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SSRN 2023年

作者： Zhu, Min Zhang, Handi Jiao, Anran Karniadakis, George Em Lu, Lu Department of Chemical and Biomolecular Engineering University of Pennsylvania PhiladelphiaPA19104 United States Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Department of Computer and Information Science University of Pennsylvania PhiladelphiaPA19104 United States Division of Applied Mathematics Brown University ProvidenceRI02912 United States School of Engineering Brown University ProvidenceRI02912 United States

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural operators such as deep operator networks (DeepONets) provide a new simulation paradigm in science and engineering. Pure data-driven neural operators and deep learning models, in general, are usually limited to interpolation scenarios, where new predictions utilize inputs within the support of the training set. However, in the inference stage of real-world applications, the input may lie outside the support, i.e., extrapolation is required, which may result to large errors and unavoidable failure of deep learning models. Here, we address this challenge of extrapolation for deep neural operators. First, we systematically investigate the extrapolation behavior of DeepONets by quantifying the extrapolation complexity via the 2-Wasserstein distance between two function spaces and propose a new strategy of bias-variance trade-off for extrapolation with respect to model capacity. Subsequently, we develop a complete workflow, including extrapolation determination, and we propose five reliable learning methods that guarantee a safe prediction under extrapolation by requiring additional information-the governing PDEs of the system or sparse new observations. The proposed methods are based on either fine-tuning a pre-trained DeepONet or multifidelity learning. We demonstrate the effectiveness of the proposed framework for various types of parametric PDEs. Our systematic comparisons provide practical guidelines for selecting a proper extrapolation method depending on the available information, desired accuracy, and required inference speed. © 2023, The Authors. All rights reserved.

关键词： Extrapolation

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CONVERGENCE SPEED AND APPROXIMATION ACCURACY OF NUMERICAL MCMC

arXiv

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arXiv 2022年

作者： Cui, Tiangang Dong, Jing Jasra, Ajay Tong, Xin T. School of Mathematics Monash University Australia Graduate School of Business Columbia University United States Applied Mathematics and Computational Science Program Computer Electrical Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Saudi Arabia Department of Mathematics National University of Singapore Singapore

When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how perturbation of MCMC affects the convergence speed and Monte Carlo estimation accuracy. Our results show that when the original Markov chain converges to stationarity fast enough and the perturbed transition kernel is a good approximation to the original transition kernel, the corresponding perturbed sampler has similar convergence speed and high approximation accuracy as well. We discuss two different analysis frameworks: ergodicity and spectral gap, both are widely used in the literature. Our results can be easily extended to obtain non-asymptotic error bounds for MCMC estimators. We also demonstrate how to apply our convergence and approximation results to the analysis of specific sampling algorithms, including Random walk Metropolis and Metropolis adjusted Langevin algorithm with perturbed target densities, and parallel tempering Monte Carlo with perturbed densities. Finally we present some simple numerical examples to verify our theoretical claims. Copyright © 2022, The Authors. All rights reserved.

关键词： Inverse problems

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High-speed and low-power molecular dynamics processing unit(MDPU)with ab initio accuracy

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npj Computational Materials 2024年第1期10卷 559-568页

作者： Pinghui Mo Yujia Zhang Zhuoying Zhao Hanhan Sun Junhua Li Dawei Guan Xi Ding Xin Zhang Bo Chen Mengchao Shi Duo Zhang Denghui Lu Yinan Wang Jianxing Huang Fei Liu Xinyu Li Mohan Chen Jun Cheng Bin Liang Weinan E Jiayu Dai Linfeng Zhang Han Wang Jie Liu College of Integrated Circuits Hunan UniversityChangsha410082P.R.China College of Electrical and Information Engineering Hunan UniversityChangsha410082P.R.China College of Computer National University of Defense TechnologyChangsha410073P.R.China Department of Physics National University of Defense TechnologyChangsha410073P.R.China DP Technology 100080 BeijingP.R.China AI for Science Institute 100080 BeijingP.R.China Academy for Advanced Interdisciplinary Studies Peking University100871 BeijingP.R.China HEDPS CAPTCollege of EngineeringPeking University100871 BeijingP.R.China School of Mathematical Science Peking University100871 BeijingP.R.China State Key Laboratory of Physical Chemistry of Solid Surfaces iChEMCollege of Chemistry and Chemical EngineeringXiamen UniversityXiamen361005P.R.China School of Integrated Circuits Peking University100871 BeijingP.R.China Center for Machine Learning Research Peking University100871 BeijingP.R.China Institute of Applied Physics and Computational Mathematics 100088 BeijingP.R.China Greater Bay Area Institute for Innovation Hunan UniversityGuangzhou511300P.R.China Department of Electrical and Computer Engineering University of WashingtonSeattleWA98195USA

