Motivated by indirect measurements and applications from nanometrology with a
mixed noise model, we develop a novel algorithm for jointly estimating the
posterior and the noise parameters in Bayesian inverse problems. We propose to
solve the problem by an expectation maximization (EM) algorithm. Based on the
current noise parameters, we learn in the E-step a conditional normalizing flow
that approximates the posterior. In the M-step, we propose to find the noise
parameter updates again by an EM algorithm, which has analytical formulas. We
compare the training of the conditional normalizing flow with the forward and
reverse KL, and show that our model is able to incorporate information from
many measurements, unlike previous approaches.

通过期望最大化算法，我们提出使用条件归一化流来近似后验概率，在贝叶斯逆问题中联合估计后验和噪声参数，应用于间接测量和纳米计量领域，该模型能够整合多种测量信息。

混合噪声和条件深度推理网络的后验估计

Mixed Noise and Posterior Estimation with Conditional DeepGEM

As the global deployment of carbon capture and sequestration (CCS) technology
intensifies in the fight against climate change, it becomes increasingly
imperative to establish robust monitoring and detection mechanisms for
potential underground CO2 leakage, particularly through pre-existing or induced
faults in the storage reservoir's seals. While techniques such as history
matching and time-lapse seismic monitoring of CO2 storage have been used
successfully in tracking the evolution of CO2 plumes in the subsurface, these
methods lack principled approaches to characterize uncertainties related to the
CO2 plumes' behavior. Inclusion of systematic assessment of uncertainties is
essential for risk mitigation for the following reasons: (i) CO2 plume-induced
changes are small and seismic data is noisy; (ii) changes between regular and
irregular (e.g., caused by leakage) flow patterns are small; and (iii) the
reservoir properties that control the flow are strongly heterogeneous and
typically only available as distributions. To arrive at a formulation capable
of inferring flow patterns for regular and irregular flow from well and seismic
data, the performance of conditional normalizing flow will be analyzed on a
series of carefully designed numerical experiments. While the inferences
presented are preliminary in the context of an early CO2 leakage detection
system, the results do indicate that inferences with conditional normalizing
flows can produce high-fidelity estimates for CO2 plumes with or without
leakage. We are also confident that the inferred uncertainty is reasonable
because it correlates well with the observed errors. This uncertainty stems
from noise in the seismic data and from the lack of precise knowledge of the
reservoir's fluid flow properties.

在全球推广碳捕获和封存（CCS）技术以应对气候变化的过程中，建立健全的监测和检测机制以应对潜在的地下 CO2 泄漏，特别是通过储存库密封物的预存在或诱导的断层，变得更加重要。通过历史匹配和时变地震监测等技术已成功跟踪 CO2 在地下的演化过程，但是这些方法缺乏对 CO2 波动行为相关不确定性的原则性方法。为了进行风险缓解，系统评估不确定性是至关重要的，因为：（i）CO2 波动引发的变化很小，地震数据是嘈杂的；（ii）正常和异常（例如泄漏引起的）流动模式之间的变化很小；（iii）控制流动的储层属性很异质且通常只能作为分布信息获得。通过在一系列精心设计的数值实验中分析条件归一化流的性能，可以得出一种能够根据井和地震数据进行正常和异常流动模式推断的公式。尽管这些推断在早期 CO2 泄漏检测系统的背景下还是初步的，但结果表明，条件归一化流可以产生具有或不具有泄漏情况下的 CO2 波动的高精度估计。我们也相信推断的不确定性是合理的，因为它与观察误差很好地相关。这种不确定性源于地震数据中的噪声以及对储层流体流动性的精确知识的缺乏。

CO2 流动模式推断 —— 可行性研究

Inference of CO2 flow patterns -- a feasibility study

Accelerated magnetic resonance (MR) imaging attempts to reduce acquisition
time by collecting data below the Nyquist rate. As an ill-posed inverse
problem, many plausible solutions exist, yet the majority of deep learning
approaches generate only a single solution. We instead focus on sampling from
the posterior distribution, which provides more comprehensive information for
downstream inference tasks. To do this, we design a novel conditional
normalizing flow (CNF) that infers the signal component in the measurement
operator's nullspace, which is later combined with measured data to form
complete images. Using fastMRI brain and knee data, we demonstrate fast
inference and accuracy that surpasses recent posterior sampling techniques for
MRI. Code is available at this https URL

该研究利用一种新型条件归一化流设计，结合采集数据和测量算子的零空间，从后验分布中抽样得到更全面的信息，以达到更快速和精准的磁共振成像。

用于加速多线圈磁共振成像的条件正态流模型

A Conditional Normalizing Flow for Accelerated Multi-Coil MR Imaging

Model independent techniques for constructing background data templates using
generative models have shown great promise for use in searches for new physics
processes at the LHC. We introduce a major improvement to the CURTAINs method
by training the conditional normalizing flow between two side-band regions
using maximum likelihood estimation instead of an optimal transport loss. The
new training objective improves the robustness and fidelity of the transformed
data and is much faster and easier to train.
We compare the performance against the previous approach and the current
state of the art using the LHC Olympics anomaly detection dataset, where we see
a significant improvement in sensitivity over the original CURTAINs method.
Furthermore, CURTAINsF4F requires substantially less computational resources to
cover a large number of signal regions than other fully data driven approaches.
When using an efficient configuration, an order of magnitude more models can be
trained in the same time required for ten signal regions, without a significant
drop in performance.

本文提出了一种新的方法来构建背景数据模板，通过最大似然估计训练两个侧带区域之间的条件归一化流，可用于在 LHC 中搜索新物理过程。该方法比之前的方法更具鲁棒性和准确性。