For more than a decade, remarkable scientific progress in computational fluid dynamics (CFD) has been achieved via powerful collection of tools for exascale simulations, data-driven approaches, and machine-learning (or statistical learning) techniques that enable efficient simulations of multiscale and multiphysics problems.
With the prospect of exascale simulations in the next decade, it is clear that new flexible tools and specialized algorithms are required to take advantage of such unprecedented computing environment. For example, in the DOE ASCAC subcommittee report, it is stated ``new algorithms will need to be designed to optimize not only for floating-point performance and accuracy, but also to minimize associated data movement, power, and energy cost". Furthermore, robust and fault-resilient algorithms are increasingly attracting attention in exascale simulations against expected and repeated software or hardware error. Hence, new algorithms for exascale simulations inherently require the seamless integration of robustness, resilience, correctness, and efficiency.
Computational fluid dynamics has been developed following different pathways to address for complex flow physics problems. Many researches have focused on building up their own model to describe and address multi-resolution and multi-physics applications. Based on the recent introduction of data-driven algorithms via machine-learning techniques in computer simulations, computational fluid dynamics must rely also on data-driven approaches as much as on the anticipated improvements in computer hardware. In data science, data from various heterogeneous sources can be used effectively to accelerate simulations via multiple fidelity information fusion without additional complex models, equations, and extra state variables. This could result in establishing a new paradigm of multifidelity simulations in computational fluid dynamics.
In this thesis, we address these new requirements for new algorithms in exascale simulations and introduce a novel framework including fault-resilient, robust, and efficient algorithms via multiple fidelity information fusion realized via statistical learning tools. This achievement addresses the new capability that statistical learning techniques can bring to traditional scientific computing algorithms.
This thesis proposes two possible directions of a next generation of computational frameworks for exascale simulations. The first direction addresses resilience via information fusion with auxiliary data. In exascale simulations, if each processor can share some global information about the simulation from a coarse, limited accuracy but relatively costless auxiliary simulator we can effectively fill-in the missing spatial data at the required times by a statistical learning technique based on multi-level Gaussian process regression, on-the-fly. The second direction addresses efficiency via adaptive projective time integration. The aforementioned auxiliary data provide additional information about dynamics-informed timestepping via Diffusion maps, which leads to significant acceleration of CFD simulations.
This thesis also presents and demonstrates methods of a robust nonlinear information fusion with multiple fidelity, multi-scale, parameterized data via manifold-driven regression algorithms. Finally, all multiple fidelity data can be integrated without complex models or equations.
Put simply, ensuring resilience, efficiency will be required for all new algorithm for simulations at the exascale and beyond. Finally, this thesis sets the foundations of a new class of algorithms that will combine traditional CFD with cutting-edge machine learning techniques. Moreover, it integrates physics, mathematics and computer science for exascale simulations.
"Statistical Learning Tools for Information Fusion in Computational Fluid Dynamics"
Applied Mathematics Theses and Dissertations.
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