Molecular dynamics(MD)is an indispensable atomistic-scale computational tool widely-used in various *** the past decades,nearly all ab initio MD and machine-learning MD have been based on the general-purpose central/graphics processing units(CPU/GPU),which are well-known to suffer from their intrinsic“memory wall”and“power wall”***,nowadays MD calculations with ab initio accuracy are extremely time-consuming and power-consuming,imposing serious restrictions on the MD simulation size and *** solve this problem,here we propose a special-purpose MD processing unit(MDPU),which could reduce MD time and power consumption by about 103 times(109 times)compared to state-of-the-art machine-learningMD(ab initio MD)based on CPU/GPU,while keeping ab initio *** significantly-enhanced performance,the proposed MDPU may pave a way for the accurate atomistic-scale analysis of large-size and/or longduration problems which were impossible/impractical to compute before.

关键词： consuming power MDP

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Stochastic Optimisation Framework using the Core Imaging Library and Synergistic Image Reconstruction Framework for PET Reconstruction

arXiv

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arXiv 2024年

作者： Papoutsellis, Evangelos da Costa-Luis, Casper Deidda, Daniel Delplancke, Claire Duff, Margaret Fardell, Gemma Gillman, Ashley Jorgensen, Jakob S. Kereta, Zeljko Ovtchinnikov, Evgueni Pasca, Edoardo Schramm, Georg Thielemans, Kris Finden Ltd Rutherford Appleton Laboratory Harwell Campus United Kingdom Scientific Computing Department Science & Technology Facilities Council Harwell Campus United Kingdom National Physical Laboratory Electricité de France Research and Development France Australian e-Health Res. Ctr. CSIRO BrisbaneQLD Australia Department of Applied Mathematics and Computer Science Technical University of Denmark Denmark Department of Computer Science University College London United Kingdom Department of Imaging and Pathology Division of Nuclear Medicine KU Leuven Leuven Belgium Institute of Nuclear Medicine University College London United Kingdom

We introduce a stochastic framework into the open- source Core Imaging Library (CIL) which enables easy development of stochastic algorithms. Five such algorithms from the literature are developed, Stochastic Gradient Descent, Stochastic Average Gradient (-Amélioré), (Loopless) Stochastic Variance Reduced Gradient. We showcase the functionality of the framework with a comparative study against a deterministic algorithm on a simulated 2D PET dataset, with the use of the open-source Synergistic Image Reconstruction Framework. We observe that stochastic optimisation methods can converge in fewer passes of the data than a standard deterministic algorithm1. © 2024, CC BY.

关键词： Positron emission tomography

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A hybrid mental health prediction model using Support Vector Machine, Multilayer Perceptron, and Random Forest algorithms

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Healthcare Analytics 2023年 3卷 100185-100185页

作者： Mohamed, E. Syed Naqishbandi, Tawseef Ahmad Bukhari, Syed Ahmad Chan Rauf, Insha Sawrikar, Vilas Hussain, Arshad Department of Computer Science and Engineering B.S. Abdur Rahman Crescent Institute of Science and Technology Chennai 600048 India Division of Computer Science Mathematics and Science Collins College of Professional Studies St. John's University NY United States Department of Psychiatry Government Medical College Srinagar Jammu and Kashmir 190010 India Department of Clinical and Health Psychology University of Edinburgh Edinburgh United Kingdom

