Interface learning in fluid dynamics: statistical inference of closures within micro-macro coupling models (2008.04490v1)

Abstract: Many complex multiphysics systems in fluid dynamics involve using solvers with varied levels of approximations in different regions of the computational domain to resolve multiple spatiotemporal scales present in the flow. The accuracy of the solution is governed by how the information is exchanged between these solvers at the interface and several methods have been devised for such coupling problems. In this article, we construct a data-driven model by spatially coupling a microscale lattice Boltzmann method (LBM) solver and macroscale finite difference method (FDM) solver for reaction-diffusion systems. The coupling between the micro-macro solvers has one to many mapping at the interface leading to the interface closure problem, and we propose a statistical inference method based on neural networks to learn this closure relation. The performance of the proposed framework in a bifidelity setting partitioned between the FDM and LBM domain shows its promise for complex systems where analytical relations between micro-macro solvers are not available.

• The paper presents an ML framework that statistically infers interface closures between microscale LBM and macroscale FDM solvers.
• The paper validates its approach using reaction-diffusion simulations, demonstrating improved performance over traditional zeroth-order methods.
• The paper highlights the promise of AI-driven techniques in complex fluid dynamics, offering a robust alternative when analytical closures are impractical.

Interface Learning in Fluid Dynamics: Statistical Inference of Closures Within Micro-Macro Coupling Models

The paper "Interface learning in fluid dynamics: statistical inference of closures within micro-macro coupling models" by Suraj Pawar, Shady E. Ahmed, and Omer San explores a sophisticated approach to handling multiscale and multiphysics problems in fluid dynamics through micro-macro coupling. Traditional methods face significant challenges in these systems due to the discrepancies in scales and variable types between macroscopic and microscopic models. This paper introduces a ML-driven framework for statistically inferring interface closures, specifically addressing the complex interaction between microscale lattice Boltzmann method (LBM) solvers and macroscale finite difference method (FDM) solvers within reaction-diffusion systems.

Methodological Overview

The paper focuses on the integration of LBM and FDM solvers to model reaction-diffusion systems, exemplified by the FitzHugh-Nagumo model. Traditional models utilize domain decomposition techniques that sequentially solve parts of the computational domain, requiring seamless exchange of information across the interfaces to avoid computational discrepancies and ensure solution accuracy. However, deriving analytical closure models for these interfaces is often infeasible due to complex variable interactions and geometries.

The authors propose a neural network-based statistical approach, leveraging data-driven methods to learn the interface closure without necessitating explicit derivation of analytical relations. The framework's flexibility allows it to be applicable across different coupling models, such as RANS-LES or FDM-FVM.

Numerical Experiments

Incorporating computational simulations over a discretized domain, the authors examine the framework's efficacy through comparisons with classical coupling methods. Utilizing a bifidelity setup, wherein the left domain employs the FDM solver while the right domain uses LBM, the results through ML-driven methods are compared against both zeroth-order (CE-0) and first-order Chapman-Enskog expansions (CE-1).

The ML approach yields promising results, notably outperforming CE-0 methods, while the CE-1 approach continues to exhibit superior accuracy due to its numerical approximation's grounding in known analytical relations. However, the ML-based method demonstrates robustness, especially when such analytical solutions are unattainable or complex.

Implications and Future Direction

With roots in interface closure within micro-macro coupling for fluid dynamics, this research sets a precedent for employing ML techniques to overcome multiscale challenges in computational modeling. Practically, this work presents a novel path for addressing complex systems where traditional numerical methods face limitations, particularly in scenarios where obtaining analytical expressions is impractical.

The quintessential implication of this paper lies in its contribution to the evolving landscape of computational fluid dynamics, where AI and ML are increasingly integral to model development and simulation accuracy. By demonstrating meaningful advancements in predictive accuracy and computational efficiency, this framework encourages further exploration and adoption of data-driven methods for interface learning.

Subsequent research might delve into expanding this framework to accommodate higher-dimensional systems, intricate geometric complexities, and multiphysics scenarios, further validating and enhancing the applicability of machine learning techniques in scientific computation.

Conclusion

This paper emphasizes the potential for ML-based solutions to address some of the enduring challenges in fluid dynamics modeling, particularly within micro-macro coupling contexts. Although traditional methods like CE-1 exhibit superior numerical robustness due to their analytical foundations, the flexibility and adaptability demonstrated by ML provide a compelling alternative for complex systems lacking straightforward analytical solutions. As computational capabilities continue to evolve, the integration of AI methodologies in scientific research, as demonstrated by this paper, will likely play an increasingly influential role in shaping the future of engineering simulations and predictive modeling.