Predictions for physical systems often rely upon knowledge acquired from ensembles of entities, e.g., ensembles of cells in biological sciences. For qualitative and quantitative analysis, these ensembles are simulated with parametric families of mechanistic models (MM). Two classes of methodologies, based on Bayesian inference and Population of Models, currently prevail in parameter estimation for physical systems. However, in Bayesian analysis, uninformative priors for MM parameters introduce undesirable bias. Here, we propose how to infer parameters within the framework of stochastic inverse problems (SIP), also termed data-consistent inversion, wherein the prior targets only uncertainties that arise due to MM non-invertibility. To demonstrate, we introduce new methods to solve SIP based on rejection sampling, Markov chain Monte Carlo, and generative adversarial networks (GANs). In addition, to overcome limitations of SIP, we reformulate SIP based on constrained optimization and present a novel GAN to solve the constrained optimization problem.

翻译：物理系统的预测通常依赖于对实体集合（例如生物学中的细胞群体）所获取的知识。为进行定性与定量分析，这些集合通过参数化机理模型族进行模拟。当前，基于贝叶斯推断和群体模型的两类方法在物理系统的参数估计中占据主导地位。然而，在贝叶斯分析中，机理模型参数的无信息先验会引入不良偏倚。本文提出如何在随机逆问题框架（亦称数据一致性反演）中推断参数，该框架中的先验仅针对由机理模型不可逆性引起的不确定性。为验证该框架，我们引入了基于拒绝采样、马尔可夫链蒙特卡罗和生成对抗网络的新方法来解决随机逆问题。此外，为克服随机逆问题的局限性，我们基于约束优化重新构建了随机逆问题，并提出了一种新型生成对抗网络来求解该约束优化问题。