Computer models play a crucial role in numerous scientific and engineering domains. To ensure the accuracy of simulations, it is essential to properly calibrate the input parameters of these models through statistical inference. While Bayesian inference is the standard approach for this task, employing Markov Chain Monte Carlo methods often encounters computational hurdles due to the costly evaluation of likelihood functions and slow mixing rates. Although variational inference (VI) can be a fast alternative to traditional Bayesian approaches, VI has limited applicability due to boundary issues and local optima problems. To address these challenges, we propose flexible VI methods based on deep generative models that do not require parametric assumptions on the variational distribution. We embed a surjective transformation in our framework to avoid posterior truncation at the boundary. Additionally, we provide theoretical conditions that guarantee the success of the algorithm. Furthermore, our temperature annealing scheme can prevent being trapped in local optima through a series of intermediate posteriors. We apply our method to infectious disease models and a geophysical model, illustrating that the proposed method can provide fast and accurate inference compared to its competitors.

翻译：计算机模型在众多科学与工程领域中发挥着关键作用。为确保模拟的准确性，必须通过统计推断对模型的输入参数进行合理校准。尽管贝叶斯推断是完成该任务的标准方法，但采用马尔可夫链蒙特卡洛方法往往因似然函数计算成本高昂及混合速率缓慢而面临计算瓶颈。虽然变分推断（VI）可作为传统贝叶斯方法的快速替代方案，但由于边界问题与局部最优困境，其适用性受限。为应对这些挑战，我们提出基于深度生成模型的灵活变分推断方法，该方法无需对变分分布进行参数化假设。我们在框架中嵌入满射变换以避免边界处的后验截断，并提供确保算法成功的理论条件。此外，我们的温度退火方案可通过一系列中间后验分布避免陷入局部最优。我们将所提方法应用于传染病模型与地球物理模型中，结果表明，与竞争方法相比，该法能实现快速精准的推断。