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

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

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Symplectic Discretization Approach for Developing New Proximal Point Algorithm

arXiv

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arXiv 2023年

作者： Yuan, Ya-Xiang Zhang, Yi Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China

The rapid advancements in high-dimensional statistics and machine learning have increased the use of first-order methods. Many of these methods can be regarded as instances of the proximal point algorithm. Given the importance of the proximal point algorithm, there has been growing interest in developing its accelerated variants. However, some existing accelerated proximal point algorithms exhibit oscillatory behavior, which can impede their numerical convergence rate. In this paper, we first introduce an ODE system and demonstrate its o(1/t2) convergence rate and weak convergence property. Next, we apply the Symplectic Euler Method to discretize the ODE and obtain a new accelerated proximal point algorithm, which we call the Symplectic Proximal Point Algorithm. The reason for using the Symplectic Euler Method is its ability to preserve the geometric structure of the ODEs. Theoretically, we demonstrate that the Symplectic Proximal Point Algorithm achieves an o(1/k2) convergence rate and that the sequences generated by our method converge weakly to the solution set. Practically, our numerical experiments illustrate that the Symplectic Proximal Point Algorithm significantly reduces oscillatory behavior, leading to improved long-time behavior and faster numerical convergence *** Codes 47J20, 47H05, 65K15, 65Y20, 90C25, 90C52 © 2023, CC BY.

关键词： Lyapunov functions

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Quantized Constant-Envelope Waveform Design for Massive MIMO DFRC Systems

arXiv

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arXiv 2024年

作者： Wu, Zheyu Liu, Ya-Feng Chen, Wei-Kun Masouros, Christos The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The School of Mathematics and Statistics Beijing Key Laboratory on MCAACI Beijing Institute of Technology Beijing100081 China The Department of Electronic and Electrical Engineering University College London Torrington Place LondonWC1E 7JE United Kingdom

Both dual-functional radar-communication (DFRC) and massive multiple-input multiple-output (MIMO) have been recognized as enabling technologies for 6G wireless networks. This paper considers the advanced waveform design for hardware-efficient massive MIMO DFRC systems. Specifically, the transmit waveform is imposed with the quantized constant-envelope (QCE) constraint, which facilitates the employment of low-resolution digital-to-analog converters (DACs) and power-efficient amplifiers. The waveform design problem is formulated as the minimization of the mean square error (MSE) between the designed and desired beampatterns subject to the constructive interference (CI)-based communication quality of service (QoS) constraints and the QCE constraint. To solve the formulated problem, we first utilize the penalty technique to transform the discrete problem into an equivalent continuous penalty model. Then, we propose an inexact augmented Lagrangian method (ALM) algorithm for solving the penalty model. In particular, the ALM subproblem at each iteration is solved by a custom-built block successive upper-bound minimization (BSUM) algorithm, which admits closed-form updates, making the proposed inexact ALM algorithm computationally efficient. Simulation results demonstrate the superiority of the proposed approach over existing state-of-the-art ones. In addition, extensive simulations are conducted to examine the impact of various system parameters on the trade-off between communication and radar performances. Copyright © 2024, The Authors. All rights reserved.

关键词： Mean square error

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Derivative-Free Optimization with Transformed Objective Functions (DFOTO) and the Algorithm Based on the Least Frobenius Norm Updating Quadratic Model

arXiv

引用

arXiv 2023年

作者： Xie, Peng-Cheng Yuan, Ya-Xiang State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Zhong Guan Cun Donglu 55 Beijing100190 China University of Chinese Academy of Sciences Zhong Guan Cun Donglu 55 Beijing100190 China

