Speaker
Description
High-fidelity pore-scale flow simulations are indispensable for characterizing transport phenomena in complex porous media. Techniques like the Lattice Boltzmann Method (LBM) and direct Stokes solvers explicitly resolve three-dimensional pore-space flow fields, capturing essential effects of pore connectivity, multiscale heterogeneity, and intricate boundary conditions. However, their prohibitive computational cost restricts application to large domains, high resolutions, or multiple flow scenarios. This limitation has spurred interest in surrogate models that can replicate pore-scale solutions at a dramatically reduced computational cost while preserving physical accuracy.
This work introduces the Shearlet Neural Operator (SNO), a novel neural operator based on shearlet representations, as an efficient surrogate for pore-scale flow solvers. In contrast to conventional Fourier-based neural operators—which rely on global sinusoidal bases and struggle with localized, anisotropic, or non-smooth features—the SNO harnesses the multiscale and directional properties of shearlets. This allows it to efficiently represent localized flow structures, sharp gradients, and anisotropic patterns, making it particularly well-suited for problems involving multiscale geometries and non-smooth solutions, including regimes with shocks or sharp transitions.
Formulated to learn mappings between function spaces, the SNO directly approximates the solution operator that maps pore geometry and boundary conditions to velocity fields. By operating in a multiscale shearlet domain, it naturally accommodates varying resolutions and captures both global flow behavior and fine-scale local features. This design overcomes key limitations of Fourier-based neural operators, whose globally supported basis functions hinder their ability to represent localized phenomena and scale-dependent structures effectively.
The methodology is first validated on a series of controlled benchmark problems designed to test its capability in representing multiscale features, anisotropy, and sharp spatial variations. These benchmarks highlight the SNO's robustness and expressiveness in regimes where Fourier-based operators exhibit degraded accuracy. Subsequently, the approach is applied to a physically relevant pore-scale flow problem: predicting three-dimensional velocity fields. Trained on simulation data, the resulting surrogate mode estimates the velocity fields while achieving orders-of-magnitude acceleration in computational speed.
The Shearlet Neural Operator offers a scalable, resolution-aware, and physically expressive surrogate. By integrating multiscale directional representations with operator learning, this framework provides a promising pathway toward fast, accurate simulation of flow in complex porous media, with potential extensions to broader classes of multiscale and non-smooth physical systems.
| Country | Brazil |
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