平衡噪声的多级即时稀疏网格代理用于将蒙特卡洛模型耦合到连续模型中，应用于异质催化
Noise-balanced multilevel on-the-fly sparse grid surrogates for coupling Monte Carlo models into continuum models with application to heterogeneous catalysis
AI总结：
本文提出一种平衡噪声的多级即时稀疏网格代理方法，用于将微观蒙特卡洛模型与宏观连续模型耦合，应用于异质催化中的多尺度模拟。
摘要：
利用高保真度、微观蒙特卡洛模型为连续模型提供非线性响应的多尺度模拟很容易变得计算上不可行。为高保真度蒙特卡洛模型构建代理模型可以解决这个问题，但会带来一些挑战。其中一个挑战是底层蒙特卡洛数据中的采样噪声，这会导致不可控的误差，可能污染代理模型，尽管在无噪声数据的情况下，代理模型可能非常准确。另一个挑战是当响应依赖于许多宏观变量时出现的“维度灾难”。这些问题通过一种新颖的平衡噪声稀疏网格插值方法得到解决，该方法以近似最优的方式控制每个数据点的蒙特卡洛采样量。该方法还通过多级即时构造来补充多尺度模拟。除了其效率外，特别吸引人的是该方法的易用性，仅需一个超参数控制整个代理模型的构建——从代理的准确性保证收敛到需要创建哪些数据以及以何种准确性创建。该方法在异质催化中进行了挑战性示例的演示，将微观的速率蒙特卡洛模型耦合到宏观反应器模拟中。
英文摘要：
Multiscale simulations utilizing high-fidelity, microscopic Monte Carlo models to provide the nonlinear response for continuum models can easily become computationally intractable. Surrogate models for the high-fidelity Monte Carlo models can overcome this but come with some challenges. One such challenges arise by the sampling noise in the underlying Monte Carlo data, which leads to uncontrolled errors possibly corrupting the surrogate even though it would be highly accurate in the case of noise-free data. Another challenge arises by the 'curse of dimensionality' when the response depends on many macro-variables. These points are addressed by a novel noise-balanced sparse grids interpolation approach which, in a quasi-optimal fashion, controls the amount of Monte Carlo sampling for each data point. The approach is complemented by a multilevel on-the-fly construction during the multiscale simulation. Besides its efficiency, a particularly appealing feature is the ease of use of the approach with only a single hyperparameter controlling the whole surrogate construction - from the surrogate's accuracy with guaranteed convergence to which data needs to be created with which accuracy. The approach is demonstrated on challenging examples from heterogeneous catalysis, coupling microscopic kinetic Monte Carlo models into macroscopic reactor simulations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
