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Research on Multimodal Brain Tumor Segmentation Algorithm Based on Feature Decoupling and Information Bottleneck Theory

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Computers, Materials & Continua 2025年第2期82卷 3281-3307页

作者： Xuemei Yang Yuting Zhou Shiqi Liu Junping Yin China Academy of Engineering Physics Graduate SchoolBeijing100193China Shanghai Zhangjiang Institute of Mathematics Biomedical LaboratoryShanghai201203China Institute of Applied Physics and Computational Mathematics Tang Chuang CentreBeijing100094China

Aiming at the problems of information loss and the relationship between features and target tasks in multimodal medical image segmentation, a multimodal medical image segmentation algorithm based on feature decoupling and information bottleneck theory is proposed in this paper. Based on the reversible network, the bottom-up learning method for different modal information is constructed, which enhances the features’ expression ability and the network’s learning ability. The feature fusion module is designed to balance multi-directional information flow. To retain the information relevant to the target task to the maximum extent and suppress the information irrelevant to the target task, the feature decoupling module is designed to ensure a strong correlation between the feature and the target task. A loss function based on information bottleneck theory was intended to improve information quality and remove redundant information. Based on BraTs2021, BraTs2023-MET and ANNLIB datasets, the proposed algorithm is analyzed qualitatively and quantitatively in this paper. In the quantitative experiment, the Dice coefficient of the proposed algorithm was increased by 0.110 on average compared with other methods, and the HD95 was decreased by 28.568 on average compared with other methods. In qualitative analysis, the proposed algorithm can effectively segment the incoherent region between the lesion and the lesion boundary and achieve accurate segmentation of the lesion.

关键词： Image fusion image segmentation deep learning

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The High-Order Variable-Coefficient Explicit-Implicit-Null Method for Diffusion and Dispersion Equations

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应用数学与计算数学学报 2025年第1期7卷 115-150页

作者： Meiqi Tan Juan Cheng Chi-Wang Shu Graduate School China Academy of Engineering PhysicsBeijing 100088China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088China HEDPS Center for Applied Physics and TechnologyCollege of EngineeringPeking UniversityBeijing 100871China Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA

For the high-order diffusion and dispersion equations,the general practice of the explicit-implicit-null(EIN)method is to add and subtract an appropriately large linear highest derivative term with a constant coefficient at one side of the equation,and then apply the standard implicit-explicit method to the equivalent *** call this approach the con-stant-coefficient EIN method in this paper and hereafter denote it by"CC-EIN".To reduce the error in the CC-EIN method,the variable-coefficient explicit-implicit-null(VC-EIN)method,which is obtained by adding and subtracting a linear highest derivative term with a variable coefficient,is proposed and studied in this *** with the local discon-tinuous Galerkin(LDG)spatial discretization,the VC-EIN method is shown to be uncon-ditionally stable and can achieve high order of accuracy for both one-dimensional and two-dimensional quasi-linear and nonlinear *** addition,although the computational cost slightly increases,the VC-EIN method can obtain more accurate results than the CC-EIN method,if the diffusion coefficient or the dispersion coefficient has a few high and narrow bumps and the bumps only account for a small part of the whole computational domain.

关键词： Diffusion equation Dispersion equation Stability Explicit-implicit-null(EIN)time discretization Local discontinuous Galerkin(LDG)method

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Optimizations and applications in large-scale scenes of Monte Carlo geometry conversion code CMGC

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Nuclear Science and Techniques 2025年第4期36卷 220-232页

作者： Xin Wang Ling-Yu Zhang Xue-Ming Shi Zhen Wu Jun-Li Li Gui-Ming Qin Yuan-Guang Fu CAEP Software Center for High Performance Numerical Simulation Beijing 100088China Institute of Applied Physics and Computational Mathematics Beijing 100088China Department of Engineering Physics Tsinghua UniversityBeijing 100084China

In response to the demand for rapid geometric modeling in Monte Carlo radiation transportation calculations for large-scale and complex geometric scenes,functional improvements,and algorithm optimizations were performed using CAD-to-Monte Carlo geometry conversion(CMGC)*** representation(BRep)to constructive solid geometry(CSG)conversion and visual CSG modeling were combined to address the problem of non-convertible geometries such as spline *** splitting surface assessment method in BRep-to-CSG conversion was optimized to reduce the number of Boolean operations using an Open ***,in turn,reduced the probability of CMGC conversion *** auxiliary surface generation algorithm was optimized to prevent the generation of redundant auxiliary surfaces that cause an excessive decomposition of CAD geometry *** optimizations enhanced the usability and stability of the CMGC model *** was applied successfully to the JMCT transportation calculations for the conceptual designs of five China Fusion Engineering Test Reactor(CFETR)*** rapid replacement of different blanket schemes was achieved based on the baseline CFETR *** geometric solid number of blankets ranged from hundreds to tens of *** correctness of the converted CFETR models using CMGC was verified through comparisons with the MCNP calculation *** CMGC supported radiation field evaluations for a large urban scene and detailed ship *** enabled the rapid conversion of CAD models with thousands of geometric solids into Monte Carlo CSG *** analysis of the JMCT transportation simulation results further demonstrated the accuracy and effectiveness of the CMGC.

