A resilient and efficient CFD framework: Statistical learning tools for multi-fidelity and heterogeneous information fusion

JOURNAL OF COMPUTATIONAL PHYSICS

卷:344

Article

Lee, Seungjoon¹  Kevrekidis, Ioannis G.^2,3  Karniadakis, George Em¹ 

[1] Brown Univ, Div Appl Math, Providence, RI 02912 USA

[2] Princeton Univ, Dept Chem & Biol Engn, Princeton, NJ 08544 USA

[3] Princeton Univ, PACM, Princeton, NJ 08544 USA

关键词: Gappy data;    Patch dynamics;    Machine learning;    Domain decomposition;    Exascale simulation;    Gaussian process regression;    Diffusion maps;   

DOI  :  10.1016/j.jcp.2017.05.021

来源: Elsevier

【 摘 要 】

Exascale-level simulations require fault-resilient algorithms that are robust against repeated and expected software and/or hardware failures during computations, which may render the simulation results unsatisfactory. 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 - multi-level Gaussian process regression, on the fly; this has been demonstrated in previous work [1]. Based on the previous work, we also employ another (nonlinear) statistical learning technique, Diffusion Maps, that detects computational redundancy in time and hence accelerate the simulation by projectivetime integration, giving the overall computation a patch dynamics flavor. Furthermore, we are now able to perform information fusion with multi-fidelity and heterogeneous data (including stochastic data). Finally, we set the foundations of a new framework in CFD, called patch simulation, that combines information fusion techniques from, in principle, multiple fidelity and resolution simulations (and even experiments) with a new adaptive timestep refinement technique. We present two benchmark problems (the heat equation and the Navier-Stokes equations) to demonstrate the new capability that statistical learning tools can bring to traditional scientific computing algorithms. For each problem, we rely on heterogeneous and multi-fidelity data, either from a coarse simulation of the same equation or from a stochastic, particle-based, more microscopic simulation. We consider, as such auxiliary models, a Monte Carlo random walk for the heat equation and a dissipative particle dynamics (DPD) model for the Navier-Stokes equations. More broadly, in this paper we demonstrate the symbiotic and synergistic combination of statistical learning, domain decomposition, and scientific computing in exascale simulations. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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