Computational models are used in a variety of fields to improve our understanding of complex physical phenomena. Recently, the realism of model predictions has been greatly enhanced by transitioning from deterministic to stochastic frameworks, where the effects of the intrinsic variability in parameters, loads, constitutive properties, model geometry and other quantities can be more naturally included. A general stochastic system may be characterized by a large number of arbitrarily distributed and correlated random inputs, and a limited support response with sharp gradients or event discontinuities. This motivates continued research into novel adaptive algorithms for uncertainty propagation, particularly those handling high dimensional, arbitrarily distributed random inputs and non-smooth stochastic responses. In this work, we generalize a previously proposed multi-resolution approach to uncertainty propagation to develop a method that improves computational efficiency, can handle arbitrarily distributed random inputs and non-smooth stochastic responses, and naturally facilitates adaptivity, i.e., the expansion coefficients encode information on solution refinement. Our approach relies on partitioning the stochastic space into elements that are subdivided along a single dimension, or, in other words, progressive refinements exhibiting a binary tree representation. We also show how these binary refinements are particularly effective in avoiding the exponential increase in the multi-resolution basis cardinality and significantly reduce the regression complexity for moderate to high dimensional random inputs. The performance of the approach is demonstrated through previously proposed uncertainty propagation benchmarks and stochastic multi-scale finite element simulations in cardiovascular flow.

中文翻译：

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应用于心血管建模的不确定性传播的广义多分辨率扩展

计算模型用于各种领域，以提高我们对复杂物理现象的理解。最近，通过从确定性框架过渡到随机框架，模型预测的真实性得到了极大的增强，其中参数、载荷、本构属性、模型几何形状和其他数量的内在可变性的影响可以更自然地包括在内。一般随机系统的特征可能是大量任意分布和相关的随机输入，以及具有陡峭梯度或事件不连续性的有限支持响应。这激发了对用于不确定性传播的新型自适应算法的持续研究，特别是那些处理高维、任意分布的随机输入和非平滑随机响应的算法。在这项工作中，我们将先前提出的不确定性传播的多分辨率方法推广到开发一种提高计算效率的方法，可以处理任意分布的随机输入和非平滑随机响应，并自然地促进适应性，即扩展系数编码关于解决方案细化的信息。我们的方法依赖于将随机空间划分为沿单个维度细分的元素，或者换句话说，呈现出二叉树表示的渐进式细化。我们还展示了这些二元改进如何在避免多分辨率基础基数的指数增长方面特别有效，并显着降低中到高维随机输入的回归复杂性。