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首页> 外文期刊>Journal of Computational Physics >Sampling-free linear Bayesian update of polynomial chaos representations
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Sampling-free linear Bayesian update of polynomial chaos representations

机译：多项式混沌表示的无采样线性贝叶斯更新

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摘要

We present a fully deterministic approach to a probabilistic interpretation of inverse problems in which unknown quantities are represented by random fields or processes, described by possibly non-Gaussian distributions. The description of the introduced random fields is given in a " white noise" framework, which enables us to solve the stochastic forward problem through Galerkin projection onto polynomial chaos. With the help of such a representation the probabilistic identification problem is cast in a polynomial chaos expansion setting and the Baye's linear form of updating. By introducing the Hermite algebra this becomes a direct, purely algebraic way of computing the posterior, which is comparatively inexpensive to evaluate. In addition, we show that the well-known Kalman filter is the low order part of this update. The proposed method is here tested on a stationary diffusion equation with prescribed source terms, characterised by an uncertain conductivity parameter which is then identified from limited and noisy data obtained by a measurement of the diffusing quantity.
机译：我们为逆问题的概率解释提供了一种完全确定性的方法，其中未知数量由随机字段或过程表示，可能由非高斯分布描述。引入的随机场的描述在“白噪声”框架中给出，这使我们能够通过将Galerkin投影到多项式混沌上来解决随机正向问题。在这种表示的帮助下，概率识别问题被引入多项式混沌扩展设置和贝叶斯线性更新形式中。通过引入Hermite代数，这成为计算后验的直接，纯代数方式，评估起来相对便宜。此外，我们证明了众所周知的卡尔曼滤波器是此更新的低阶部分。在规定的源项下，在固定的扩散方程上测试提出的方法，该方程的特征是不确定的电导率参数，然后从通过测量扩散量获得的有限且有噪声的数据中识别出来。

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