{"title":"Constrained Gaussian process regression: an adaptive approach for the estimation of hyperparameters and the verification of constraints with high probability","authors":"G. Perrin, S. Veiga","doi":"10.1615/jmachlearnmodelcomput.2021039837","DOIUrl":"https://doi.org/10.1615/jmachlearnmodelcomput.2021039837","url":null,"abstract":"This paper focuses on the Gaussian Process regression (GPR) of non-linear functions subject to multiple linear constraints, such as boundedness, monotonicity or convexity. It presents an algorithm allowing to optimize, in a concerted way, the statistical moments of the Gaussian process used for the regression, and the position of a reduced number of points where the constraints are required to hold, such that the constraints are verified in the whole input space, with high probability, at a reasonable computational cost. After having presented the theoretical bases and the numerical implementation of this algorithm, this paper illustrates its efficiency though the analysis of several test functions of increasing dimensions.","PeriodicalId":320604,"journal":{"name":"Journal of Machine Learning for Modeling and Computing","volume":"150 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130905157","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}
{"title":"The Role of Stiffness in Training and Generalization of ResNets","authors":"Joshua Hudson, Marta D Elia, H. Najm, K. Sargsyan","doi":"10.1615/jmachlearnmodelcomput.2023047131","DOIUrl":"https://doi.org/10.1615/jmachlearnmodelcomput.2023047131","url":null,"abstract":".","PeriodicalId":320604,"journal":{"name":"Journal of Machine Learning for Modeling and Computing","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124835385","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}
Alonso Ogueda, E. Martinez, VISWANATHAN ARUNACHALAM, P. Seshaiyer
{"title":"Machine Learning for Predicting the Dynamics of Infectious Diseases during travel through Physics Informed Neural Networks","authors":"Alonso Ogueda, E. Martinez, VISWANATHAN ARUNACHALAM, P. Seshaiyer","doi":"10.1615/jmachlearnmodelcomput.2023047213","DOIUrl":"https://doi.org/10.1615/jmachlearnmodelcomput.2023047213","url":null,"abstract":"In the past few years, approaches such as physics informed neural networks (PINNs) have been applied to a variety of applications that can be modeled by linear and nonlinear ordinary and partial differential equations. Specifically, this work builds on the application of PINNs to a SIRD (susceptible, infectious, recovered, and dead) compartmental model and enhances it to build new mathematical models that incorporate transportation between populations and their impact on the dynamics of infectious diseases. Our work employs neural networks capable of learning how diseases spread, forecasting their progression, and finding their unique parameters. We show how these approaches are capable of predicting the behavior of a disease described by governing differential equations that include parameters and variables associated with the movement of the population between neighboring cities. We show that our model validates real data and also how such PINNs based methods predict optimal parameters for given datasets.","PeriodicalId":320604,"journal":{"name":"Journal of Machine Learning for Modeling and Computing","volume":"32 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123518194","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}