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Machine-learning custom-made basis functions for partial differential equations

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arXiv 2021年

作者： Meuris, Brek Qadeer, Saad Stinis, Panos Advanced Computing Mathematics and Data Division Pacific Northwest National Laboratory RichlandWA99354 United States Department of Applied Mathematics University of Washington SeattleWA98195 United States Department of Mechanical Engineering University of Washington SeattleWA98195 United States

Spectral methods are an important part of scientific computing’s arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the solution of a PDE. The last decade has seen the emergence of deep learning as a strong contender in providing efficient representations of complex functions. In the current work, we present an approach for combining deep neural networks with spectral methods to solve PDEs. In particular, we use a deep learning technique known as the Deep Operator Network (DeepONet), to identify candidate functions on which to expand the solution of PDEs. We have devised an approach which uses the candidate functions provided by the DeepONet as a starting point to construct a set of functions which have the following properties: i) they constitute a basis, 2) they are orthonormal, and 3) they are hierarchical i.e., akin to Fourier series or orthogonal polynomials. We have exploited the favorable properties of our custom-made basis functions to both study their approximation capability and use them to expand the solution of linear and nonlinear time-dependent *** Codes 65M70 Copyright © 2021, The Authors. All rights reserved.

关键词： Partial differential equations

Automating gamification personalization: To the user and beyond

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arXiv 2021年

作者： Rodrigues, Luiz Toda, Armando M. Oliveira, Wilk Palomino, Paula T. Vassileva, Julita Isotani, Seiji Laboratory of Applied Computing to Education and Advanced Social Technology Institute of Mathematics and Computer Science University of São Paulo São Carlos Brazil Lab Department of Computer Science University of Saskatchewan Saskatoon Canada

Personalized gamification explores knowledge about the users to tailor gamification designs to improve one-size-fits-all gamification. The tailoring process should simultaneously consider user and contextual characteristics (e.g., activity to be done and geographic location), which leads to several occasions to tailor. Consequently, tools for automating gamification personalization are needed. The problems that emerge are that which of those characteristics are relevant and how to do such tailoring are open questions, and that the required automating tools are lacking. We tackled these problems in two steps. First, we conducted an exploratory study, collecting participants’ opinions on the game elements they consider the most useful for different learning activity types (LAT) via survey. Then, we modeled opinions through conditional decision trees to address the aforementioned tailoring process. Second, as a product from the first step, we implemented a recommender system that suggests personalized gamification designs (which game elements to use), addressing the problem of automating gamification personalization. Our findings i) present empirical evidence that LAT, geographic locations, and other user characteristics affect users’ preferences, ii) enable defining gamification designs tailored to user and contextual features simultaneously, and iii) provide technological aid for those interested in designing personalized gamification. The main implications are that demographics, game-related characteristics, geographic location, and LAT to be done, as well as the interaction between different kinds of information (user and contextual characteristics), should be considered in defining gamification designs and that personalizing gamification designs can be improved with aid from our recommender system. © 2021, CC BY.

关键词： Recommender systems

Dose Requirements for Fused Multi-Modal Electron Tomography

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Microscopy and microanalysis : the official journal of Microscopy Society of America, Microbeam Analysis Society, Microscopical Society of Canada 2023年第1期29卷 1968-1969页

作者： Manassa, Jason Schwartz, Jonathan Jiang, Yi Zheng, Huihuo Fessler, Jeffrey A. Wendy Di, Zichao Hovden, Robert Department of Materials Science and Engineering University of Michigan Ann Arbor MI United States Advanced Photon Source Facility Argonne National Laboratory Lemont IL United States Argonne Leadership Computing Facility Argonne National Laboratory Lemont IL United States Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor MI United States Mathematics and Computer Science Division Argonne National Laboratory Lemont IL United States Applied Physics Program University of Michigan Ann Arbor MI United States

The projection extension method: A spectrally accurate technique for complex domains

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arXiv 2021年

作者： Qadeer, Saad Nazockdast, Ehssan Griffith, Boyce E. Advanced Computing Mathematics and Data Division Pacific Northwest National Laboratory RichlandWA99354 United States Department of Applied Physical Sciences University of North Carolina Chapel HillNC27599 United States Departments of Mathematics Applied Physical Sciences and Biomedical Engineering University of North Carolina Chapel HillNC United States

An essential ingredient of a spectral method is the choice of suitable bases for test and trial spaces. On complex domains, these bases are harder to devise, necessitating the use of domain partitioning techniques such as the spectral element method. In this study, we introduce the Projection Extension (PE) method, an approach that yields spectrally accurate solutions to various problems on complex geometries without requiring domain decomposition. This technique builds on the insights used by extension methodologies such as the immersed boundary smooth extension and Smooth Forcing Extension (SFE) methods that are designed to improve the order of accuracy of the immersed boundary method. In particular, it couples an accurate extension procedure, that functions on arbitrary domains regardless of connectedness or regularity, with a least squares minimization of the boundary conditions. The resulting procedure is stable under iterative application and straightforward to generalize to higher dimensions. Moreover, it rapidly and robustly yields exponentially convergent solutions to a number of challenging test problems, including elliptic, parabolic, Newtonian fluid flow, and viscoelastic *** Codes 65M70 Copyright © 2021, The Authors. All rights reserved.