Derivative-free optimization (DFO) problems are optimization problems where the derivative information is unavailable. The least Frobenius norm updating quadratic interpolation model function is one of the essential under-determined model functions for model-based derivative-free trust-region methods. This article proposes derivative-free optimization with transformed objective functions (DFOTO) and gives a model-based trust-region method with the least Frobenius norm model. The model updating formula is based on Powell’s formula and can be easily implemented. The method shares the same framework with those for problems without transformations, and its query scheme is given. We propose the definitions related to optimality-preserving transformations to understand the interpolation model in our method when minimizing transformed objective functions. We prove the existence of model optimality-preserving transformations beyond translation transformations. The necessary and sufficient condition for such transformations is given. An interesting discovery is that, as a fundamental transformation, the affine transformation with a (non-trivial) positive multiplication coefficient is not model optimality-preserving. We also analyze the corresponding least Frobenius norm updating model and its interpolation error when the objective function is affinely transformed. The convergence property of a provable algorithmic framework containing the least Frobenius norm updating quadratic model for minimizing transformed objective functions is given. Numerical results show that our method can successfully solve most test problems with objective optimality-preserving transformations, even though some of such transformations will change the optimality of the model function. To our best knowledge, this is the first work providing the model-based derivative-free algorithm and analysis for transformed problems with the function evaluation oracle. This article also proposes the "moving-targe

关键词： Interpolation

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A New Two-dimensional Model-based Subspace Method for Large-scale Unconstrained Derivative-free Optimization: 2D-MoSub

arXiv

引用

arXiv 2023年

作者： Xie, Pengcheng Yuan, Ya-Xiang State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Zhong Guan Cun Donglu No.55 Beijing China University of Chinese Academy of Sciences Zhong Guan Cun Donglu No.55 Beijing China

This paper proposes the method 2D-MoSub (2-dimensional model-based subspace method), which is a novel derivative-free optimization (DFO) method based on the subspace method for general unconstrained optimization and especially aims to solve large-scale DFO problems. Our method combines 2-dimensional quadratic interpolation models and trust-region techniques to iteratively update the points and explore the 2-dimensional subspace. Its framework includes initialization, constructing the interpolation set, building the quadratic interpolation model, performing trust-region trial steps, and updating the trust-region radius and subspace. We introduce the framework and computational details of 2D-MoSub, and discuss the poisedness and quality of the interpolation set in the corresponding 2-dimensional subspace. We also analyze some properties of our method, including the model’s approximation error with projection property and the algorithm’s convergence. Numerical results demonstrate the effectiveness and efficiency of 2D-MoSub for solving a variety of unconstrained optimization *** Codes 90C56, 90C30, 65K05, 90C90 Copyright © 2023, The Authors. All rights reserved.

关键词： Interpolation

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An Efficient Benders Decomposition Approach for Optimal Large-Scale Network Slicing

arXiv

引用

arXiv 2023年

作者： Chen, Wei-Kun Wu, Zheyu Zhang, Rui-Jin Liu, Ya-Feng Dai, Yu-Hong Luo, Zhi-Quan The School of Mathematics and Statistics Beijing Key Laboratory on MCAACI Beijing Institute of Technology Beijing100081 China The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The Shenzhen Research Institute of Big Data The Chinese University of Hong Kong Shenzhen518172 China

This paper considers the network slicing (NS) problem which attempts to map multiple customized virtual network requests to a common shared network infrastructure and allocate network resources to meet diverse service requirements. This paper proposes an efficient customized Benders decomposition algorithm for globally solving the large-scale NP-hard NS problem. The proposed algorithm decomposes the hard NS problem into two relatively easy function placement (FP) and traffic routing (TR) subproblems and iteratively solves them enabling the information feedback between each other, which makes it particularly suitable to solve large-scale problems. Specifically, the FP subproblem is to place service functions into cloud nodes in the network, and solving it can return a function placement strategy based on which the TR subproblem is defined;and the TR subproblem is to find paths connecting two nodes hosting two adjacent functions in the network, and solving it can either verify that the solution of the FP subproblem is an optimal solution of the original problem, or return a valid inequality to the FP subproblem that cuts off the current infeasible solution. The proposed algorithm is guaranteed to find the globally optimal solution of the NS problem. By taking the special structure of the NS problem into consideration, we successfully develop two families of valid inequalities that render the proposed algorithm converge much more quickly and thus much more efficient. Numerical results demonstrate that the proposed valid inequalities effectively accelerate the convergence of the decomposition algorithm, and the proposed algorithm significantly outperforms the existing algorithms in terms of both solution efficiency and quality. Copyright © 2023, The Authors. All rights reserved.

