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Machine discovery of partial differential equations from spatiotemporal data

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arXiv 2019年

作者： Yuan, Ye Li, Junlin Li, Liang Jiang, Frank Tang, Xiuchuan Zhang, Fumin Liu, Sheng Goncalves, Jorge Voss, Henning U. Li, Xiuting Kurths, Jürgen Ding, Han School of Artificial Intelligence and Automation State Key Laboratory of Digital Manufacturing Equipments and Technology Huazhong University of Science and Technology Wuhan430074 China School of Artificial Intelligence and Automation Key Laboratory of Image Processing and Intelligent Control Huazhong University of Science and Technology Wuhan430074 China School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm11428 Sweden School of Mechanical Science and Engineering Huazhong University of Science and Technology Wuhan430074 China School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta30332 United States School of Power and Mechanical Engineering Wuhan University Wuhan430074 China Department of Engineering University of Cambridge CambridgeCB2 1PZ United Kingdom Luxembourg Centre for Systems Biomedicine University of Luxembourg BelvauxL-4367 Luxembourg Citigroup Biomedical Imaging Center Weill Cornell Medical College New York10021 United States Research Domain IV - Transdisciplinary Concepts & Methods Potsdam Institute for Climate Impact Research Potsdam14473 Germany School of Mechanical Science and Engineering State Key Laboratory of Digital Manufacturing Equipments and Technology Huazhong University of Science and Technology Wuhan430074 China

The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery (S3d), decides which physical terms are necessary and which can be removed (because they are physically negligible in the sense that they do not affect the dynamics too much) from a pool of candidate functions. The method is built on the recent development of Sparse Bayesian Learning;which enforces the sparsity in the to-be-identified PDEs, and therefore can balance the model complexity and fitting error with theoretical guarantees. Without leveraging prior knowledge or assumptions in the discovery process, we use an automated approach to discover ten types of PDEs, including the famous Navier-Stokes and sine-Gordon equations, from simulation data alone. Moreover, we demonstrate our data-driven discovery process with the Complex Ginzburg-Landau Equation (CGLE) using data measured from a traveling-wave convection experiment. Our machine discovery approach presents solutions that has the potential to inspire, support and assist physicists for the establishment of physical laws from measured spatiotemporal data, especially in notorious fields that are often too complex to allow a straightforward establishment of physical law, such as biophysics, fluid dynamics, neuroscience or nonlinear optics. Copyright © 2019, The Authors. All rights reserved.

关键词： Nonlinear optics

Semi-automated extraction of retinal blood vessel network with Bifurcation and crossover points 12th

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Semi-automated extraction of retinal blood vessel network wi...

12th International Symposium on Visual Computing, ISVC 2016

作者： Nougrara, Z. Kihal, N. Meunier, J. Faculty of Mathematics and Computer Science Department of Mathematics University of Sciences and Technology of Oran Oran Algeria Signal and Image Processing Laboratory Electronics and Computer Science Faculty USTHB Algiers Algeria Department of Computer Science and Operations Research University of Montreal Montreal Canada

ISBN: (纸本)9783319508313

Among different retinal analysis tasks, blood vessel extraction plays an important role as it is often the first essential step before any measurement can be made for various applications such as biometric authentication or diagnosis of retinal vascular diseases. In this paper, we present a new method for extraction of blood vessel network with its nodes (bifurcation and crossover points) from retinal images. The first step is to identify pixels with homogeneous vessel elements with a set of four directional filters. Then another step is applied to extract local linear components assuming that a vessel is a set of short linear segments. Through an optimization process this information is combined to extract the vessel network and its nodes. The proposed algorithm was tested on the publicly available DRIVE retinal fundus image database. The experimental results show good precision, recal. The proposed algorithm was tested on the publicly available DRIVE retinal fundus image database. The experimental results show good precision, recall and F-measure compared to ground truth and a state-of-the-art algorithm for the same dataset. © Springer International Publishing AG 2016.

