{"title":"Leveraging neural networks to estimate parameters with confidence intervals","authors":"Nigel Mathias, Lauren Weir, Brandon Corbett, Prashant Mhaskar","doi":"10.1002/cjce.25438","DOIUrl":null,"url":null,"abstract":"<p>This manuscript presents a proof of concept for the estimation of parameters in a bioprocess while providing reliable confidence intervals. Specifically, Bayesian inference is used to estimate the uncertainty in the prediction of a parameter due to the presence of measurement noise in the process. The resultant joint probability distribution is utilized to infer the confidence interval of the resultant estimates. This method is numerically applied using a technique known as nested sampling. This algorithm iteratively samples parameters from a pre-determined range of values to compare model predictions and obtain a probability density function. One challenge typically associated with this algorithm is in the determination of the prediction error, especially when a high-fidelity dynamic model is being utilized. For the motivating example in the present manuscript, where a high-fidelity simulated bioprocess is being considered, the use of the high-fidelity model provided by Sartorius AG as part of the estimation algorithm poses computational challenges. To overcome this challenge, a universal approximator such as a parameterized neural network is used. This neural network is designed to simulate the results of the first principles model (while also capturing the dependence of the model parameters on the output), and once trained can provide near instantaneous results making the use of nested sampling computationally tractable for the application. Simulation results demonstrate the feasibility and capability of the proposed approach.</p>","PeriodicalId":9400,"journal":{"name":"Canadian Journal of Chemical Engineering","volume":"103 2","pages":"666-678"},"PeriodicalIF":1.6000,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cjce.25438","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Canadian Journal of Chemical Engineering","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/cjce.25438","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, CHEMICAL","Score":null,"Total":0}
引用次数: 0
Abstract
This manuscript presents a proof of concept for the estimation of parameters in a bioprocess while providing reliable confidence intervals. Specifically, Bayesian inference is used to estimate the uncertainty in the prediction of a parameter due to the presence of measurement noise in the process. The resultant joint probability distribution is utilized to infer the confidence interval of the resultant estimates. This method is numerically applied using a technique known as nested sampling. This algorithm iteratively samples parameters from a pre-determined range of values to compare model predictions and obtain a probability density function. One challenge typically associated with this algorithm is in the determination of the prediction error, especially when a high-fidelity dynamic model is being utilized. For the motivating example in the present manuscript, where a high-fidelity simulated bioprocess is being considered, the use of the high-fidelity model provided by Sartorius AG as part of the estimation algorithm poses computational challenges. To overcome this challenge, a universal approximator such as a parameterized neural network is used. This neural network is designed to simulate the results of the first principles model (while also capturing the dependence of the model parameters on the output), and once trained can provide near instantaneous results making the use of nested sampling computationally tractable for the application. Simulation results demonstrate the feasibility and capability of the proposed approach.
本手稿提出了一个概念验证,用于估算生物过程中的参数,同时提供可靠的置信区间。具体来说,贝叶斯推理用于估算由于过程中存在测量噪声而导致的参数预测不确定性。利用由此产生的联合概率分布来推断结果估计值的置信区间。这种方法使用一种称为嵌套采样的技术进行数值计算。该算法从预先确定的数值范围内反复采样参数,以比较模型预测值并获得概率密度函数。这种算法通常面临的一个挑战是如何确定预测误差,尤其是在使用高保真动态模型时。在本手稿的激励性示例中,考虑了高保真模拟生物过程,使用 Sartorius AG 提供的高保真模型作为估算算法的一部分带来了计算上的挑战。为了克服这一挑战,我们使用了参数化神经网络等通用近似器。这种神经网络旨在模拟第一原理模型的结果(同时还能捕捉模型参数对输出的依赖性),一旦经过训练,就能提供近乎瞬时的结果,从而使嵌套采样的应用在计算上变得简单易行。仿真结果证明了所提方法的可行性和能力。
期刊介绍:
The Canadian Journal of Chemical Engineering (CJChE) publishes original research articles, new theoretical interpretation or experimental findings and critical reviews in the science or industrial practice of chemical and biochemical processes. Preference is given to papers having a clearly indicated scope and applicability in any of the following areas: Fluid mechanics, heat and mass transfer, multiphase flows, separations processes, thermodynamics, process systems engineering, reactors and reaction kinetics, catalysis, interfacial phenomena, electrochemical phenomena, bioengineering, minerals processing and natural products and environmental and energy engineering. Papers that merely describe or present a conventional or routine analysis of existing processes will not be considered.