关键词： Navier Stokes equations

A modified orthogonal matching pursuit for construction of sparse probabilistic Boolean networks

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arXiv 2020年

作者： Xiao, Guiyun Bai, Zheng-Jian Ching, Wai-Ki School of Mathematical Sciences Xiamen University Xiamen361005 China School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling & High Performance Scientific Computing Xiamen University Xiamen361005 China Advanced Modeling and Applied Computing Laboratory Department of Mathematics The University of Hong Kong Pokfulam Road Hong Kong

Probabilistic Boolean Networks play a remarkable role in the modelling and control of gene regulatory networks. In this paper, we consider the inverse problem of constructing a sparse probabilistic Boolean network from the prescribed transition probability matrix. We propose a modified orthogonal matching pursuit for solving the inverse problem. We provide some conditions under which the proposed algorithm can recover a sparse probabilistic Boolean network. We also report some numerical results to illustrate the effectiveness of the proposed algorithm. Copyright © 2020, The Authors. All rights reserved.

关键词： Inverse problems

Curiosity-Driven Science: The in Situ Jungle Biomechanics Lab in the Amazon Rainforest

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arXiv 2024年

作者： Stupski, S. David Ferrer, Laura Casas Harrison, Jacob S. Jackson, Justina Mansilla, Carolina Paucarhuanca Lívano, Loribeth Maricielo Bolo Narla, Avaneesh Chai, Chew Clark, Elizabeth Ha, Nami Nina, Jaime Quispe Wold, Ethan Reyes-Quinteros, Johana Gallice, Geoffrey Bhamla, Saad Department of Biology University of Washington SeattleWA United States School of Chemical and Biomolecular Engineering Georgia Institute of Technology AtlantaGA United States Center for Education Integrating Science Mathematics and Computing Georgia Institute of Technology AtlantaGA United States Department of Engineering Pontifical Catholic University of Peru Lima Peru Department of Applied Physics Stanford University StanfordCA United States Department of Bioengineering Stanford University StanfordCA United States Advanced Light Source Lawrence Berkeley National Laboratory BerkeleyCA United States Nature Travel Photography Madre de Dios Tambopata Peru Alliance for a Sustainable Amazon PotomacMD United States Department of Natural History Florida Museum of Natural History University of Florida GainesvilleFL United States

Field work is an essential component not just for organismal biology, but also for the expanding umbrella of disciplines which have turned their attention towards living systems. Observing organisms in naturalistic contexts is a critical component of discovery;however, conducting field research can be a massive barrier for scientists who do not have experience working with organisms in a naturalistic context under challenging field conditions. Here we propose 8 critical steps for organizing and executing interdisciplinary curiosity-driven field research, drawing on the insights from The in Situ Jungle Biomechanics Lab (JBL). The JBL program is a field research course that helps early-career scientists gain experience in organizing and conducting interdisciplinary field research. JBL uses a curiosity-driven approach to field science education by encouraging early-career researchers to explore scientific questions in the Peruvian Amazon with a non-prescriptive approach to research output. We achieve an inclusive research space by bringing scientists from across disciplines together, with local communities to collaborate and spark new questions and ideas. To stoke curiosity, the JBL imparts a naturalist tradition set forth by organismal biologists of the 20th century who have extolled the merits of observing the natural world as a form of scientific exploration. © 2024, CC BY-NC-ND.

关键词： Biotic

The application of proximal visible and near-infrared spectroscopy to estimate soil organic matter on the Triffa Plain of Morocco

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International Soil and Water Conservation Research 2020年第2期8卷 195-204页

作者： Ayoub Lazaar Abdul Mounem Mouazen Kamal EL Hammouti Michael Fullen Biswajeet Pradhan Muhammad Sohail Memon Karim Andich Abdelilah Monir Laboratory of Applied Geosciences Department of GeologyFaculty of ScienceMohammed First UniversityOujdaMorocco Division of Mechatronics Biostatistics and Sensors(MeBioS)Faculty of Bioscience EngineeringKasteelpark Arenberg 30B-3001 HeverleeBelgium Faculty of Science and Engineering University of WolverhamptonWolverhamptonWV11LYUnited Kingdom Center for Advanced Modelling and Geospatial Information Systems(CAMGIS) Faculty of Engineering and Information TechnologyUniversity of Technology SydneySydney2007NSWAustralia Faculty of Agricultural Engineering Sindh Agriculture UniversityTandojam70060Pakistan Laboratory of Applied Geomatics and Soil Science National Institute of Agronomic Research(INRA)OujdaMorocco Department of Mathematics EDP and Scientific Computing TeamMoulay Ismail UniversityMéknesMorocco

