Distribution shifts, where statistical properties differ between training and test datasets, present a significant challenge in real-world machine learning applications where they directly impact model generalization and robustness. In this study, we explore model adaptation and generalization by utilizing synthetic data to systematically address distributional disparities. Our investigation aims to identify the prerequisites for successful model adaptation across diverse data distributions, while quantifying the associated uncertainties. Specifically, we generate synthetic data using the Van der Waals equation for gases and employ quantitative measures such as Kullback-Leibler divergence, Jensen-Shannon distance, and Mahalanobis distance to assess data similarity. These metrics en able us to evaluate both model accuracy and quantify the associated uncertainty in predictions arising from data distribution shifts. Our findings suggest that utilizing statistical measures, such as the Mahalanobis distance, to determine whether model predictions fall within the low-error "interpolation regime" or the high-error "extrapolation regime" provides a complementary method for assessing distribution shift and model uncertainty. These insights hold significant value for enhancing model robustness and generalization, essential for the successful deployment of machine learning applications in real-world scenarios.

翻译：分布偏移（即训练数据集与测试数据集之间的统计特性差异）对真实世界机器学习应用构成重大挑战，直接影响模型泛化能力与鲁棒性。本研究通过利用合成数据系统性地处理分布差异，探索模型自适应与泛化问题。我们的研究旨在识别跨不同数据分布实现成功模型自适应的先决条件，同时量化相关不确定性。具体而言，我们使用范德瓦尔斯方程生成合成数据，并采用Kullback-Leibler散度、Jensen-Shannon距离及马氏距离等定量指标评估数据相似性。这些度量使我们能够评估模型精度，同时量化因数据分布偏移导致的预测不确定性。研究结果表明，利用马氏距离等统计指标判断模型预测属于低误差"插值区域"或高误差"外推区域"，为评估分布偏移与模型不确定性提供了互补方法。这些发现对增强模型鲁棒性与泛化能力具有重要价值，是机器学习应用在真实场景中成功部署的关键。