The prevalence and burden of mental health disorders are on the rise in conflict zones, and if left untreated, they can lead to considerable lifetime disability. Following the repeal of Article 370, political unrest spread quickly, forcing the Indian government to impose safety precautions such as lockdowns and communication ban. Consequently, the region of Kashmir experienced a marked rise in anxiety as a result of these lifestyle changes. Machine learning has proven useful in the early diagnosis and prognosis of certain diseases. Therefore, this study aims to classify anxiety problems early by utilising a pre-clinical mental health dataset collected after the abrogation of article 370 in Kashmir. The first part of the paper aims at developing and implementing a prediction model based on classification into one of the five pre-clinical anxiety stages, i.e., Stage 1: minimal anxiety, Stage 2: mild anxiety, Stage 3: moderate anxiety, Stage 4: severe anxiety, and Stage 5: very severe anxiety. The second part offers recommendations for those suffering from anxiety disorders. Feature selection and prediction are used to predict the correct stage of anxiety for best possible medical intervention. Three different algorithms: Support Vector Machine(SVM), Multilayer Perceptron (MLP), and Random Forest (RF), are employed for predicting anxiety stages. Among them, random forest (RF) achieved 98.13% accuracy. A forecasted likelihood condition was assessed to provide a suitable recommendation. Further, accuracy and kappa statistics are used to assess the performance of the suggested model, which offers a significant addition to predicting anxiety early, and exhibits high prediction and recommendation accuracy. This study aims to assist mental health professionals and experts in making quick and accurate choices. © 2023 The Author(s)

关键词： Machine learning Mental health Multilayer Perceptron Prediction Random Forest Support Vector Machine

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Advantage of Machine Learning over Maximum Likelihood in Limited-Angle Low-Photon X-Ray Tomography

Advantage of Machine Learning over Maximum Likelihood in Lim...

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IS and T International Symposium on Electronic Imaging: Machine Learning for Scientific Imaging, MLSI 2022

作者： Guo, Zhen Song, Jung Ki Barbastathis, George Glinsky, Michael E. Vaughan, Courtenay T. Larson, Kurt W. Alpert, Bradley K. Levine, Zachary H. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology CambridgeMA02139 United States Department of Mechanical Engineering Massachusetts Institute of Technology CambridgeMA02139 United States Centre Singapore138002 Singapore Sandia National Laboratory AlbuquerqueNM87123 United States Applied and Computational Mathematics Division National Institute of Standards and Technology Boulder CO80305 United States Quantum Measurement Division National Institute of Standards and Technology GaithersburgMD20899 United States

Limited-angle X-ray tomography reconstruction is an ill-conditioned inverse problem in general. Especially when the projection angles are limited and the measurements are taken in a photon-limited condition, reconstructions from classical algorithms such as filtered backprojection may lose fidelity and acquire artifacts due to the missing-cone problem. To obtain satisfactory reconstruction results, prior assumptions, such as total variation minimization and nonlocal image similarity, are usually incorporated within the reconstruction algorithm. In this work, we introduce deep neural networks to determine and apply a prior distribution in the reconstruction process. Our neural networks learn the prior directly from synthetic training samples. The neural nets thus obtain a prior distribution that is specific to the class of objects we are interested in reconstructing. In particular, we used deep generative models with 3D convolutional layers and 3D attention layers which are trained on 3D synthetic integrated circuit (IC) data from a model dubbed CircuitFaker. We demonstrate that, when the projection angles and photon budgets are limited, the priors from our deep generative models can dramatically improve the IC reconstruction quality on synthetic data compared with maximum likelihood estimation. Training the deep generative models with synthetic IC data from CircuitFaker illustrates the capabilities of the learned prior from machine learning. We expect that if the process were reproduced with experimental data, the advantage of the machine learning would persist. The advantages of machine learning in limited angle X-ray tomography may further enable applications in low-photon nanoscale imaging. © 2022, Society for Imaging science and Technology

