Pub Date : 2022-01-01DOI: 10.1007/s40314-022-01769-7
Anusha Vulimiri, Sireesha Veeramachaneni
{"title":"Einstein Heronian mean aggregation operator and its application in decision making problems","authors":"Anusha Vulimiri, Sireesha Veeramachaneni","doi":"10.1007/s40314-022-01769-7","DOIUrl":"https://doi.org/10.1007/s40314-022-01769-7","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79389148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-26DOI: 10.1007/s40314-021-01731-z
Swapnil Kale, D. Pradhan
{"title":"Error estimates of fictitious domain method with an $$H^1$$ penalty approach for elliptic problems","authors":"Swapnil Kale, D. Pradhan","doi":"10.1007/s40314-021-01731-z","DOIUrl":"https://doi.org/10.1007/s40314-021-01731-z","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77549450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
N. T. Mücke, B. Sanderse, Sander M. Boht'e, C. Oosterlee
In the context of solving inverse problems for physics applications within a Bayesian framework, we present a new approach, Markov Chain Generative Adversarial Neural Networks (MCGANs), to alleviate the computational costs associated with solving the Bayesian inference problem. GANs pose a very suitable framework to aid in the solution of Bayesian inference problems, as they are designed to generate samples from complicated high-dimensional distributions. By training a GAN to sample from a low-dimensional latent space and then embedding it in a Markov Chain Monte Carlo method, we can highly efficiently sample from the posterior, by replacing both the high-dimensional prior and the expensive forward map. We prove that the proposed methodology converges to the true posterior in the Wasserstein-1 distance and that sampling from the latent space is equivalent to sampling in the high-dimensional space in a weak sense. The method is showcased on two test cases where we perform both state and parameter estimation simultaneously. The approach is shown to be up to two orders of magnitude more accurate than alternative approaches while also being up to two orders of magnitude computationally faster, in multiple test cases, including the important engineering setting of detecting leaks in pipelines.
{"title":"Markov Chain Generative Adversarial Neural Networks for Solving Bayesian Inverse Problems in Physics Applications","authors":"N. T. Mücke, B. Sanderse, Sander M. Boht'e, C. Oosterlee","doi":"10.2139/ssrn.3991779","DOIUrl":"https://doi.org/10.2139/ssrn.3991779","url":null,"abstract":"In the context of solving inverse problems for physics applications within a Bayesian framework, we present a new approach, Markov Chain Generative Adversarial Neural Networks (MCGANs), to alleviate the computational costs associated with solving the Bayesian inference problem. GANs pose a very suitable framework to aid in the solution of Bayesian inference problems, as they are designed to generate samples from complicated high-dimensional distributions. By training a GAN to sample from a low-dimensional latent space and then embedding it in a Markov Chain Monte Carlo method, we can highly efficiently sample from the posterior, by replacing both the high-dimensional prior and the expensive forward map. We prove that the proposed methodology converges to the true posterior in the Wasserstein-1 distance and that sampling from the latent space is equivalent to sampling in the high-dimensional space in a weak sense. The method is showcased on two test cases where we perform both state and parameter estimation simultaneously. The approach is shown to be up to two orders of magnitude more accurate than alternative approaches while also being up to two orders of magnitude computationally faster, in multiple test cases, including the important engineering setting of detecting leaks in pipelines.","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74783616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-09DOI: 10.1007/s40314-021-01682-5
R. Manohar, R. K. Sinha
{"title":"A posteriori $$L^{infty }(L^{infty })$$-error estimates for finite-element approximations to parabolic optimal control problems","authors":"R. Manohar, R. K. Sinha","doi":"10.1007/s40314-021-01682-5","DOIUrl":"https://doi.org/10.1007/s40314-021-01682-5","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81471693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-06DOI: 10.1007/s40314-021-01679-0
A. Chanda, Hiranmoy Garai, L. Dey, V. Rakočević, T. Senapati
{"title":"$$(psi , phi )$$-Wardowski contraction pairs and some applications","authors":"A. Chanda, Hiranmoy Garai, L. Dey, V. Rakočević, T. Senapati","doi":"10.1007/s40314-021-01679-0","DOIUrl":"https://doi.org/10.1007/s40314-021-01679-0","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89715655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-26DOI: 10.1007/s40314-021-01625-0
T. Su, D. Hang
{"title":"Second-order optimality conditions for efficiency in $$C^{1, 1}$$-smooth quasiconvex multiobjective programming problem","authors":"T. Su, D. Hang","doi":"10.1007/s40314-021-01625-0","DOIUrl":"https://doi.org/10.1007/s40314-021-01625-0","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86132385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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