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Accurate and Efficient Cardiac Digital Twin from surface ECGs: Insights into Identifiability of Ventricular Conduction System

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arXiv 2024年

作者： Grandits, Thomas Gillette, Karli Plank, Gernot Pezzuto, Simone Department of Mathematics and Scientific Computing University of Graz Austria Euler Institute Università della Svizzera italiana Switzerland Scientific Computing and Imaging Institute University of Utah United States Department of Biomedical Engineering University of Utah United States Gottfried Schatz Research Center: Medical Physics and Biophysics Medical University of Graz Austria BioTechMed-Graz Austria

Digital twins for cardiac electrophysiology are an enabling technology for precision cardiology. Current forward models are advanced enough to simulate the cardiac electric activity under different pathophysiological conditions and accurately replicate clinical signals like torso electrocardiograms (ECGs). In this work, we address the challenge of matching subject-specific QRS complexes using anatomically accurate, physiologically grounded cardiac digital twins. By fitting the initial conditions of a cardiac propagation model, our non-invasive method predicts activation patterns during sinus rhythm. For the first time, we demonstrate that distinct activation maps can generate identical surface ECGs. To address this non-uniqueness, we introduce a physiological prior based on the distribution of Purkinje-muscle junctions. Additionally, we develop a digital twin ensemble for probabilistic inference of cardiac activation. Our approach marks a significant advancement in the calibration of cardiac digital twins and enhances their credibility for clinical application. © 2024, CC BY-SA.

关键词： Cardiology

Scaling Laws of Graph Neural Networks for Atomistic Materials Modeling

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arXiv 2025年

作者： Li, Chaojian Ye, Zhifan Pasini, Massimiliano Lupo Choi, Jong Youl Wan, Cheng Lin, Yingyan Balaprakash, Prasanna Computational Sciences and Engineering Division Oak Ridge National Laboratory United States Computer Science and Mathematics Division Oak Ridge National Laboratory United States Computing and Computational Sciences Directorate Oak Ridge National Laboratory United States Georgia Institute of Technology United States

Atomistic materials modeling is a critical task with wide-ranging applications, from drug discovery to materials science, where accurate predictions of the target material property can lead to significant advancements in scientific discovery. Graph Neural Networks (GNNs) represent the state-of-the-art approach for modeling atomistic material data thanks to their capacity to capture complex relational structures. While machine learning performance has historically improved with larger models and datasets, GNNs for atomistic materials modeling remain relatively small compared to large language models (LLMs), which leverage billions of parameters and terabyte-scale datasets to achieve remarkable performance in their respective domains. To address this gap, we explore the scaling limits of GNNs for atomistic materials modeling by developing a foundational model with billions of parameters, trained on extensive datasets in terabyte-scale. Our approach incorporates techniques from LLM libraries to efficiently manage large-scale data and models, enabling both effective training and deployment of these large-scale GNN models. This work addresses three fundamental questions in scaling GNNs: the potential for scaling GNN model architectures, the effect of dataset size on model accuracy, and the applicability of LLM-inspired techniques to GNN architectures. Specifically, the outcomes of this study include (1) insights into the scaling laws for GNNs, highlighting the relationship between model size, dataset volume, and accuracy, (2) a foundational GNN model optimized for atomistic materials modeling, and (3) a GNN codebase enhanced with advanced LLM-based training techniques. Our findings lay the groundwork for large-scale GNNs with billions of parameters and terabyte-scale datasets, establishing a scalable pathway for future advancements in atomistic materials modeling. Copyright © 2025, The Authors. All rights reserved.

