Bayesian Uncertainty Quantification for Microfluidics: Assessing and Improving the Reliability of Reduced-Order Models and Sample Detection Schemes

微流体处理非常小的流体体积和几何形状，并实现了有前途的应用，包括药物发现的芯片实验室和医学中的液体注入表面（LIS）。然而，测量数据和数学模型中的不确定性，以及得出的结论和决定，往往没有统计量化。在贝叶斯不确定性量化（UQ）中，数据和模型是系统集成的。它在包括天气和选举预测在内的广泛领域显示出巨大的潜力。不幸的是，它仍然很少应用于微流体。因此，该项目的目标是表明贝叶斯UQ为涉及微流体的研究和应用提供了巨大的好处，并且即使对于复杂的物理现象也是实际和计算上可行的。因此，采用两个有趣且相关的小尺度流体力学测试案例，一个基础研究案例和一个应用案例，将复杂的贝叶斯方法应用于微流体实验中嘈杂和不确定的数据。在第一种情况下，将开发振动表面上液体薄膜中孔动力学的预测降阶模型，并使用贝叶斯模型比较进行定量评估。所得到的模型将增强我们对空穴动力学的理解，并有助于LIS的设计。在第二种情况下，将开发一种从微通道中通过等速电泳传输的噪声测量数据中检测低浓度样品的自动化方案。一个复杂的探测器将与贝叶斯统计相结合，以便在不确定的情况下做出可追溯和透明的决定。因此，这将允许微流体检测方案的自动化使用，例如在医疗诊断或高通量筛选应用中。为了使其他研究人员能够迅速将贝叶斯UQ的应用方法转移到他们具体的微流体问题和应用中，将提供教程案例和概念证明。这个高度跨学科的项目结合了流体动力学实验，数学建模和贝叶斯统计，为微流体问题提供新颖可靠的答案。这个项目的结果可能会允许贝叶斯UQ的更复杂的应用。例如，一个有趣的问题是对复杂微流体的基于物理的模型和数据驱动的模型或机器学习模型进行定量比较和组合。贝叶斯UQ的方法将在本项目中应用，为今后的研究提供坚实的基础。

Microfluidics deals with very small fluid volumes and geometries and enables promising applications including lab-on-a-chips for drug discovery and liquid-infused surfaces (LIS) in medicine. Often however, the uncertainty in the measurement data and mathematical models, as well as the drawn conclusions and decisions, are not statistically quantified. In Bayesian uncertainty quantification (UQ), data and models are systematically integrated. It has demonstrated tremendous potential in a broad range including weather and election prediction. Unfortunately, it is still seldom applied in microfluidics.The goal of this project is therefore to show that Bayesian UQ offers a great benefit for research and applications involving microfluidics, and is practically and computationally feasible even for complex physical phenomena. Therefore, two interesting and relevant test cases involving small scale fluid mechanics, one basic research and one application case, are used to apply sophisticated Bayesian methods to noisy and uncertain data from microfluidic experiments. In the first case, a predictive reduced-order model for the dynamics of holes in thin liquid films on vibrating surfaces will be developed and quantitatively assessed using Bayesian model comparison. The resulting model will enhance our understanding of the hole dynamics and help in the design of LIS. In the second case, an automatized detection scheme for samples at low concentration from noisy measurement data in microchannels transported via isotachophoresis will be developed. A sophisticated detector will be integrated with Bayesian statistics to allow for traceable and transparent decisions under uncertainty. Consequently, this then will allow the automatized usage of microfluidic detection schemes, for example in medical diagnostics or high-throughput screening applications. To allow other researchers to rapidly transfer the applied methods of Bayesian UQ to their specific microfluidic problems and applications, tutorial cases as well as proof-of-concepts will be provided. This highly interdisciplinary project combines fluid dynamic experiments, mathematical modeling, and Bayesian statistics to provide novel and reliable answers to microfluidic problems. The results of this project might allow for even more involved applications of Bayesian UQ. For example, one interesting question would be to quantitatively compare, and combine, physic-based models and data-driven or machine learning models for complex microfluidics. Methods from Bayesian UQ, as will be applied in this project, provide a solid foundation for this future research.