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Shape of my heart: Cardiac models through learned signed distance functions

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arXiv 2023年

作者： Verhülsdonk, Jan Grandits, Thomas Costabal, Francisco Sahli Pinetz, Thomas Krause, Rolf Auricchio, Angelo Haase, Gundolf Pezzuto, Simone Effland, Alexander Institute for Applied Mathematics University of Bonn Germany Department of Mathematics and Scientific Computing University of Graz Austria Institute for Biological and Medical Engineering Pontificia Universidad Católica de Chile Chile Center for Computational Medicine in Cardiology Università della Svizzera italiana Switzerland FernUni Schweiz Brig Switzerland Instituto Cardiocentro Ticino EOC Switzerland Department of Mathematics University of Trento Italy

The efficient construction of anatomical models is one of the major challenges of patient-specific in-silico models of the human heart. Current methods frequently rely on linear statistical models, allowing no advanced topological changes, or requiring medical image segmentation followed by a meshing pipeline, which strongly depends on image resolution, quality, and modality. These approaches are therefore limited in their transferability to other imaging domains. In this work, the cardiac shape is reconstructed by means of three-dimensional deep signed distance functions with Lipschitz regularity. For this purpose, the shapes of cardiac MRI reconstructions are learned to model the spatial relation of multiple chambers. We demonstrate that this approach is also capable of reconstructing anatomical models from partial data, such as point clouds from a single ventricle, or modalities different from the trained MRI, such as the electroanatomical mapping (EAM). Copyright © 2023, The Authors. All rights reserved.

关键词： Image resolution

Fast And Automatic Floating Point Error Analysis With CHEF-FP

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Fast And Automatic Floating Point Error Analysis With CHEF-F...

International Symposium on Parallel and Distributed Processing (IPDPS)

作者： Garima Singh Baidyanath Kundu Harshitha Menon Alexander Penev David J. Lange Vassil Vassilev European Council for Nuclear Research Meyrin Switzerland Department of Physics Princeton University Princeton New Jersey USA Lawrence Livermore National Laboratory Center for Applied Scientific Computing Livermore California USA Faculty of Mathematics and Informatics University of Plovdiv Plovdiv Bulgaria

As we reach the limit of Moore’s Law, researchers are exploring different paradigms to achieve unprecedented performance. Approximate computing (AC), which relies on the ability of applications to tolerate some error in the results to trade-off accuracy for performance, has shown significant promise. Despite the success of AC in domains such as Machine Learning, its acceptance in High-Performance computing (HPC) is limited due to its stringent requirement of accuracy. We need tools and techniques to identify regions of the code that are amenable to approximations and their impact on the application output quality so as to guide developers to employ selective approximation. To this end, we propose CHEF-FP, a flexible, scalable, and easy-to-use source-code transformation tool based on Automatic Differentiation (AD) for analysing approximation errors in HPC ***-FP uses Clad, an efficient AD tool built as a plugin to the Clang compiler and based on the LLVM compiler infrastructure, as a backend and utilizes its AD abilities to evaluate approximation errors in C++ code. CHEF-FP works at the source level by injecting error estimation code into the generated adjoints. This enables the error-estimation code to undergo compiler optimizations resulting in improved analysis time and reduced memory usage. We also provide theoretical and architectural augmentations to source code transformation-based AD tools to perform FP error analysis. In this paper, we primarily focus on analyzing errors introduced by mixed-precision AC techniques, the most popular approximate technique in HPC. We also show the applicability of our tool in estimating other kinds of errors by evaluating our tool on codes that use approximate functions. Moreover, we demonstrate the speedups achieved by CHEF-FP during analysis time as compared to the existing state-of-the-art tool as a result of its ability to generate and insert approximation error estimate code directly into the derivative sourc

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Using a Fast Adaptive Function Approximator to calculate Protein-Filament Binding Kinetics

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arXiv 2023年

作者： Zhang, Zihan Lamson, Adam Blackwell, Robert Department of Applied Mathematics University of Washington SeattleWA98195 United States Center for Computational Biology Flatiron Institute New YorkNY10010 United States Scientific Computing Core Flatiron Institute New YorkNY10010 United States

The cytoskeleton, consisting of biopolymer filaments, molecular motors, and passive crosslinking proteins, provides the internal structure of cells that facilitate movement, growth, and cell division. Understanding the microscopic motor-filament kinetics and dynamics is essential for comprehending macroscopic behaviors of reconstituted cytoskeletal assemblies, such as self-organized flow and active stress. In this study, we employ an adaptive fast Chebyshev approximator based on tree search and parallel computing to accurately recover the equilibrium distribution of crosslinking proteins. Therefore, it satisfies detailed balance in binding through kinetic Monte Carlo sampling while maintaining cost-effectiveness. Additionally, we offer expandable features, including segregating the simulation process via pre-building and allowing the free-loading of different closed-form formulations of the motor's potential energy. Overall, this research contributes to computational advancement in function approximation and has the potential to better describe the evolution of cytoskeletal active matter. © 2023, CC BY.

