Toward Efficient Stokes Flow Simulations in Multi-Observable Thermo-Chemical Tomography Using Model Order Reduction

The prevalence of viscous-dominated regimes within the Earth’s interior gives rise to Stokes-like flow systems in numerous geodynamical applications. A prominent example is sublithospheric mantle convection, which constitutes the primary driving mechanism behind the evolution of dynamic topography. In this context, numerical simulations provide more physically consistent estimates of the Lithosphere–Asthenosphere Boundary (LAB) depth than those derived from first-order isostatic approximations [1].

However, the associated computational overburden is exceptionally high, particularly when accounting for material nonlinearities. The challenge is further complicated when attempting to incorporate them within a Markov Chain Monte Carlo (MCMC) framework that requires an exceptionally large number of evaluations [2], limiting their applicability to large-scale studies and underscores the need for novel and computationally efficient Reduced-Order Modeling (ROM) methodologies [3].

Results from linear Model Order Reduction (MOR) techniques indicate that the complexity of the problem surpasses the capabilities of projection-based ROMs designed to produce globally accurate solutions. This work introduces a localized, goal-oriented criterion to enhance linear reducibility and employs Neural Network (NN) surrogates to replace high-fidelity solver evaluations. These methodological advances jointly underpin the development of a hybrid offline–online reduction framework that efficiently reduces computational complexity while preserving the required levels of accuracy, enabling seamless model updates during parameter-space exploration.

 

REFERENCES

[1] Afonso, J. C., Rawlinson, N., Yang, Y., Schutt, D. L., Jones, A. G., Fullea, J., & Griffin, W. L. (2016). 3-D multiobservable probabilistic inversion for the compositional and thermal structure of the lithosphere and upper mantle: III. Thermochemical tomography in the Western-Central U.S. Journal of Geophysical Research: Solid Earth, 121(10), 7337–7370. https://doi.org/10. 1002/2016jb013049

[2] Ortega-Gelabert, O., Zlotnik, S., Afonso, J. C., & Diez, P. (2020). Fast Stokes Flow Simulations for Geophysical-Geodynamic Inverse Problems and Sensitivity Analyses Based on Reduced Order Modeling. Journal of Geophysical Research: Solid Earth, 125(3). https://doi.org/10.1029/ 2019jb018314

[3] Hesthaven, J.S., Rozza, G., Stamm, B. (2015). Certified Reduced Basis Methods for Parametrized Partial Differential Equations. SpringerBriefs in Mathematics. Springer International Publishing AG, Cham. https://doi.org/10.1007/978-3-319-22470-1