关键词： Monte Carlo CAD BRep to CSG CMGC

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Soliton resolution for the energy-critical wave equation with an inverse-square potential in the radial case

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Science China mathematics 2025年

作者： Xuanying Li Changxing Miao Lifeng Zhao School of Mathematical Sciences University of Science and Technology of China Institute of Applied Physics and Computational Mathematics

In this paper, we present the soliton resolution for the energy-critical wave equation with an inverse square potential in the radial case and all dimensions N≥3. A crucial ingredient of our analysis involves the energy channel for the linearized wave equation with inverse square potentials, which incorporates the distorted Hankel transform.

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Semi-Supervised Deep Sobolev Regression: Estimation and Variable Selection by ReQU Neural Network

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IEEE Transactions on Information Theory 2025年第4期71卷 2955-2981页

作者： Ding, Zhao Duan, Chenguang Jiao, Yuling Yang, Jerry Zhijian Wuhan University School of Mathematics and Statistics Hubei Wuhan430072 China Wuhan University School of Artificial Intelligence National Center for Applied Mathematics in Hubei Hubei Key Laboratory of Computational Science School of Mathematics and Statistics Hubei Wuhan430072 China Wuhan University National Center for Applied Mathematics in Hubei Wuhan Institute for Math & Al School of Mathematics and Statistics Hubei Key Laboratory of Computational Science Hubei Wuhan430072 China

We propose SDORE, a Semi-supervised Deep SObolev REgressor, for the nonparametric estimation of the underlying regression function and its gradient. SDORE employs deep ReQU neural networks to minimize the empirical risk with gradient norm regularization, allowing the approximation of the regularization term by unlabeled data. Our study includes a thorough analysis of the convergence rates of SDORE in L2-norm, achieving the minimax optimality. Further, we establish a convergence rate for the associated plug-in gradient estimator, even in the presence of significant domain shift. These theoretical findings offer valuable insights for selecting regularization parameters and determining the size of the neural network, while showcasing the provable advantage of leveraging unlabeled data in semi-supervised learning. To the best of our knowledge, SDORE is the first provable neural network-based approach that simultaneously estimates the regression function and its gradient, with diverse applications such as nonparametric variable selection. The effectiveness of SDORE is validated through an extensive range of numerical simulations. © 1963-2012 IEEE.

关键词： Self-supervised learning

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Towards Model Discovery Using Domain Decomposition and PINNs 11

Towards Model Discovery Using Domain Decomposition and PINNs

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11th Vienna International Conference on Mathematical Modelling, MATHMOD 2025

作者： Saha, Tirtho S. Heinlein, Alexander Reisch, Cordula Institute of Mechanics and Computational Mechanics Leibniz University Hannover Germany Delft Institute of Applied Mathematics Netherlands Institute for Partial Differential Equations TU Braunschweig Germany

We enhance machine learning algorithms for learning model parameters in complex systems represented by differential equations with domain decomposition methods. The study evaluates the performance of two approaches, namely (vanilla) Physics-Informed Neural Networks (PINNs) and Finite Basis Physics-Informed Neural Networks (FBPINNs), in learning the dynamics of test models with a quasi-stationary longtime behavior. We test the approaches for data sets in different dynamical regions and with varying noise level. As results, the FBPINN approach better captures the overall dynamical behavior compared to the vanilla PINN approach, even in cases with data only from a time domain with quasi-stationary dynamics. Copyright © 2025 The Authors.

关键词： Domain decomposition methods

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Self-consistent pressure-dependent on-site Coulomb correction for zero-temperature equations of state of f-electron metals

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Physical Review B 2025年第11期111卷 115139-115139页

作者： Bei-Lei Liu Yue-Chao Wang Xingyu Gao Hai-Feng Liu National Key Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing 100094 China

The f-electron materials display many anomalous properties under pressure, making them of great interest in high-pressure physics and related industrial fields. However, the f-electrons pose a substantial challenge to simulations since the electron correlation effects. In this work, we present a first-principles calculation scheme for the equations of state (EoS) of f-electron materials. The self-consistent pressure-dependent on-site Coulomb correction is performed based on our recently developed doubly screened Coulomb correction approach. We investigated pressure dependence of the on-site Coulomb interaction, zero-temperature EoS over a wide range of pressures and the phase stabilities of four prototypical lanthanide and actinide metals, Pr, Eu, Th, and U. The simulated compressive properties agree better with the experimental data than those obtained by conventional density functional theory (DFT) and fixed-parameter DFT+U approaches. The pressure-induced phase transitions can also be well described.