关键词： Cost effectiveness

An Adaptive Sampling Augmented Lagrangian Method for Stochastic Optimization with Deterministic Constraints

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arXiv 2023年

作者： Bollapragada, Raghu Karamanli, Cem Keith, Brendan Lazarov, Boyan Petrides, Socratis Wang, Jingyi Operations Research and Industrial Engineering The University of Texas at Austin AustinTX78712 United States Division of Applied Mathematics Brown University ProvidenceRI02912 United States Center for Design Optimization Lawrence Livermore National Laboratory LivermoreCA94550 United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 United States

The primary goal of this paper is to provide an efficient solution algorithm based on the augmented Lagrangian framework for optimization problems with a stochastic objective function and deterministic constraints. Our main contribution is combining the augmented Lagrangian framework with adaptive sampling, resulting in an efficient optimization methodology validated with practical examples. To achieve the presented efficiency, we consider inexact solutions for the augmented Lagrangian subproblems, and through an adaptive sampling mechanism, we control the variance in the gradient estimates. Furthermore, we analyze the theoretical performance of the proposed scheme by showing equivalence to a gradient descent algorithm on a Moreau envelope function, and we prove sublinear convergence for convex objectives and linear convergence for strongly convex objectives with affine equality constraints. The worst-case sample complexity of the resulting algorithm, for an arbitrary choice of penalty parameter in the augmented Lagrangian function, is O(ϵ−3−δ), where ϵ > 0 is the expected error of the solution and δ > 0 is a user-defined parameter. If the penalty parameter is chosen to be O(ϵ−1), we demonstrate that the result can be improved to O(ϵ−2), which is competitive with the other methods employed in the literature. Moreover, if the objective function is strongly convex with affine equality constraints, we obtain O(ϵ−1 log(1/ϵ)) complexity. Finally, we empirically verify the performance of our adaptive sampling augmented Lagrangian framework in machine learning optimization and engineering design problems, including topology optimization of a heat sink with environmental uncertainty. Copyright © 2023, The Authors. All rights reserved.

关键词： Gradient methods

Engineering quantum states with neutral atoms

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arXiv 2024年

作者： Balewski, Jan Kornjača, Milan Klymko, Katherine Darbha, Siva Hirsbrunner, Mark R. Lopes, Pedro L.S. Liu, Fangli Camps, Daan National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA United States QuEra Computing Inc. BostonMA United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA United States Dept. of Physics Institute for Condensed Matter Theory University of Illinois at Urbana-Champaign UrbanaIL United States

Aquila, an analog quantum simulation platform developed by QuEra computing, supports control of the position and coherent evolution of up to 256 neutral atoms. This study details novel experimental protocols designed for analog quantum simulators that generate Bell state entanglement far away from the blockade regime, construct a Z2 state with a defect induced by an ancilla, and optimize the driving fields schedule to prepare excited states with enhanced fidelity. We additionally evaluate the effectiveness of readout error mitigation techniques in improving the fidelity of measurement results. All experiments were executed on Aquila from QuEra and facilitated by the AWS Braket interface. Our experimental results closely align with theoretical predictions and numerical simulations. The insights gained from this study showcase Aquila’s capabilities in handling complex quantum simulations and computations, and also pave the way for new avenues of research in quantum information processing and physics that employ programmable analog hardware platforms. Copyright © 2024, The Authors. All rights reserved.

关键词： Excited states

Multilevel-in-Layer Training for Deep Neural Network Regression

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arXiv 2022年

作者： Ponce, Colin Mao, Christina Li, Ruipeng Vassilevski, Panayot Center for Applied Scientific Computing Lawrence Livermore National Laboratory United States Global Security Computing Applications Division Lawrence Livermore National Laboratory United States Fariborz Maseeh Department of Mathematics Statistics Portland State University United States

A common challenge in regression is that for many problems, the degrees of freedom required for a high-quality solution also allows for overfitting. Regularization is a class of strategies that seek to restrict the range of possible solutions so as to discourage overfitting while still enabling good solutions, and different regularization strategies impose different types of restrictions. In this paper, we present a multilevel regularization strategy that constructs and trains a hierarchy of neural networks, each of which has layers that are wider versions of the previous network’s layers. We draw intuition and techniques from the field of Algebraic Multigrid (AMG), traditionally used for solving linear and nonlinear systems of equations, and specifically adapt the Full Approximation Scheme (FAS) for nonlinear systems of equations to the problem of deep learning. Training through V-cycles then encourage the neural networks to build a hierarchical understanding of the problem. We refer to this approach as multilevel-in-width to distinguish from prior multilevel works which hierarchically alter the depth of neural networks. The resulting approach is a highly flexible framework that can be applied to a variety of layer types, which we demonstrate with both fully-connected and convolutional layers. We experimentally show with PDE regression problems that our multilevel training approach is an effective regularizer, improving the generalize performance of the neural networks studied. © 2022, CC BY.

