (PINN) models the dynamics of a system by integrating the governing physical laws into the architecture of a neural network.<n>Existing PINN frameworks rely on fully observed time-course data, the acquisition of which could be prohibitive for many systems.<n>In this study, we developed a new PINN learning paradigm, namely Constrained Learning, that enables the approximation of first-order derivatives or motions using non-time course or partially observed data.
  arXiv  Detail & Related papers  (2025-04-17T06:06:53Z)
• Towards Model Discovery Using Domain Decomposition and PINNs [44.99833362998488]
  The study evaluates the performance of two approaches, namely Physics-Informed Neural Networks (PINNs) and Finite Basis Physics-Informed Neural Networks (FBPINNs) We find a better performance for the FBPINN approach compared to the vanilla PINN approach, even in cases with data from only a quasi-stationary time domain with few dynamics.
  arXiv  Detail & Related papers  (2024-10-02T14:38:37Z)
• 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)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• ConCerNet: A Contrastive Learning Based Framework for Automated Conservation Law Discovery and Trustworthy Dynamical System Prediction [82.81767856234956]
  This paper proposes a new learning framework named ConCerNet to improve the trustworthiness of the DNN based dynamics modeling. We show that our method consistently outperforms the baseline neural networks in both coordinate error and conservation metrics.
  arXiv  Detail & Related papers  (2023-02-11T21:07:30Z)
• Capturing Actionable Dynamics with Structured Latent Ordinary Differential Equations [68.62843292346813]
  We propose a structured latent ODE model that captures system input variations within its latent representation. Building on a static variable specification, our model learns factors of variation for each input to the system, thus separating the effects of the system inputs in the latent space.
  arXiv  Detail & Related papers  (2022-02-25T20:00:56Z)
• Constructing Neural Network-Based Models for Simulating Dynamical Systems [59.0861954179401]
  Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. This paper provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome.
  arXiv  Detail & Related papers  (2021-11-02T10:51:42Z)
• Physics-guided Deep Markov Models for Learning Nonlinear Dynamical Systems with Uncertainty [6.151348127802708]
  We propose a physics-guided framework, termed Physics-guided Deep Markov Model (PgDMM) The proposed framework takes advantage of the expressive power of deep learning, while retaining the driving physics of the dynamical system.
  arXiv  Detail & Related papers  (2021-10-16T16:35:12Z)
• A deep learning framework for solution and discovery in solid mechanics [1.4699455652461721]
  We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to learning and discovery in solid mechanics. We explain how to incorporate the momentum balance and elasticity relations into PINN, and explore in detail the application to linear elasticity.
  arXiv  Detail & Related papers  (2020-02-14T08:24:53Z)

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.