关键词： Materials properties

Monte Carlo PINNs: deep learning approach for forward and inverse problems involving high dimensional fractional partial differential equations

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arXiv 2022年

作者： Guo, Ling Wu, Hao Yu, Xiaochen Zhou, Tao Department of Mathematics Shanghai Normal University Shanghai China School of Mathematical sciences Tongji University Shanghai China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

We introduce a sampling based machine learning approach, Monte Carlo physics informed neural networks (MC-PINNs), for solving forward and inverse fractional partial differential equations (FPDEs). As a generalization of physics informed neural networks (PINNs), our method relies on deep neural network surrogates in addition to a stochastic approximation strategy for computing the fractional derivatives of the DNN outputs. A key ingredient in our MC-PINNs is to construct an unbiased estimation of the physical soft constraints in the loss function. Our directly sampling approach can yield less overall computational cost compared to fPINNs proposed in [1] and thus provide an opportunity for solving high dimensional fractional PDEs. We validate the performance of MC-PINNs method via several examples that include high dimensional integral fractional Laplacian equations, parametric identification of time-space fractional PDEs, and fractional diffusion equation with random inputs. The results show that MC-PINNs is flexible and promising to tackle high-dimensional FPDEs. © 2022, CC BY.

关键词： Deep neural networks

Force-based gradient descent method for ab initio atomic structure relaxation

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Physical Review B 2022年第10期106卷 104101-104101页

作者： Yukuan Hu Xingyu Gao Yafan Zhao Xin Liu Haifeng Song State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China University of Chinese Academy of Sciences Beijing 100049 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 China CAEP Software Center for High Performance Numerical Simulation Beijing 100088 China

Force-based algorithms for ab initio atomic structure relaxation, such as conjugate gradient methods, usually get stuck in the line minimization processes along search directions, where expensive ab initio calculations are triggered frequently to test trial positions before locating the next iterate. We present a force-based gradient descent method, WANBB, that circumvents the deficiency. At each iteration, WANBB enters the line minimization process with a trial step size capturing the local curvature of the energy surface. The exit is controlled by a nonrestrictive criterion that tends to accept early trials. These two ingredients streamline the line minimization process in WANBB. The numerical simulations on nearly 80 systems with good universality demonstrate the considerable compression of WANBB on the cost for the unaccepted trials compared with conjugate gradient methods. We also observe across the board significant and universal speedups as well as the superior robustness of WANBB over several widely used methods. The latter point is theoretically established. The implementation of WANBB is pretty simple, in that no a priori physical knowledge is required and only three parameters are present without tuning.

关键词： Crystal structure Structural properties Density functional theory development

Correction to: Optimal Error Estimates for Gegenbauer Approximations in Fractional Spaces

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Journal of scientific computing 2025年第2期103卷 1-2页

作者： Xie, Ruiyi Liu, Wenjie Wang, Haiyong Wu, Boying School of Mathematics Harbin Institute of Technology Harbin People’s Republic of China Key Laboratory of Computing and Stochastic Mathematics Ministry of Education (LCSM) Changsha People’s Republic of China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan People’s Republic of China China and Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan People’s Republic of China

Physics-constrained coupled neural differential equations for one dimensional blood flow modeling

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Computers in Biology and Medicine 2025年 186卷 109644-109644页

作者： Csala, Hunor Mohan, Arvind Livescu, Daniel Arzani, Amirhossein Department of Mechanical Engineering University of Utah Salt Lake CityUT United States Scientific Computing and Imaging Institute University of Utah Salt Lake CityUT United States Computational Physics and Methods Los Alamos National Laboratory Los AlamosNM United States

Background: computational cardiovascular flow modeling plays a crucial role in understanding blood flow dynamics. While 3D models provide acute details, they are computationally expensive, especially with fluid–structure interaction (FSI) simulations. 1D models offer a computationally efficient alternative, by simplifying the 3D Navier–Stokes equations through axisymmetric flow assumption and cross-sectional averaging. However, traditional 1D models based on finite element methods (FEM) often lack accuracy compared to 3D averaged solutions. Methods: This study introduces a novel physics-constrained machine learning technique that enhances the accuracy of 1D cardiovascular flow models while maintaining computational efficiency. Our approach, utilizing a physics-constrained coupled neural differential equation (PCNDE) framework, demonstrates superior performance compared to conventional FEM-based 1D models across a wide range of inlet boundary condition waveforms and stenosis blockage ratios. A key innovation lies in the spatial formulation of the momentum conservation equation, departing from the traditional temporal approach and capitalizing on the inherent temporal periodicity of blood flow. Results: This spatial neural differential equation formulation switches space and time and overcomes issues related to coupling stability and smoothness, while simplifying boundary condition implementation. The model accurately captures flow rate, area, and pressure variations for unseen waveforms and geometries, having 3–5 times smaller error than 1D FEM, and less than 1.2% relative error compared to 3D averaged training data. We evaluate the model's robustness to input noise and explore the loss landscapes associated with the inclusion of different physics terms. Conclusion: This advanced 1D modeling technique offers promising potential for rapid cardiovascular simulations, achieving computational efficiency and accuracy. By combining the strengths of physics-based and data-d