关键词： Deep neural networks

Teacher training at the Federal University of ABC during the Covid 2019 pandemic

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Teacher training at the Federal University of ABC during the...

International Symposium on Computers in Education (SIIE)

作者： Carolina Corrêa de Carvalho Carla Lopes Rodriguez Marcella dos Santos Abreu Center for Engineering Modeling and Applied Social Sciences (CECS) Federal University of ABC - UFABC São Bernardo do Campo SP Brazil Center for Mathematics Computing and Cognition (CMCC) Federal University of ABC - UFABC Santo André SP Brazil Center for Human Sciences and Letters (CCHL) Federal University of Piauí - UFPI Teresina PI Brazil

This article presents the formative experience called "Planejamento de Cursos Virtuais (PCV)" translated as Virtual Course Planning (VCP), which took place in 2020 at the Federal University of ABC (UFABC), a public higher education institution located in the ABC region of São Paulo, Brazil. The aim of this initiative was to address institutional demands in the emergent context of the COVID-19 pandemic, in response to the need for suspension of academic activities and the urgency to integrate digital technologies into the teaching-learning process. The methodological approach of the course prioritized the involvement of a multidisciplinary team in the planning, development, implementation, and monitoring of collaborative actions mediated in a remote format. Among the results obtained from the training, it is worth highlighting the engagement of 30% of UFABC teachers who approached dialogical practices in online education, with potential impacts on the continuity of their teaching work, as reported by participants in the evaluation of the process.

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Improved Deterministic Algorithms for Non-monotone Submodular Maximization

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arXiv 2022年

作者： Sun, Xiaoming Zhang, Jialin Zhang, Shuo Zhang, Zhijie Institute of Computing Technology Chinese Academy of Sciences Beijing China School of Computer Science and Technology University of Chinese Academy of Sciences Beijing China Center for Applied Mathematics of Fujian Province School of Mathematics and Statistics Fuzhou University Fuzhou China

Submodular maximization is one of the central topics in combinatorial optimization. It has found numerous applications in the real world. In the past decades, a series of algorithms have been proposed for this problem. However, most of the state-of-the-art algorithms are randomized. There remain non-negligible gaps with respect to approximation ratios between deterministic and randomized algorithms in submodular maximization. In this paper, we propose deterministic algorithms with improved approximation ratios for non-monotone submodular maximization. Specifically, for the matroid constraint, we provide a deterministic 0.283 − o(1) approximation algorithm, while the previous best deterministic algorithm only achieves a 1/4 approximation ratio. For the knapsack constraint, we provide a deterministic 1/4 approximation algorithm, while the previous best deterministic algorithm only achieves a 1/6 approximation ratio. For the linear packing constraints with large widths, we provide a deterministic 1/6−∊ approximation algorithm. To the best of our knowledge, there is currently no deterministic approximation algorithm for the constraints. Copyright © 2022, The Authors. All rights reserved.

关键词： Approximation algorithms

Improved Real-Time Post-Processing for Quantum Random Number Generators

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arXiv 2023年

作者： Li, Qian Sun, Xiaoming Zhang, Xingjian Zhou, Hongyi Shenzhen lnternational Center For Industrial And Applied Mathematics Shenzhen Research Institute of Big Data Shenzhen China State Key Lab of Processors Institute of Computing Technology Chinese Academy of Sciences Beijing100190 China Center for Quantum Information Institute for Interdisciplinary Information Sciences Tsinghua University Beijing100084 China

Randomness extraction is a key problem in cryptography and theoretical computer science. With the recent rapid development of quantum cryptography, quantum-proof randomness extraction has also been widely studied, addressing the security issues in the presence of a quantum adversary. In contrast with conventional quantum-proof randomness extractors characterizing the input raw data as min-entropy sources, we find that the input raw data generated by a large class of trusted-device quantum random number generators can be characterized as the so-called reverse block source. This fact enables us to design improved extractors. Specifically, we propose two novel quantum-proof randomness extractors for reverse block sources that realize real-time block-wise extraction. In comparison with the general min-entropy randomness extractors, our designs achieve a significantly higher extraction speed and a longer output data length with the same seed length. In addition, they enjoy the property of online algorithms, which process the raw data on the fly without waiting for the entire input raw data to be available. These features make our design an adequate choice for the real-time post-processing of practical quantum random number generators. Applying our extractors to the raw data generated by a widely used quantum random number generator, we achieve a simulated extraction speed as high as 300 Gbps. Copyright © 2023, The Authors. All rights reserved.

关键词： Extraction