关键词： Blood vessels

Machine Learning for the Zwicky Transient Facility

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arXiv 2019年

作者： Mahabal, Ashish Rebbapragada, Umaa Walters, Richard Masci, Frank J. Blagorodnova, Nadejda van Roestel, Jan Ye, Quan-Zhi Biswas, Rahul Burdge, Kevin Chang, Chan-Kao Duev, Dmitry A. Golkhou, V. Zach Miller, Adam A. Nordin, Jakob Ward, Charlotte Adams, Scott Bellm, Eric C. Branton, Doug Bue, Brian Cannella, Chris Connolly, Andrew Dekany, Richard Feindt, Ulrich Hung, Tiara Fortson, Lucy Frederick, Sara Fremling, C. Gezari, Suvi Graham, Matthew Groom, Steven Kasliwal, Mansi M. Kulkarni, Shrinivas Kupfer, Thomas Lin, Hsing Wen Lintott, Chris Lunnan, Ragnhild Parejko, John Prince, Thomas A. Riddle, Reed Rusholme, Ben Saunders, Nicholas Sedaghat, Nima Shupe, David L. Singer, Leo P. Soumagnac, Maayane T. Szkody, Paula Tachibana, Yutaro Tirumala, Kushal van Velzen, Sjoert Wight, Darryl Division of Physics Mathematics and Astronomy California Institute of Technology PasadenaCA91125 United States Center for Data Driven Discovery California Institute of Technology PasadenaCA91125 United States Jet Propulsion Laboratory California Institute of Technology PasadenaCA91109 United States Caltech O tical Observatories California Institute of Technolo Pasadena CA91125 United States Infrared Processing and Analysis Center California Institute of Technology MS 100-22 PasadenaCA91125 United States Department of Astrophysics IMAPP Radboud University Nijmegen P.O.Box 9010 Nijmegen6500 GL Netherlands The Oskar Klein Centre De artment of Ph sics Stockholm Universit AlbaNova StockholmSE-106 91 Sweden Institute of Astronom National Central Universit 32001 Taiwan Department of Astronomy University of Washington SeattleWA98195 United States eScience Institute Universit of Washin ton SeattleWA98195 United States Center for Interdisciplinary Exploration and Research in Astrophysics Department of Physics and Astronomy Northwestern University 2145 Sheridan Road EvanstonIL60208 United States Adler Planetarium ChicagoIL60605 United States Institute of Physics Humboldt-Universität zu Berlin Newtonstr. 15 Berlin12489 Germany Department of Astronomy University of Maryland College ParkMD20742 United States Space Telescope Science Institute 3700 San Martin Drive BaltimoreMD21218 United States DIRAC Institute Department of Astronomy University of Washington 3910 15th Avenue NE SeattleWA98195 United States Zooniverse Oxford Astro h sics Den s Wilkinson Buildin Keble Road OxfordOX1 3RH United Kingdom School of Physics and Astronomy 116 Church Street SE University of Minnesota MinneapolisMN55455 United States Department of Astronomy California Institute of Technology PasadenaCA91125 United States Kavli Institute for Theoretical Physics University of California Santa BarbaraCA93106 United States Department of Physics University

The Zwicky Transient Facility is a large optical survey in multiple filters producing hundreds of thousands of transient alerts per night. We describe here various machine learning (ML) implementations and plans to make the maximal use of the large data set by taking advantage of the temporal nature of the data, and further combining it with other data sets. We start with the initial steps of separating bogus candidates from real ones, separating stars and galaxies, and go on to the classification of real objects into various classes. Besides the usual methods (e.g., based on features extracted from light curves) we also describe early plans for alternate methods including the use of domain adaptation, and deep learning. In a similar fashion we describe efforts to detect fast moving asteroids. Copyright © 2019, The Authors. All rights reserved.

关键词： Surveys

From social to individuals: A parsimonious path of multi-level models for crowdsourced preference aggregation

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arXiv 2018年

作者： Xu, Qianqian Xiong, Jiechao Cao, Xiaochun Huang, Qingming Yao, Yuan Key Laboratory of Intelligent Information Processing Institute of Computing Technology Chinese Academy of Sciences Beijing1000190 China Institute of Information Engineering Chinese Academy of Sciences Beijing100093 China Tencent AI Lab Shenzhen518057 BICMR-LMAM-LMEQF-LMP School of Mathematical Sciences Peking University Beijing100871 China University of Chinese Academy of Sciences Institute of Computing Technology of Chinese Academy of Sciences Beijing100190 China Department of Mathematics and by courtesy Computer Science and Engineering Hong Kong University of Science and Technology Hong Kong Hong Kong

