In a fissile material, the inherent multiplicity of neutrons born through induced fissions leads to correlations in their detection statistics. The correlations between neutrons can be used to trace back some characteristics of the fissile material. This technique known as neutron noise analysis has applications in nuclear safeguards or waste identification. It provides a non-destructive examination method for an unknown fissile material. This is an example of an inverse problem where the cause is inferred from observations of the consequences. However, neutron correlation measurements are often noisy because of the stochastic nature of the underlying processes. This makes the resolution of the inverse problem more complex since the measurements are strongly dependent on the material characteristics. A minor change in the material properties can lead to very different outputs. Such an inverse problem is said to be ill-posed. For an ill-posed inverse problem the inverse uncertainty quantification is crucial. Indeed, seemingly low noise in the data can lead to strong uncertainties in the estimation of the material properties. Moreover, the analytical framework commonly used to describe neutron correlations relies on strong physical assumptions and is thus inherently biased. This paper addresses dual goals. Firstly, surrogate models are used to improve neutron correlations predictions and quantify the errors on those predictions. Then, the inverse uncertainty quantification is performed to include the impact of measurement error alongside the residual model bias.

本文重点介绍了具有高输出方差的随机模拟器的多目标优化，其中输入空间是有限的，并且目标函数的评估昂贵。我们依靠贝叶斯优化算法，这些算法使用概率模型来对要优化的功能进行预测。所提出的方法是用于估计帕累托最佳溶液的帕累托主动学习（PAL）算法的扩展，该算法使其适合随机环境。我们将其命名为随机模拟器（PAL）的Pareto主动学习。通过数值实验对一组双维，双目标测试问题进行数值实验评估了PAL的表现。与其他基于标量的和随机搜索的方法相比，PAL表现出卓越的性能。

本文侧重于异步八卦协议中的非渐近扩散时间。异步八卦协议被设计为通过随机交换相关图中的消息来在节点网络中执行分布式计算。为了在节点之间实现共识，必须更新最少数量的消息。我们为常规案例提供了与此类数量的概率。我们为完全连接的图表提供了一个明确的公式，其仅根据节点的数量和任何图表的近似，这取决于图形的频谱。

本文介绍了复数几何形状中变换扩散过程的数值模拟的通用框架。这项工作遵循了在微观尺度下对多孔系统中有机物微生物降解的微生物降解模拟的先前。我们显着地推广并改善了马赛克方法，从而产生了更通用和有效的数值模拟方案。特别地，关于从图中的扩散过程的模拟，在该研究中，我们提出了一种完全明确的半隐式数值方案，可以显着降低计算复杂性。我们通过将结果与经典格子Boltzmann方法（LBM）提供的结果进行比较来验证了我们的方法。对于相同的数据集，我们在比前的工作（几个小时）上的计算时间（即，10-15分钟）中获得了类似的结果。除了经典的LBM方法需要大约3周的计算时间。