Physics-Adaptive Digital Twin with Neural-Operator Reduced-Order Modelling

Year : 2026 | Volume : 13 | Issue : 02 | Page : 89 103
By

Subash Ranjan Kabat,

Bibhu Prasad Ganthia,

  1. Associate Professor and Principal, Electrical Engineering, Radhakrishna Institute of Technology and Engineering, Bhubaneswar, Odisha, India
  2. Assistant Professor, Electrical Engineering, Radhakrishna Institute of Technology and Engineering, Bhubaneswar, Odisha, India

Abstract

This study proposes a novel Physics-Adaptive Digital Twin with Neural-Operator Reduced-Order Modelling (PADT-NO) framework for predictive modelling of complex, nonlinear, and multiscale fluid flows. The proposed mathematical framework integrates fundamental conservation laws, Navier–Stokes dynamics, physics-constrained neural operators, adaptive reduced-order modelling, and uncertainty-aware state estimation within a unified computational architecture. Unlike conventional computational fluid dynamics and purely data-driven approaches, the proposed model dynamically couples high-fidelity physical information with a low-dimensional latent representation while preserving essential mass, momentum, and energy constraints. An adaptive mode-selection mechanism automatically modifies the reduced-order model complexity according to changes in flow regimes, enabling efficient representation of transient and strongly nonlinear flow structures. A physics-constrained learning objective simultaneously minimizes observational error, governing-equation residuals, boundary-condition violations, conservation errors, stability deviations, and uncertainty-calibration errors. The digital twin further incorporates parameter and model uncertainties to generate probabilistic flow predictions rather than deterministic estimates alone. The proposed framework is designed for rapid prediction, real-time monitoring, parameter estimation, and many-query fluid simulations while reducing computational dependence on expensive high-fidelity solvers. The resulting formulation provides a scalable mathematical pathway for next-generation intelligent fluid-mechanics modelling, particularly for turbulent, transient, and multiphysics flow systems. The system lowers the computing costs of high-fidelity solvers while supporting many-query fluid simulations, parameter estimation, real-time monitoring, and quick prediction. It offers a scalable approach to intelligent fluid-mechanics modelling with enhanced computational efficiency and predictive flexibility, especially for turbulent, transient, and multiphysics flow systems.

 

Keywords: Physics-informed modelling; digital twin; neural operators; reduced-order modelling; fluid dynamics

[This article belongs to Recent Trends in Fluid Mechanics ]

How to cite this article: Subash Ranjan Kabat, Bibhu Prasad Ganthia. Physics-Adaptive Digital Twin with Neural-Operator Reduced-Order Modelling. Recent Trends in Fluid Mechanics. 2026; 13(02):89-103.
How to cite this URL: Subash Ranjan Kabat, Bibhu Prasad Ganthia. Physics-Adaptive Digital Twin with Neural-Operator Reduced-Order Modelling. Recent Trends in Fluid Mechanics. 2026; 13(02):89-103. Available from: https://journals.stmjournals.com/rtfm/article=2026/view=257332

References

  1. Zhang Z, Shukla K, Wang Z, Morales A, Käufer T, Salauddin S, Walters N, Barrett D, Ahmed K, Triantafyllou MS, Karniadakis GE. Turbulence closure in Reynolds-averaged Navier–Stokes and flow inference around a cylinder using physics-informed neural networks and sparse experimental data. Journal of Fluid Mechanics. 2026 May;1034:A16.
  2. Kramer B, Qian E. Reduced-order modeling for engineering systems: survey and opportunities for digital twins: B. Kramer, E. Qian. Structural and Multidisciplinary Optimization. 2026 Jun;69(6):141.
  3. Azizzadenesheli K, Kovachki N, Li Z, Liu-Schiaffini M, Kossaifi J, Anandkumar A. Neural operators for accelerating scientific simulations and design. Nature Reviews Physics. 2024 May;6(5):320–8.
  4. Song S, Mukerji T, Zhang D. Physics-informed multi-grid neural operator: Theory and an application to porous flow simulation. Journal of Computational Physics. 2025 Jan 1;520:113438.
  5. Kannapinn M, Schäfer M, Weeger O. TwinLab: a framework for data-efficient training of non-intrusive reduced-order models for digital twins. Engineering Computations. 2025 Nov 25;42(7):2406–26.
  6. Mücke NT. Deep Learning for Real-Time Inverse Problems and Data Assimilation with Uncertainty Quantification for Digital Twins.
  7. Hanrahan S, Kozul M, Sandberg RD. Studying turbulent flows with physics-informed neural networks and sparse data. International Journal of Heat and Fluid Flow. 2023 Dec 1;104:109232.
  8. Liu Z, Chen Y, Song G, Song W, Xu J. Combination of physics-informed neural networks and single-relaxation-time lattice boltzmann method for solving inverse problems in fluid mechanics. Mathematics. 2023 Oct 1;11(19):4147.
  9. Kim Y, Kwak H, Nam J. Physics-informed neural networks for learning fluid flows with symmetry. Korean Journal of Chemical Engineering. 2023 Sep;40(9):2119–27.
  10. Vinuesa R, Brunton SL. Enhancing computational fluid dynamics with machine learning. Nature Computational Science. 2022 Jun;2(6):358–66.
  11. Charalampopoulos AT, Sapsis TP. Machine-learning energy-preserving nonlocal closures for turbulent fluid flows and inertial tracers. Physical Review Fluids. 2022 Feb;7(2):024305.
  12. Bin Y, Chen L, Huang G, Yang XI. Progressive, extrapolative machine learning for near-wall turbulence modeling. Physical Review Fluids. 2022 Aug;7(8):084610.
  13. Sandberg RD, Zhao Y. Machine-learning for turbulence and heat-flux model development: A review of challenges associated with distinct physical phenomena and progress to date. International journal of heat and fluid flow. 2022 Jun 1;95:108983.
  14. Chen X, Lu J, Tryggvason G. Finding closure terms directly from coarse data for 2D turbulent flow. arXiv preprint arXiv:2104.09344. 2021 Apr 19.
  15. Lu L, Jin P, Karniadakis GE. Deeponet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators. arXiv preprint arXiv:1910.03193. 2019 Oct 8.
  16. Li Z, Kovachki N, Azizzadenesheli K, Liu B, Bhattacharya K, Stuart A, Anandkumar A. Fourier neural operator for parametric partial differential equations. arXiv preprint arXiv:2010.08895. 2020 Oct 18.
  17. Lu L, Meng X, Mao Z, Karniadakis GE. DeepXDE: A deep learning library for solving differential equations. SIAM review. 2021 Jan 1;63(1):208–28.
  18. Brunton SL. Applying machine learning to study fluid mechanics. Acta Mechanica Sinica. 2021 Dec;37(12):1718–26.
  19. Raissi M, Yazdani A, Karniadakis GE. Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations. Science. 2020 Feb 28;367(6481):1026–30.
  20. Brunton SL, Noack BR, Koumoutsakos P. Machine learning for fluid mechanics. Annual review of fluid mechanics. 2020 Jan 5;52(1):477–508.
Regular Issue Subscription Review Article
Volume 13
Issue 02
Received 12/09/2026
Accepted 14/09/2026
Published 15/09/2026
Publication Time 3 Days

Login

My IP

PlumX Metrics

Support