In crowdsourced preference aggregation, it is often assumed that all the annotators are subject to a common preference or social utility function which generates their comparison behaviors in experiments. However, in reality annotators are subject to variations due to multi-criteria, abnormal, or a mixture of such behaviors. In this paper, we propose a parsimonious mixed-effects model, which takes into account both the fixed effect that the majority of annotators follows a common linear utility model, and the random effect that some annotators might deviate from the common significantly and exhibit strongly personalized preferences. The key algorithm in this paper establishes a dynamic path from the social utility to individual variations, with different levels of sparsity on personalization. The algorithm is based on the Linearized Bregman Iterations, which leads to easy parallel implementations to meet the need of large-scale data analysis. In this unified framework, three kinds of random utility models are presented, including the basic linear model with L2 loss, Bradley-Terry model, and Thurstone-Mosteller model. The validity of these multi-level models are supported by experiments with both simulated and real-world datasets, which shows that the parsimonious multi-level models exhibit improvements in both interpretability and predictive precision compared with traditional HodgeRank. Copyright © 2018, The Authors. All rights reserved.

关键词： Crowdsourcing

Multi-label inductive matrix completion for joint MGMT and IDH1 status prediction for glioma patients 1

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20th International Conference on Medical image Computing and computer-Assisted Intervention, MICCAI 2017

作者： Chen, Lei Zhang, Han Thung, Kim-Han Liu, Luyan Lu, Junfeng Wu, Jinsong Wang, Qian Shen, Dinggang Jiangsu Key Laboratory of Big Data Security and Intelligent Processing Nanjing University of Posts and Telecommunications Nanjing China Department of Radiology and BRIC University of North Carolina Chapel Hill United States School of Biomedical Engineering Med-X Research Institute Shanghai Jiao Tong University Shanghai China Department of Neurosurgery Huashan Hospital Fudan University Shanghai China Shanghai Key Lab of Medical Image Computing and Computer Assisted Intervention Shanghai China

ISBN: (数字)9783319661858

ISBN: (纸本)9783319661841

MGMT promoter methylation and IDH1 mutation in high-grade gliomas (HGG) have proven to be the two important molecular indicators associated with better prognosis. Traditionally, the statuses of MGMT and IDH1 are obtained via surgical biopsy, which is laborious, invasive and time-consuming. Accurate presurgical prediction of their statuses based on preoperative imaging data is of great clinical value towards better treatment plan. In this paper, we propose a novel Multi-label Inductive Matrix Completion (MIMC) model, highlighted by the online inductive learning strategy, to jointly predict both MGMT and IDH1 statuses. Our MIMC model not only uses the training subjects with possibly missing MGMT/IDH1 labels, but also leverages the unlabeled testing subjects as a supplement to the limited training dataset. More importantly, we learn inductive labels, instead of directly using transductive labels, as the prediction results for the testing subjects, to alleviate the overfitting issue in small-sample-size studies. Furthermore, we design an optimization algorithm with guaranteed convergence based on the block coordinate descent method to solve the multivariate non-smooth MIMC model. Finally, by using a precious single-center multi-modality presurgical brain imaging and genetic dataset of primary HGG, we demonstrate that our method can produce accurate prediction results, outperforming the previous widely-used single- or multi-task machine learning methods. This study shows the promise of utilizing imaging-derived brain connectome phenotypes for prognosis of HGG in a non-invasive manner. © Springer International Publishing AG 2017.

关键词： Forecasting

Derivation languages of splicing P systems 12th

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Derivation languages of splicing P systems

12th International Conference on Bio-Inspired Computing: Theories and Applications, BIC-TA 2017

作者： Mahalingam, Kalpana Paul, Prithwineel Song, Bosheng Pan, Linqiang Subramanian, K.G. Department of Mathematics Indian Institute of Technology Madras Chennai600036 India Key Laboratory of Image Information Processing Intelligent Control of Education Ministry of China School of Automation Huazhong University of Science and Technology WuhanHubei430074 China School of Electric and Information Engineering Zhengzhou University of Light Industry ZhengzhouHenan450002 China Faculty of Science Liverpool Hope University LiverpoolL16 9JD United Kingdom

ISBN: (纸本)9789811071782

Labelled splicing P systems are distributed parallel computing models, where sets of strings that evolve by splicing rules are labelled. In this work, we consider labelled splicing systems with the following modifications: (i) The strings in the membranes are present in arbitrary number of copies;(ii) the rules in the regions are finite in number. Results on the language family generated by the labelled splicing system in comparison with the language families of the Chomsky hierarchy, including recursively enumerable languages, are obtained, by involving only either one or two membranes in the P systems considered. © Springer Nature Singapore Pte Ltd 2017.