Soil organic matter (SOM) is a fundamental soil constituent. The estimation of this parameter in the laboratory using the classical method is complex time-consuming and requires the use of chemical re-agents. The objectives of this study were to assess the accuracy of two laboratory measurement setups of the VIS-NIR spectroscopy in estimating SOM content and determine the important spectral bands in the SOM estimation model. A total of 115 soil samples were collected from the non-root zone (0-20 cm) of soil in the study area of the Triffa Plain and then analysed for SOM in the laboratory by the Walkley-Black method. The reflectance spectra of soil samples were measured by two protocols, Contact Probe (CP) and Pistol Grip (PG)) of the ASD spectroradiometer (350-2500 nm) in the laboratory. Partial least squares regression (PLSR) was used to develop the prediction models. The results of coefficient of determination (R2) and the root mean square error (RMSE) showed that the pistol grip offers reasonable accuracy with an R2=0.93 and RMSE=0.13 compared to the contact probe protocol with an R2=0.85 and RMSE = 0.19. The near-Infrared range were more accurate than those in the visible range for pre-dicting SOM using the both setups (CP and PG). The significant wavelengths contributing to the pre-diction of SOM for (PG) setup were at:424, 597, 1432, 1484, 1830,1920, 2200, 2357 and 2430 nm, while were at 433, 587, 1380, 1431, 1929, 2200 and 2345 nm for (CP) setup.

关键词： Soil organic matter VIS-NIR spectroscopy Reflectance spectra SOM estimation SOM analysis

A Markov-Driven Portfolio Execution Strategy with Market Impact

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高等学校计算数学学报（英文版） 2018年第4期11卷 701-728页

作者： Qingqing Yang Wai-Ki Ching Tak-Kuen Siu Zhiwen Zhang Advanced Modeling and Applied Computing Laboratory Department of Mathematics The University of Hong Kong Pokfulam Road Hong Kong Department of Applied Finance and Actuarial Studies Faculty of Business and Economics Macquarie University Sydney NSW 2109 Australia

In this paper,we propose a framework for studying optimal agency execution strategies in a Limit Order Book (LOB) under a Markov-modulated market *** Almgren-Chriss's market impact model [1] is extended to a more general situation where multiple venues are available for investors to submit *** the assumption of risk-neutrality,a compact recursive formula is derived,using the value iterative method,to calculate the optimal agency execution *** original optimal control problem is then converted to a constrained quadratic optimization problem,which can be solved by using the Quadratic Programming (Qp) *** examples are given to illustrate the efficiency and effective of our proposed methods.

关键词： Hamilton-Jacobi-Bellman (HJB) equation Limit Order Book (LOB) Dynamic Programming (DP) principle market impact Quadratic Programming (Qp) regime-switching value iteration method

Methane fluxes in an artificial valley reservoir according to field observations and mathematical modeling 11

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Methane fluxes in an artificial valley reservoir according t...

11th International Conference and Early Career Scientists School on Environmental Observations, modeling and Information Systems, ENVIROMIS 2020

作者： Lomov, V. Stepanenko, V. Grechushnikova, M. Repina, I. Land Hydrology Department Faculty of Geography Moscow State University Russia Laboratory for Supercomputer Modeling of the Earth System Processes Research Computing Center Moscow Russia Meteorology and Climatology Department Faculty of Geography Moscow State University Russia Moscow Center of Fundamental and Applied Mathematics Russia Institute of Water Problems RAS Moscow Russia A.M. Obukhov Institute of Atmospheric Physics RAS Moscow Russia

A very important problem nowadays is to assess anthropogenic impact on global warming. Increasing greenhouse gas concentrations in the atmosphere is the main reason for the rising global planet temperatures. The most important greenhouse gases (GHGs) are carbon dioxide and methane. The forcing made by carbon dioxide has been studied for a long time, while less attention has been focused on methane in this regard. However, more and more evidence indicates significant methane emissions into the atmosphere from anthropogenic sources. Less studied, but also important sources of methane are artificial reservoirs. In order to more accurately estimate methane emissions from the reservoirs, it is necessary to study the processes occurring with methane in the aquatic ecosystems in detail. For this purpose, in this study a Mozhaysk reservoir located in Moscow region is chosen. Studies of the spatial and temporal variations of methane fluxes have been carried out on this site for 6 years since 2015. In addition, this reservoir is used for validation of a well-known model, LAKE. This model can be used as an instrument for detailed estimation of methane emissions into the atmosphere from the surface of reservoirs. © Published under licence by IOP Publishing Ltd.

关键词： Methane