关键词： Photons

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Weak solution for time-fractional strongly coupled three species cooperating model

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Partial Differential Equations in applied mathematics 2023年 7卷

作者： Manimaran, J. Bhuvaneswari, V. Shangerganesh, L. Division of Mathematics School of Advanced Sciences Vellore Institute of Technology Chennai Campus Chennai 600 127 India Department of Mathematics with Computer Applications PSG College of Arts & Science Coimbatore 641 014 India Department of Applied Sciences National Institute of Technology Goa Goa Farmagudi 403 401 India

This article investigates the solvability of the time-fractional strongly coupled three-species cooperating system of equations with the Dirichlet boundary conditions. This model expresses the interactions of cooperating species. First, a suitable approximation problem is considered to overcome the strong degeneracy of the original model. Then, we establish the existence of a weak solution for the proposed system using the Faedo–Galerkin method and some compactness arguments. © 2023 The Authors

关键词： Faedo Galerkin method Fractional PDE Weak solution

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High Hospitalization Rates and Risk Factors Among Frail Patients With Cirrhosis: A 10-year Population-based Cohort Study

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Clinical Gastroenterology and Hepatology 2025年第7期23卷 1152-1163页

作者： Hasjim, Bima J. Mohammadi, Mohsen Balbale, Salva N. Paukner, Mitchell Banea, Therese Shi, Haoyan Furmanchuk, Al'ona VanWagner, Lisa B. Zhao, Lihui Duarte-Rojo, Andres Doll, Julianna Mehrotra, Sanjay Ladner, Daniela P. Northwestern University Transplant Outcomes Research Collaborative (NUTORC) Comprehensive Transplant Center (CTC) Northwestern University Chicago Illinois United States Center for Engineering and Health McCormick School of Engineering and Applied Science Northwestern University Chicago Illinois United States Department of Industrial Engineering and Management Sciences McCormick School of Engineering Northwestern University Evanston IL United States Division of Gastroenterology and Hepatology Department of Medicine Northwestern University Feinberg School of Medicine Chicago Illinois United States Center for Health Services and Outcomes Research Institute of Public Health and Medicine & Northwestern Quality Improvement Research & Education in Surgery (NQUIRES) Department of Surgery Northwestern University Feinberg School of Medicine Chicago Illinois United States Center of Innovation for Complex Chronic Healthcare (CINCCH) Edward Hines Jr. VA Hospital Hines IL United States Division of Biostatistics Department of Preventive Medicine Northwestern University Feinberg School of Medicine Chicago Illinois United States Department of Mathematics Northwestern University Evanston IL United States Department of Computer Science McCormick School of Engineering Northwestern University Evanston IL United States Department of General Internal Medicine Feinberg School of Medicine Northwestern University Chicago Illinois United States Division of Digestive and Liver Diseases Department of Medicine University of Texas Southwestern Medical Center Dallas Texas United States Division of Transplantation Department of Surgery Northwestern University Feinberg School of Medicine Chicago Illinois United States

