用在线学习加速多相流模拟，减少85%计算时间
Online learning to accelerate nonlinear PDE solvers: applied to multiphase porous media flow
- 用无量纲参数作输入，动态调节松弛因子优化求解
- 在三维真实模型中实现非线性迭代次数显著减少
- 可嵌入开源模拟器，适合大规模地质模拟场景
我们提出一种基于在线/自适应学习的非线性偏微分方程求解加速方法，应用于多相渗流问题。该方法依托四大支柱：(i) 以无量纲数作为机器学习模型输入；(ii) 采用二维简化数值模型进行离线训练；(iii) 动态调控非线性求解器的松弛参数；(iv) 在线学习实时优化模型。该策略通过动态调整单一全局参数——松弛因子，并实时自适应学习各数值模型特征，显著减少非线性迭代次数。此外，本研究对无量纲参数（机器学习特征）进行了敏感性分析，评估了多种机器学习模型的效果，在更复杂的三维真实模型中验证了该方法的有效性，并成功将机器学习模型完全集成至开源多相流模拟器，实现了最高达85%的计算时间降低。
原文摘要 · Abstract (English)
We propose a novel type of nonlinear solver acceleration for systems of nonlinear partial differential equations (PDEs) that is based on online/adaptive learning. It is applied in the context of multiphase flow in porous media. The proposed method rely on four pillars: (i) dimensionless numbers as input parameters for the machine learning model, (ii) simplified numerical model (two-dimensional) for the offline training, (iii) dynamic control of a nonlinear solver tuning parameter (numerical relaxation), (iv) and online learning for real-time improvement of the machine learning model. This strategy decreases the number of nonlinear iterations by dynamically modifying a single global parameter, the relaxation factor, and by adaptively learning the attributes of each numerical model on-the-run. Furthermore, this work performs a sensitivity study in the dimensionless parameters (machine learning features), assess the efficacy of various machine learning models, demonstrate a decrease in nonlinear iterations using our method in more intricate, realistic three-dimensional models, and fully couple a machine learning model into an open-source multiphase flow simulator achieving up to 85\% reduction in computational time.
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