关键词： Distributed computer systems

Factorization Algorithms for Temporal Psychovisual Modulation Display

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Factorization Algorithms for Temporal Psychovisual Modulatio...

作者： Gao, Zhongpai Zhai, Guangtao Zhou, Jiantao Institute of Image Communication and Information Processing Shanghai Jiao Tong University Shanghai200240 China Department of Computer and Information Science University of Macau China

Temporal psychovisual modulation (TPVM) is a new information display technology which aims to generate multiple visual percepts for different viewers on a single display simultaneously. In a TPVM system, the viewers wearing different active liquid crystal (LC) glasses with varying transparency levels can see different images (called personal views). The viewers without LC glasses can also see a semantically meaningful image (called shared view). The display frames and weights for the LC glasses in the TPVM system can be computed through nonnegative matrix factorization (NMF) with three additional constrains: 1) the values of images and modulation weights should have upper bound (i.e., limited luminance of the display and transparency level of the LC);2) the shared view without using viewing devices should be considered (i.e., the sum of all basis images should be a meaningful image);and 3) the sparsity of modulation weights should be considered due to the material property of LC. In this paper, we proposed to solve the constrained NMF problem by a modified version of hierarchical alternating least squares (HALS) algorithms. Through experiments, we analyze the choice of parameters in the setup of TPVM system. This work serves as a guideline for practical implementation of TPVM display system. © 1999-2012 IEEE.

关键词： Modulation

Multidimensional correlation spectroscopic imaging of exponential decays: From theoretical principles to in vivo human applications

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arXiv 2018年

作者： Kim, Daeun Wisnowski, Jessica L. Nguyen, Christopher T. Haldar, Justin P. Biomedical Imaging Research Institute Cedars-Sinai Medical Center CA United States Ming Hsieh Department of Electrical and Computer Engineering University of Southern California CA United States Signal and Image Processing Institute University of Southern California CA United States Radiology Children's Hospital Los Angeles CA United States Pediatrics Children's Hospital Los Angeles CA United States Harvard Medical School Cardiovascular Research Center Massachusetts General Hospital MA United States Martinos Center for Biomedical Imaging Radiology Massachusetts General Hospital MA United States

Multiexponential modeling of relaxation or diffusion MR signal decays is a popular approach for estimating and spatially mapping different microstructural tissue compartments. While this approach can be quite powerful, it is also limited by the fact that one-dimensional multiexponential modeling is an ill-posed inverse problem with substantial ambiguities. In this paper, we present an overview of a recent multidimensional correlation spectroscopic imaging approach to this problem. This approach helps to alleviate ill-posedness by leveraging multidimensional contrast encoding (e.g., 2D diffusion-relaxation encoding or 2D relaxation-relaxation encoding) combined with a regularized spatial-spectral estimation procedure. Theoretical calculations, simulations, and experimental results are used to illustrate the benefits of this approach relative to classical methods. In addition, we demonstrate an initial proof-of-principle application of this kind of approach to in vivo human MRI experiments. Copyright © 2018, The Authors. All rights reserved.

关键词： Signal encoding

Cost efficient gradient boosting 17

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Cost efficient gradient boosting

Proceedings of the 31st International Conference on Neural Information processing Systems

作者： Sven Peter Ferran Diego Fred A. Hamprecht Boaz Nadler Heidelberg Collaboratory for Image Processing Interdisciplinary Center for Scientific Computing University of Heidelberg Heidelberg Germany Robert Bosch GmbH Robert-Bosch-Straße Hildesheim Germany Department of Computer Science Weizmann Institute of Science Rehovot Israel

ISBN: (纸本)9781510860964

Many applications require learning classifiers or regressors that are both accurate and cheap to evaluate. Prediction cost can be drastically reduced if the learned predictor is constructed such that on the majority of the inputs, it uses cheap features and fast evaluations. The main challenge is to do so with little loss in accuracy. In this work we propose a budget-aware strategy based on deep boosted regression trees. In contrast to previous approaches to learning with cost penalties, our method can grow very deep trees that on average are nonetheless cheap to compute. We evaluate our method on a number of datasets and find that it outperforms the current state of the art by a large margin. Our algorithm is easy to implement and its learning time is comparable to that of the original gradient boosting. Source code is made available at http://***/svenpeter42/LightGBM-CEGB.

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