We propose a neural operator framework, termed mixture density nonlinear
manifold decoder (MD-NOMAD), for stochastic simulators. Our approach leverages
an amalgamation of the pointwise operator learning neural architecture
nonlinear manifold decoder (NOMAD) with mixture density-based methods to
estimate conditional probability distributions for stochastic output functions.
MD-NOMAD harnesses the ability of probabilistic mixture models to estimate
complex probability and the high-dimensional scalability of pointwise neural
operator NOMAD. We conduct empirical assessments on a wide array of stochastic
ordinary and partial differential equations and present the corresponding
results, which highlight the performance of the proposed framework.

我们提出了一种神经算子框架，称为混合密度非线性流形解码器（MD-NOMAD），用于随机模拟器。我们的方法利用了点对点算子学习神经结构非线性流形解码器（NOMAD）与基于混合密度的方法的融合，用于估计随机输出函数的条件概率分布。MD-NOMAD 利用概率混合模型估计复杂概率和点对点神经算子 NOMAD 的高维扩展性。我们对广泛的随机常微分方程和偏微分方程进行了实证评估，并展示了相应的结果，突出了该框架的性能。

MD-NOMAD: 混合密度非线性流形解码器用于模拟随机微分方程和不确定性传播

MD-NOMAD: Mixture density nonlinear manifold decoder for emulating  stochastic differential equations and uncertainty propagation

How can one perform Bayesian inference on stochastic simulators with
intractable likelihoods? A recent approach is to learn the posterior from
adaptively proposed simulations using neural network-based conditional density
estimators. However, existing methods are limited to a narrow range of proposal
distributions or require importance weighting that can limit performance in
practice. Here we present automatic posterior transformation (APT), a new
sequential neural posterior estimation method for simulation-based inference.
APT can modify the posterior estimate using arbitrary, dynamically updated
proposals, and is compatible with powerful flow-based density estimators. It is
more flexible, scalable and efficient than previous simulation-based inference
techniques. APT can operate directly on high-dimensional time series and image
data, opening up new applications for likelihood-free inference.

提出了一种新的基于神经网络的自适应后验变换方法，APT 可以用任意动态更新的提议来修改后验估计，采用流形密度估计器，具有更高的灵活性、可伸缩性和效率，并能直接处理高维时间序列和图像数据，并可开展无似然推断。