An accelerated hybrid data-driven/model-based approach for poroelasticity problems with multi-fidelity multi-physics data

TL;DR

This paper develops a hybrid data-driven and model-based approach to efficiently solve complex poroelasticity problems involving coupled diffusion and deformation in porous media, leveraging multi-fidelity data and accelerated algorithms.

Contribution

It introduces novel hybrid formulations that switch between model-based and data-driven methods based on data availability, improving efficiency and flexibility in simulating poroelasticity.

Findings

The hybrid approach outperforms purely model-based or data-driven methods in accuracy.

The k-dimensional tree search accelerates data retrieval in the model-free component.

Numerical experiments confirm the effectiveness and efficiency of the proposed methods.

Abstract

We present a hybrid model/model-free data-driven approach to solve poroelasticity problems. Extending the data-driven modeling framework originated from Kirchdoerfer and Ortiz (2016), we introduce one model-free and two hybrid model-based/data-driven formulations capable of simulating the coupled diffusion-deformation of fluid-infiltrating porous media with different amounts of available data. To improve the efficiency of the model-free data search, we introduce a distance-minimized algorithm accelerated by a k-dimensional tree search. To handle the different fidelities of the solid elasticity and fluid hydraulic constitutive responses, we introduce a hybridized model in which either the solid and the fluid solver can switch from a model-based to a model-free approach depending on the availability and the properties of the data. Numerical experiments are designed to verify the implementation and compare the performance of the proposed model to other alternatives.