关键词： Digital elevation model

High-Order Discontinuous Galerkin Schemes for Radiation Hydrodynamics Equations in the Equilibrium-Diffusion Limit

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SSRN

SSRN 2023年

作者： Peng, Gang Luo, Dongmi Qiu, Jianxian Chen, Yibing Command and Control Engineering College Army Engineering University of PLA Nanjing210007 China Institute of Applied Physics and Computational Mathematics National Key Laboratory of Computational Physics Beijing100088 China School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University Fujian Xiamen361005 China

In this paper, the high-order discontinuous Galerkin (DG) schemes are presented for radiation hydrodynamics equations in the equilibrium-diffusion limit. The governor equations contain two parts, one part is a hyperbolic system of conservation laws and another part is a radiative heat transfer term. The discrete schemes are constructed in three parts and possess characteristics of the high-order, oscillation-free and efficient. Firstly, the DG method and local DG (LDG) method are respectively used to discretize the hyperbolic system and radiative heat transfer term to achieve high-order spatial accuracy. Secondly, the combination of the KXRCF shock detector, Hermite WENO limiter, and positivity-preserving limiter is utilized to enhance the robustness of the discretization schemes. Finally, the implicit-explicit schemes are employed for time discretization to enable the schemes suitable for larger time steps. Numerical experiments have verified that the new schemes are high-order accuracy, oscillation-free and efficiency. © 2023, The Authors. All rights reserved.

关键词： Hydrodynamics

MC-Nonlocal-PINNs: handling nonlocal operators in PINNs via Monte Carlo sampling

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arXiv 2022年

作者： Feng, Xiaodong Qian, Yue Shen, Wanfang Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Shandong Key Laboratory of Blockchain Finance Shandong University of Finance and Economics Jinan250014 China

We propose, Monte Carlo Nonlocal physics-informed neural networks (MC-Nonlocal-PINNs), which is a generalization of MC-fPINNs in [1], for solving general nonlocal models such as integral equations and nonlocal PDEs. Similar as in MC-fPINNs, our MC-Nonlocal-PINNs handle the nonlocal operators in a Monte Carlo way, resulting in a very stable approach for high dimensional problems. We present a variety of test problems, including high dimensional Volterra type integral equations, hypersingular integral equations and nonlocal PDEs, to demonstrate the effectiveness of our approach. © 2022, CC BY.

关键词： Deep neural networks

local properties and augmented lagrangians in fully nonconvex composite optimization

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arXiv 2023年

作者： De Marchi, Alberto Mehlitz, Patrick University of the Bundeswehr Munich Department of Aerospace Engineering Institute of Applied Mathematics and Scientific Computing Neubiberg85577 Germany Philipps-Universität Marburg Department of Mathematics and Computer Science Marburg35032 Germany

A broad class of optimization problems can be cast in composite form, that is, considering the minimization of the composition of a lower semicontinuous function with a differentiable mapping. This paper investigates the versatile template of composite optimization without any convexity assumptions. First- and second-order optimality conditions are discussed. We highlight the difficulties that stem from the lack of convexity when dealing with necessary conditions in a Lagrangian framework and when considering error bounds. Building upon these characterizations, a local convergence analysis is delineated for a recently developed augmented Lagrangian method, deriving rates of convergence in the fully nonconvex *** Codes 49J52, 49J53, 65K10, 90C30, 90C33 © 2023, CC BY.

关键词： Lagrange multipliers