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Stochastic reduced order models for inverse problems under uncertainty

机译：不确定条件下反问题的随机降阶模型

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This work presents a novel methodology for solving inverse problems under uncertainty using stochastic reduced order models (SROMs). Given statistical information about an observed state variable in a system, unknown parameters are estimated probabilistically through the solution of a model-constrained, stochastic optimization problem. The point of departure and crux of the proposed framework is the representation of a random quantity using a SROM - a low dimensional, discrete approximation to a continuous random element that permits e cient and non-intrusive stochastic computations. Characterizing the uncertainties with SROMs transforms the stochastic optimization problem into a deterministic one. The non-intrusive nature of SROMs facilitates e cient gradient computations for random vector unknowns and relies entirely on calls to existing deterministic solvers. Furthermore, the method is naturally extended to handle multiple sources of uncertainty in cases where state variable data, system parameters, and boundary conditions are all considered random.The new and widely-applicable SROM framework is formulated for a general stochastic optimization problem in terms of an abstract objective function and constraining model. For demonstration purposes, however, we study its performance in the specific case of inverse identification of random material parameters in elastodynamics. We demonstrate the ability to efficiently recover random shear moduli given material displacement statistics as input data. We also show that the approach remains effective for the case where the loading in the problem is random as well.
机译：这项工作提出了一种新的方法，用于使用随机降阶模型（SROM）解决不确定性下的逆问题。给定有关系统中观察到的状态变量的统计信息，可以通过模型约束的随机优化问题的求解来概率性地估计未知参数。所提出的框架的出发点和症结是使用SROM表示随机量-连续随机元素的低维，离散近似，可以进行高效且非侵入式的随机计算。用SROM表征不确定性会将随机优化问题转化为确定性问题。 SROM的非侵入性质有助于对随机向量未知数进行有效的梯度计算，并且完全依赖于对现有确定性求解器的调用。此外，在状态变量数据，系统参数和边界条件都被认为是随机的情况下，该方法自然可以扩展为处理多种不确定性源。针对普遍的随机优化问题，该新的广泛应用的SROM框架是根据抽象的目标函数和约束模型。但是，出于演示目的，我们研究了在弹性动力学中随机材料参数的逆辨识的特定情况下的性能。我们展示了在给定材料位移统计数据作为输入数据的情况下有效恢复随机剪切模量的能力。我们还表明，该方法对于问题中的负荷也是随机的情况仍然有效。

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