Background & Aims: Cirrhosis-related inpatient hospitalizations have increased dramatically over the past decade. We used a longitudinal dataset capturing a large metropolitan area in the United States from 2011 to 2021 to evaluate contemporary hospitalization rates and risk factors among frail patients with cirrhosis. Methods: We conducted a retrospective, longitudinal cohort study using the Chicago Area Patient-Centered Outcomes Research Network (CAPriCORN) database, an electronic health record repository that aggregates de-duplicated data across 7 health care systems in the Chicago metropolitan area, from 2011 to 2021. The primary outcome of our study was the rate of hospitalization encounters. Frailty was defined by the Hospital Frailty Risk Score. Hospitalization rates were reported per 100 patients per year, and a multivariable logistic regression analysis identified predictors of annual hospitalization probability. Results: During the study period, of 36,971 patients, 16,265 patients (44%) were hospitalized (compensated, 18.4%;decompensated, 81.6%). Hospitalization rates were highest in patients with decompensated cirrhosis, reaching nearly 77.3 hospitalizations/100 patients per year. Hospitalization rates among patients with compensated cirrhosis were also high (14.2 vs 77.3 hospitalization/100 patients per year), with odds of annual hospitalization 3 times (odds ratio, 3.1;95% confidence interval, 2.9-3.4) as high among compensated patients with intermediate frailty and 5 times (odds ratio, 5.2;95% confidence interval, 4.5-6.0) as high among those with severe frailty (compared with compensated patients with low frailty). Conclusion: Compensated and decompensated cirrhosis patients with intermediate to severe frailty face a substantially increased odds of annual hospitalizations compared with those with low frailty. Future work should focus on targeted interventions to incorporate routine frailty screenings into cirrhosis care and to ultimately minimize high

关键词： Cirrhosis Frailty Hospitalizations

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Transition from Susceptible-Infected to Susceptible-Infected-Recovered Dynamics in a Susceptible-Cleric-Zombie-Recovered Active Matter Model

arXiv

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arXiv 2022年

作者： Libál, A. Forgács, P. Néda, A. Reichhardt, C. Hengartner, N. Reichhardt, Cynthia J. Olson Mathematics and Computer Science Department Babeş-Bolyai University Cluj-Napoca400084 Romania Theoretical Division Center for Nonlinear Studies Los Alamos National Laboratory Los AlamosNM87545 United States

The Susceptible-Infected (SI) and Susceptible-Infected-Recovered (SIR) models provide two distinct representations of epidemic evolution, distinguished by the lack of spontaneous recovery in the SI model. Here we introduce a new active matter epidemic model, the "Susceptible-Cleric-ZombieRecovered" (SCZR) model, in which spontaneous recovery is absent but zombies can recover with probability γ via interaction with a cleric. Upon interacting with a zombie, both susceptibles and clerics can enter the zombie state with probability β and α, respectively. By changing the intial fraction of clerics or their healing ability rate γ, we can tune the SCZR model between SI dynamics, in which no susceptibles or clerics remain at long times, and SIR dynamics, in which no zombies remain at long times. The model is relevant to certain real world diseases such as HIV where spontaneous recovery is impossible but where medical interventions by a limited number of caregivers can reduce or eliminate the spread of infection. Copyright © 2022, The Authors. All rights reserved.

关键词： Dynamics

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Pattern Formation and Flocking for Particles Near The Jamming Transition on Resource Gradient Substrates

arXiv

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arXiv 2022年

作者： Varga, L. Libál, A. Reichhardt, C. Olson Reichhardt, Cynthia J. Mathematics and Computer Science Department Babeş-Bolyai University Cluj-Napoca400084 Romania Theoretical Division Center for Nonlinear Studies Los Alamos National Laboratory Los Alamos NM87545 United States

We numerically examine a bidisperse system of active and passive particles coupled to a resource substrate. The active particles deplete the resource at a fixed rate and move toward regions with higher resources, while all of the particles interact sterically with each other. We show that at high densities, this system exhibits a rich variety of pattern forming phases along with directed motion or flocking as a function of the relative rates of resource absorption and consumption as well as the active to passive particle ratio. These include partial phase separation into rivers of active particles flowing through passive clusters, strongly phase separated states where the active particles induce crystallization of the passive particles, mixed jammed states, and fluctuating mixed fluid phases. For higher resource recovery rates, we demonstrate that the active particles can undergo motility induced phase separation, while at high densities, there can be a coherent flock containing only active particles or a solid mixture of active and passive particles. The directed flocking motion typically shows a transient in which the flow switches among different directions before settling into one direction, and there is a critical density below which flocking does not occur. We map out the different phases as function of system density, resource absorption and recovery rates, and the ratio of active to passive particles. Copyright © 2022, The Authors. All rights reserved.

关键词： Phase separation

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