Hybrid twinning using PBDW and DeepONet for the effective state estimation and prediction on partially known systems

• URL: http://arxiv.org/abs/2512.11834v1
• Date: Wed, 03 Dec 2025 12:19:00 GMT
• Title: Hybrid twinning using PBDW and DeepONet for the effective state estimation and prediction on partially known systems
• Authors: Stiven Briand Massala, Ludovic Chamoin, Massimo Picca Ciamarra,
• Abstract summary: We propose an effective hybrid approach that combines physics-based modeling with data-driven learning to enhance state estimation.<n>We validate the proposed approach on a representative problem involving the Helmholtz equation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The accurate estimation of the state of complex uncertain physical systems requires reconciling theoretical models, with inherent imperfections, with noisy experimental data. In this work, we propose an effective hybrid approach that combines physics-based modeling with data-driven learning to enhance state estimation and further prediction. Our method builds upon the Parameterized Background Data-Weak (PBDW) framework, which naturally integrates a reduced-order representation of the best-available model with measurement data to account for both anticipated and unanticipated uncertainties. To address model discrepancies not captured by the reduced-order space, and learn the structure of model deviation, we incorporate a Deep Operator Network (DeepONet) constrained to be an orthogonal complement of the best-knowledge manifold. This ensures that the learned correction targets only the unknown components of model bias, preserving the interpretability and fidelity of the physical model. An optimal sensor placement strategy is also investigated to maximize information gained from measurements. We validate the proposed approach on a representative problem involving the Helmholtz equation under various sources of modeling error, including those arising from boundary conditions and source terms.

Related papers

• Physics-Constrained Fine-Tuning of Flow-Matching Models for Generation and Inverse Problems [3.3811247908085855]
  We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems.<n>Our approach bridges generative modelling and scientific inference, opening new avenues for simulation-augmented discovery and data-efficient modelling of physical systems.
  arXiv  Detail & Related papers  (2025-08-05T09:32:04Z)
• A Framework for Strategic Discovery of Credible Neural Network Surrogate Models under Uncertainty [0.0]
  This study presents the Occam Plausibility Algorithm for surrogate models (OPAL-surrogate) OPAL-surrogate provides a systematic framework to uncover predictive neural network-based surrogate models. It balances the trade-off between model complexity, accuracy, and prediction uncertainty.
  arXiv  Detail & Related papers  (2024-03-13T18:45:51Z)
• Towards Theoretical Understandings of Self-Consuming Generative Models [56.84592466204185]
  This paper tackles the emerging challenge of training generative models within a self-consuming loop. We construct a theoretical framework to rigorously evaluate how this training procedure impacts the data distributions learned by future models. We present results for kernel density estimation, delivering nuanced insights such as the impact of mixed data training on error propagation.
  arXiv  Detail & Related papers  (2024-02-19T02:08:09Z)
• Data-driven Nonlinear Model Reduction using Koopman Theory: Integrated Control Form and NMPC Case Study [56.283944756315066]
  We propose generic model structures combining delay-coordinate encoding of measurements and full-state decoding to integrate reduced Koopman modeling and state estimation. A case study demonstrates that our approach provides accurate control models and enables real-time capable nonlinear model predictive control of a high-purity cryogenic distillation column.
  arXiv  Detail & Related papers  (2024-01-09T11:54:54Z)
• A PAC-Bayesian Perspective on the Interpolating Information Criterion [54.548058449535155]
  We show how a PAC-Bayes bound is obtained for a general class of models, characterizing factors which influence performance in the interpolating regime. We quantify how the test error for overparameterized models achieving effectively zero training error depends on the quality of the implicit regularization imposed by e.g. the combination of model, parameter-initialization scheme.
  arXiv  Detail & Related papers  (2023-11-13T01:48:08Z)
• Measuring and Modeling Uncertainty Degree for Monocular Depth Estimation [50.920911532133154]
  The intrinsic ill-posedness and ordinal-sensitive nature of monocular depth estimation (MDE) models pose major challenges to the estimation of uncertainty degree. We propose to model the uncertainty of MDE models from the perspective of the inherent probability distributions. By simply introducing additional training regularization terms, our model, with surprisingly simple formations and without requiring extra modules or multiple inferences, can provide uncertainty estimations with state-of-the-art reliability.
  arXiv  Detail & Related papers  (2023-07-19T12:11:15Z)
• Extension of Dynamic Mode Decomposition for dynamic systems with incomplete information based on t-model of optimal prediction [69.81996031777717]
  The Dynamic Mode Decomposition has proved to be a very efficient technique to study dynamic data. The application of this approach becomes problematic if the available data is incomplete because some dimensions of smaller scale either missing or unmeasured. We consider a first-order approximation of the Mori-Zwanzig decomposition, state the corresponding optimization problem and solve it with the gradient-based optimization method.
  arXiv  Detail & Related papers  (2022-02-23T11:23:59Z)
• Mixed Effects Neural ODE: A Variational Approximation for Analyzing the Dynamics of Panel Data [50.23363975709122]
  We propose a probabilistic model called ME-NODE to incorporate (fixed + random) mixed effects for analyzing panel data. We show that our model can be derived using smooth approximations of SDEs provided by the Wong-Zakai theorem. We then derive Evidence Based Lower Bounds for ME-NODE, and develop (efficient) training algorithms.
  arXiv  Detail & Related papers  (2022-02-18T22:41:51Z)
• Calibration and Uncertainty Quantification of Bayesian Convolutional Neural Networks for Geophysical Applications [0.0]
  It is common to incorporate the uncertainty of predictions such subsurface models should provide calibrated probabilities and the associated uncertainties in their predictions. It has been shown that popular Deep Learning-based models are often miscalibrated, and due to their deterministic nature, provide no means to interpret the uncertainty of their predictions. We compare three different approaches obtaining probabilistic models based on convolutional neural networks in a Bayesian formalism.
  arXiv  Detail & Related papers  (2021-05-25T17:54:23Z)
• A bandit-learning approach to multifidelity approximation [7.960229223744695]
  Multifidelity approximation is an important technique in scientific computation and simulation. We introduce a bandit-learning approach for leveraging data of varying fidelities to achieve precise estimates.
  arXiv  Detail & Related papers  (2021-03-29T05:29:35Z)
• Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks: Theory, Methods, and Algorithms [2.266704469122763]
  This paper proposes a new methodology for performing Bayesian inference in imaging inverse problems where the prior knowledge is available in the form of training data. We establish the existence and well-posedness of the associated posterior moments under easily verifiable conditions. A model accuracy analysis suggests that the Bayesian probability probabilities reported by the data-driven models are also remarkably accurate under a frequentist definition.
  arXiv  Detail & Related papers  (2021-03-18T11:34:08Z)

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.