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The Tandem Neural Network Architecture (TNNA) algorithm was an inversion framework through reverse mapping. Its reliability strongly depended on accurate surrogate modeling within the true posterior region of parameters. For reactive transport problems, establishing a globally accurate surrogate model required a large number of numerical model samples, which considerably limited the efficiency of inversion processes. To address this challenge, the TNNA-AUS-MF inversion method was proposed, in which the original TNNA was integrated with a multi-fidelity (MF) surrogate model and an adaptive updating sampling (AUS) strategy. In this method, multi-fidelity surrogate models were iteratively established based on the conventional TNNA and local samples to update the inversion results. The proposed algorithm was validated using a hypothetical cation-exchange experiment. By controlling the number of initial surrogate model samples, six scenarios with different initial surrogate model accuracies were designed. The results showed that the TNNA-AUS-MF significantly reduced the number of forward simulations while yielding more reliable inversion results compared with the TNNA method. Furthermore, it was demonstrated that the neural network could establish nonlinear relationships between low- and high-fidelity models, and that incorporating the adaptive updating sampling strategy effectively enhanced the performance of the inversion algorithm.

, authors=Jun-jun CHEN¹, Zhen-xue DAI^{2, *}, authorsList=Jun-jun CHEN, Zhen-xue DAI, authorCompany=null, correspAuthors=Zhen-xue DAI, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1314922112045904044, articleId=1314922111450312874, tenantId=1146029695717560320, journalId=1234093305789726721, language=CN, title=基于改进串联式神经网络的反应性溶质运移参数反演研究, columnId=1234106386565624579, journalTitle=中国环境科学, columnName=水污染与控制, runingTitle=null, highlight=null, articleAbstract=

串联式神经网络（TNNA）是一种通过逆向建模实现参数反演的算法框架，其可靠性高度依赖于替代模型在参数真实后验分布区域的预测精度．对于反应性溶质运移问题，构建高精度的全局替代模型通常需要大量样本数据，在一定程度上限制了反演计算效率．为此，本研究提出了一种基于多保真度（MF）替代模型自适应更新策略（AUS）的TNNA反演算法（TNNA-AUS-MF）．该方法在传统TNNA算法的基础上，通过反演结果引导的局部采样建立多保真度替代模型，并在迭代过程中逐步更新模型参数反演结果．算法验证基于一个假想的阳离子交换实验开展．通过控制初始替代模型样本数目，设计了6种不同初始替代模型精度的反演计算场景．结果表明，TNNA-AUS-MF算法相比于TNNA算法，能够显著减少正演模拟调用次数并改善反演结果．此外，少样本场景的研究结果验证了利用神经网络构建低保真和高保真模型间非线性关系的可行性，并表明结合自适应更新采样策略能够有效提升反演算法性能．

, authors=陈骏骏¹, 戴振学^{2, *}, authorsList=陈骏骏, 戴振学, authorCompany=null, correspAuthors=戴振学, authorNote=, correspAuthorsNote=, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=aMvBFAoQSDrCK9IVspQzYw==, magXml=kSwWoleToH+tI0TwfYgPnA==, pdfUrl=null, pdf=d0jRHPfhjdWSVFV68sh14g==, pdfFileSize=2324272, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=+fbHFsofvksu/9z2iCR7HQ==, mapNumber=null, fund=null)}, authors=[Author(id=1314922113853649076, tenantId=1146029695717560320, journalId=1234093305789726721, articleId=1314922111450312874, orderNo=0, firstName=null, middleName=null, lastName=null, nameCn=null, orcid=null, stid=null, country=null, authorPic=null, dead=0, email=junjunchen@cumt.edu.cn, emailSecond=null, emailThird=null, correspondingAuthor=0, authorType=1, ext={EN=AuthorExt(id=1314922113937535158, tenantId=1146029695717560320, journalId=1234093305789726721, articleId=1314922111450312874, authorId=1314922113853649076, language=EN, stringName=Jun-jun CHEN, firstName=Jun-jun, middleName=null, lastName=CHEN, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=¹, address=^1.National and Local Joint Engineering Laboratory of Internet Application Technology on Mine, China University of Mining and Technology, Xuzhou 221008, China, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null), CN=AuthorExt(id=1314922114063364279, tenantId=1146029695717560320, journalId=1234093305789726721, articleId=1314922111450312874, authorId=1314922113853649076, language=CN, stringName=陈骏骏, firstName=null, middleName=null, lastName=null, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=¹, address=^1.中国矿业大学矿山互联网应用技术国家地方联合工程实验室，江苏 徐州 221008, bio={"content":"

陈骏骏（1990-），男，浙江东阳人，副教授，博士，主要从事地下水模型参数反演算法研究．发表论文20余篇．junjunchen@cumt.edu.cn.

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陈骏骏（1990-），男，浙江东阳人，副教授，博士，主要从事地下水模型参数反演算法研究．发表论文20余篇．junjunchen@cumt.edu.cn.

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