关键词： Resource allocation

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Helmholtz decomposition based windowed Green function methods for elastic scattering problems on a half-space

arXiv

引用

arXiv 2023年

作者： Yin, Tao Zhang, Lu Zheng, Weiying Zhu, Xiaopeng LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences Zhejiang University Hangzhou310027 China LSEC NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China School of Mathematical Science University of Chinese Academy of Sciences Beijing100049 China

This paper proposes a new Helmholtz decomposition based windowed Green function (HD-WGF) method for solving the time-harmonic elastic scattering problems on a half-space with Dirichlet boundary conditions in both 2D and 3D. The Helmholtz decomposition is applied to separate the pressure and shear waves, which satisfy the Helmholtz and Helmholtz/Maxwell equations, respectively, and the corresponding boundary integral equations of type (I + T) = f, that couple these two waves on the unbounded surface, are derived based on the free-space fundamental solution of Helmholtz equation. This approach avoids the treatment of the complex elastic displacement tensor and traction operator that involved in the classical integral equation method for elastic problems. Then a smooth "slow-rise" windowing function is introduced to truncate the boundary integral equations and a "correction" strategy is proposed to ensure the uniformly fast convergence for all incident angles of plane incidence. Numerical experiments for both two and three dimensional problems are presented to demonstrate the accuracy and efficiency of the proposed method. Copyright © 2023, The Authors. All rights reserved.

关键词： Boundary integral equations

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Improved Turbo Message Passing for Compressive Robust Principal Component Analysis: Algorithm Design and Asymptotic Analysis

arXiv

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arXiv 2024年

作者： He, Zhuohang Ma, Junjie Yuan, Xiaojun The National Key Laboratory of Wireless Communications University of Electronic Science and Technology of China Chengdu611731 China The Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100864 China

Compressive Robust Principal Component Analysis (CRPCA) naturally arises in various applications as a means to recover a low-rank matrix low-rank matrix L and a sparse matrix S from compressive measurements. In this paper, we approach the problem from a Bayesian inference perspective. We establish a probabilistic model for the problem and develop an improved turbo message passing (ITMP) algorithm based on the sum-product rule and the appropriate approximations. Additionally, we establish a state evolution framework to characterize the asymptotic behavior of the ITMP algorithm in the large-system limit. By analyzing the established state evolution, we further propose sufficient conditions for the global convergence of our algorithm. Our numerical results validate the theoretical results, demonstrating that the proposed asymptotic framework accurately characterize the dynamical behavior of the ITMP algorithm, and the phase transition curve specified by the sufficient condition agrees well with numerical simulations. © 2024, CC BY.

关键词： Asymptotic analysis

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A PRE-TRAINING DEEP LEARNING METHOD FOR SIMULATING THE LARGE BENDING DEFORMATION OF BILAYER PLATES

arXiv

引用

arXiv 2023年

作者： Li, Xiang Liao, Yulei Ming, Pingbing LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We propose a deep learning based method for simulating the large bending deformation of bilayer plates. Inspired by the greedy algorithm, we propose a pre-training method on a series of nested domains, which accelerate the convergence of training and find the absolute minimizer more effectively. The proposed method exhibits the capability to converge to an absolute minimizer, overcoming the limitation of gradient flow methods getting trapped in the local minimizer basins. We showcase better performance with fewer numbers of degrees of freedom for the relative energy errors and relative L2-errors of the minimizer through numerical experiments. Furthermore, our method successfully maintains the L2-norm of the isometric constraint, leading to an improvement of *** Codes 39-08, 49S05, 65K10, 65Q20, 74-10, 74K20, 74G65 Copyright © 2023, The Authors. All rights reserved.

关键词： Degrees of freedom (mechanics)

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SPECTRAL BARRON SPACE AND DEEP NEURAL NETWORK APPROXIMATION

arXiv

引用

arXiv 2023年

作者： Liao, Yulei Ming, Pingbing LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We prove the sharp embedding between the spectral Barron space and the Besov space. Given the spectral Barron space as the target function space, we prove a dimension-free result that if the neural network contains L hidden layers with N units per layer, then the upper and lower bounds of the L2-approximation error are O(N−sL) with 0 MSC Codes 32C22, 32K05, 33C20, 41A25, 41A46, 42A38, 68T07 Copyright © 2023, The Authors. All rights reserved.

关键词： Deep neural networks

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