This work presents an efficient approach for accelerating multilevel Markov
Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity
machine learning models. While conventional techniques for large-scale Bayesian
inference often substitute computationally expensive high-fidelity models with
machine learning models, thereby introducing approximation errors, our approach
offers a computationally efficient alternative by augmenting high-fidelity
models with low-fidelity ones within a hierarchical framework. The multilevel
approach utilizes the low-fidelity machine learning model (MLM) for inexpensive
evaluation of proposed samples thereby improving the acceptance of samples by
the high-fidelity model. The hierarchy in our multilevel algorithm is derived
from geometric multigrid hierarchy. We utilize an MLM to acclerate the coarse
level sampling. Training machine learning model for the coarsest level
significantly reduces the computational cost associated with generating
training data and training the model. We present an MCMC algorithm to
accelerate the coarsest level sampling using MLM and account for the
approximation error introduced. We provide theoretical proofs of detailed
balance and demonstrate that our multilevel approach constitutes a consistent
MCMC algorithm. Additionally, we derive conditions on the accuracy of the
machine learning model to facilitate more efficient hierarchical sampling. Our
technique is demonstrated on a standard benchmark inference problem in
groundwater flow, where we estimate the probability density of a quantity of
interest using a four-level MCMC algorithm. Our proposed algorithm accelerates
multilevel sampling by a factor of two while achieving similar accuracy
compared to sampling using the standard multilevel algorithm.

利用多层次马尔可夫链蒙特卡洛 (MCMC) 抽样算法的低保真机器学习模型，本文提出了一种有效的方法来加速大规模问题的抽样。通过在层次结构框架中将高保真模型与低保真模型相结合，我们的方法提供了一种计算高效的替代方案，以改善样本的接受率。我们的技术在地下水流问题中获得了相似的准确性，同时将多层抽样加速了两倍。

利用机器学习模型加速多层级马尔可夫链蒙特卡洛

Accelerating Multilevel Markov Chain Monte Carlo Using Machine Learning  Models

Drawing large graphs appropriately is an important step for the visual
analysis of data from real-world networks. Here we present a novel multilevel
algorithm to compute a graph layout with respect to a recently proposed metric
that combines layout stress and entropy. As opposed to previous work, we do not
solve the linear systems of the maxent-stress metric with a typical numerical
solver. Instead we use a simple local iterative scheme within a multilevel
approach. To accelerate local optimization, we approximate long-range forces
and use shared-memory parallelism. Our experiments validate the high potential
of our approach, which is particularly appealing for dynamic graphs. In
comparison to the previously best maxent-stress optimizer, which is sequential,
our parallel implementation is on average 30 times faster already for static
graphs (and still faster if executed on one thread) while producing a
comparable solution quality.

本文介绍了一种利用多层算法计算基于布局应力和熵的新型度量的图形布局的算法。与以前的工作不同，我们不是用典型的数值求解器解决最大熵 - 应力度量的线性系统，而是在多级方法中使用简单的本地迭代方案。为了加速局部优化，我们近似长程力并使用共享内存并行性。根据实验证明了我们的方法的高潜力，特别适合动态图，与之前最好的最大熵 - 应力优化器相比，我们的并行实施对于静态图像平均快 30 倍，而产生相似的解决方案质量。