关键词： Coulomb interactions

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Predator Prey Scavenger Model using Holling’s Functional Response of Type III and Physics-Informed Deep Neural Networks

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International Journal of applied and computational mathematics 2025年第2期11卷 1-32页

作者： Panchal, Aneesh Beniwal, Kirti Kumar, Vivek Department of Computational and Data Sciences Indian Institute of Science Karnataka Bangalore 560012 India Department of Applied Mathematics Delhi Technological University Delhi New Delhi 110042 India

Nonlinear mathematical models introduce the relation between various physical and biological interactions present in nature. One of the most famous models is the Lotka–Volterra model which defined the interaction between predator and prey species present in nature. However, predators, scavengers, and prey populations coexist in a natural system where scavengers can additionally rely on the dead bodies of predators present in the system. Keeping this in mind, the formulation and simulation of the predator–prey scavenger model is introduced in this paper. For the predation response, respective prey species are assumed to have Holling’s functional response of type III. The proposed model is tested for various simulations and is found to be showing satisfactory results in different scenarios. After simulations, the American forest dataset is taken for parameter estimation which imitates the real-world case. For parameter estimation, a physics-informed deep neural network is used with the Adam backpropagation method which prevents the avalanche effect in trainable parameters updation. For neural networks, mean square error and physics-informed informed error are considered. After the neural network, the hence-found parameters are fine-tuned using the Broyden–Fletcher–Goldfarb–Shanno algorithm. Finally, the hence-found parameters using a natural dataset are tested for stability using Jacobian stability analysis. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2025.

关键词： Broyden–Fletcher–Goldfarb–Shanno optimization Physics-informed deep neural network Predator prey scavenger model Stability analysis

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Theoretical investigation of the laser-induced three-dimensional vibration excitation of neutral N2Ar

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Physical Review A 2025年第4期111卷 042822-042822页

作者： Ting Xu YinSong Tang Xiaoqing Hu JinPeng Ma SiQi Pei CongCong Jia Yong Wu JianGuo Wang National Key Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 China

In this paper, the laser-driven three-dimensional vibration excitation dynamics of N2Ar dimer are simulated using the full time-dependent wave-packet simulation method. The three-dimensional vibrational wave functions are obtained first by solving the Schrödinger equation involving the rotation of N2, vibration of N2-Ar, and intermolecular interaction. The solved vibration wave functions have both the angular quantum number m and the symmetric or antisymmetric properties with respect to the N2-Ar axis. The theoretical calculation shows that laser-induced molecular vibrational excitation needs to satisfy the selection rules of nonresonant Raman processes. Two modes of excitation are further distinguished as follows: (1) Δm=±2 and the symmetry does not change; here, the van der Waals bond will be strengthened. (2) Δm=±1 and the symmetry is reversed; here, the dimer will be partially excited into a linear structure. Our results point out that the N2Ar initially located in the ground vibrational state mainly prefers the excitation of mode (1), but the one located in the first excited state will undergo two modes of excitation simultaneously.

关键词： Van der Waals forces

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Chemical reaction mechanisms and models of energetic materials: A perspective

Energetic Materials Frontiers

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Energetic Materials Frontiers 2025年第1期6卷 129-144页

作者： Meng, Li Song, Qing-guan Yao, Chuang Zhang, Lei Pang, Si-ping School of Materials Science & Engineering Beijing Institute of Technology Beijing100081 China Institute of Applied Physics and Computational Mathematics Beijing100088 China Institute of Chemical Materials China Academy of Engineering Physics Mianyang621999 China of Chongqing School of Materials Science and Engineering Yangtze Normal University Chongqing408100 China

Energetic materials (EMs) are a kind of metastable functional materials with certain potential barriers, overcoming which can quickly release the energy stored in EMs. A thorough understanding of reaction mechanisms and accurate quantification of reaction rates are fundamental issues for optimizing energy output, ensuring hazard mitigation, and assessing the safety levels of EMs. This perspective provides an overview of research progress in chemical reaction mechanisms and models, with a particular emphasis on organic EMs and reactive metals. Organic EMs are mainly composed of carbon, hydrogen, nitrogen, and oxygen elements, enabling supersonic and self-sustaining detonation reactions capable of significant energy output. The incorporation of reactive metals like aluminum, magnesium, and boron has been recently found to augment the combustion heat and explosion temperature of EM formulations, sparking heightened research interest. This perspective first presents both EMs’ reaction mechanisms revealed via multiscale simulations and experimental methods, including thermal decomposition, shock initiation, and post combustion. Then, quantitatively characterized expressions of the physical models derived from the revealed mechanisms, including mathematical expressions like elementary and phenomenological reaction kinetic models, and emerging data-driven machine learning models, are reviewed. Finally, the view of the application, existing problems, and further development directions are outlined. © 2024 The Authors

关键词： Reaction rates

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