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Dynamic & norm-based weights to normalize imbalance in back-propagated gradients of physics-informed neural networks 基于动态和范数的权重来归一化物理信息神经网络反向传播梯度中的不平衡
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-07-04 DOI: 10.1088/2399-6528/ace416
S. Deguchi, M. Asai
Physics-Informed Neural Networks (PINNs) have been a promising machine learning model for evaluating various physical problems. Despite their success in solving many types of partial differential equations (PDEs), some problems have been found to be difficult to learn, implying that the baseline PINNs is biased towards learning the governing PDEs while relatively neglecting given initial or boundary conditions. In this work, we propose Dynamically Normalized Physics-Informed Neural Networks (DN-PINNs), a method to train PINNs while evenly distributing multiple back-propagated gradient components. DN-PINNs determine the relative weights assigned to initial or boundary condition losses based on gradient norms, and the weights are updated dynamically during training. Through several numerical experiments, we demonstrate that DN-PINNs effectively avoids the imbalance in multiple gradients and improves the inference accuracy while keeping the additional computational cost within a reasonable range. Furthermore, we compare DN-PINNs with other PINNs variants and empirically show that DN-PINNs is competitive with or outperforms them. In addition, since DN-PINN uses exponential decay to update the relative weight, the weights obtained are biased toward the initial values. We study this initialization bias and show that a simple bias correction technique can alleviate this problem.
物理知情神经网络(PINN)是一种很有前途的机器学习模型,用于评估各种物理问题。尽管它们在求解许多类型的偏微分方程(PDE)方面取得了成功,但已经发现一些问题很难学习,这意味着基线PINN偏向于学习控制偏微分方程,而相对忽略给定的初始或边界条件。在这项工作中,我们提出了动态归一化物理知情神经网络(DN-PINN),这是一种在均匀分布多个反向传播梯度分量的情况下训练PINN的方法。DN PINN基于梯度范数确定分配给初始或边界条件损失的相对权重,并且在训练期间动态更新权重。通过几个数值实验,我们证明了DN-PINN有效地避免了多个梯度中的不平衡,提高了推理精度,同时将额外的计算成本保持在合理的范围内。此外,我们将DN PINN与其他PINN变体进行了比较,并从经验上表明DN PINN具有竞争力或优于它们。此外,由于DN-PINN使用指数衰减来更新相对权重,因此获得的权重偏向初始值。我们研究了这种初始化偏差,并表明一种简单的偏差校正技术可以缓解这个问题。
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引用次数: 0
Current-density functional theory for bosonic superfluids 玻色子超流体的电流密度泛函理论
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-07-01 DOI: 10.1088/2399-6528/ace236
Tomoya Aizawa, M. Higuchi, K. Higuchi
A finite-temperature current-density functional theory for bosonic superfluids (sf-CDFT) in the thermal equilibrium state is proposed herein. In the sf-CDFT, hydrodynamic physical quantities, such as particle number density, current density, and the order parameter of the Bose–Einstein condensation, are chosen as the basic variables. This theory enables the simultaneous reproduction of the particle number and current densities of both the superfluid and normal fluid components with incorporating effects of the interaction between these components. Specifically, these components are determined by solving two single-particle equations, i.e., the Gross–Pitaevskii–Kohn–Sham and Kohn–Sham equations. Furthermore, using the continuity equation of superfluids, we present the sum rule for the exchange-correlation energy functional of the sf-CDFT, which is useful for developing the approximate form.
本文提出了玻色子超流体在热平衡状态下的有限温度电流密度泛函理论。在sf CDFT中,流体动力学物理量,如粒子数密度、电流密度和玻色-爱因斯坦凝聚的阶参数,被选为基本变量。该理论能够同时再现超流体和正常流体组分的粒子数和电流密度,并结合这些组分之间的相互作用的影响。具体而言,这些分量是通过求解两个单粒子方程来确定的,即Gross–Pitaevskii–Kohn–Sham和Kohn–Sham方程。此外,利用超流体的连续性方程,我们给出了sf-CDFT交换相关能函数的和规则,这对发展近似形式是有用的。
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引用次数: 0
A generalized scattering theory in quantum mechanics 量子力学中的广义散射理论
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-07-01 DOI: 10.1088/2399-6528/acde44
Huai-Yu Wang
In quantum mechanics textbooks, a single-particle scattering theory is introduced. In the present work, a generalized scattering theory is presented, which can be in principle applied to the scattering problems of arbitrary number of particle. In laboratory frame, a generalized Lippmann-Schwinger scattering equation is derived. We emphasized that the derivation is rigorous, even for treating infinitesimals. No manual operation such as analytical continuation is allowed. In the case that before scattering N particles are plane waves and after the scattering they are new plane waves, the transition amplitude and transition probability are given and the generalized S matrix is presented. It is proved that the transition probability from a set of plane waves to a new set of plane waves of the N particles equal to that of the reciprocal process. The generalized theory is applied to the cases of one- and two-particle scattering as two examples. When applied to single-particle scattering problems, our generalized formalism degrades to that usually seen in the literature. When our generalized theory is applied to two-particle scattering problems, the formula of the transition probability of two-particle collision is given. It is shown that the transition probability of the scattering of two free particles is identical to that of the reciprocal process. This transition probability and the identity are needed in deriving Boltzmann transport equation in statistical mechanics. The case of identical particles is also discussed.
在量子力学教科书中,介绍了单粒子散射理论。本文提出了广义散射理论,该理论原则上可以应用于任意数目粒子的散射问题。在实验室框架下,导出了广义Lippmann-Schwinger散射方程。我们强调推导是严格的,即使对于处理无穷小。不允许进行分析延拓等人工操作。在散射前N个粒子为平面波,散射后N个粒子为新平面波的情况下,给出了粒子的跃迁幅度和跃迁概率,并给出了广义S矩阵。证明了N个粒子从一组平面波到另一组平面波的跃迁概率等于互反过程的跃迁概率。将广义理论应用于单粒子散射和双粒子散射两个例子。当应用于单粒子散射问题时,我们的广义形式退化为通常在文献中看到的形式。将广义理论应用于两粒子散射问题时,给出了两粒子碰撞跃迁概率的计算公式。结果表明,两个自由粒子散射的跃迁概率与互反过程的跃迁概率相同。统计力学中玻尔兹曼输运方程的推导需要这种跃迁概率和恒等式。我们还讨论了相同粒子的情况。
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引用次数: 0
Retraction notice – ‘Entropy optimization in MHD nanofluid flow over a curved exponentially stretching surface with binary chemical reaction and Arrhenius activation energy’ Saeed Islam et al 2020 J. Phys. Commun. 4 075021 撤回通知-“具有二元化学反应和阿伦尼乌斯活化能的MHD纳米流体在弯曲指数拉伸表面上流动的熵优化”Saeed Islam et al . 2020 J. physics。4 075021
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-06-01 DOI: 10.1088/2399-6528/accdcc
S. Islam
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引用次数: 0
Non-reciprocal transmission of coupled LC resonators through parity-time symmetry breaking 偶偶时间对称性破缺耦合LC谐振腔的非互易传输
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-06-01 DOI: 10.1088/2399-6528/acdbbb
Yi Zhou, Hao Wang, Lifeng Wang, Lei Dong, Qing-An Huang
Non-reciprocal devices that allow a signal to be transmitted only in one direction are important for full-duplex communications. Due to the requirements of miniaturized systems, there has been an increase interest in non-magnetic non-reciprocal devices in recent years. Based on parity-time (PT) symmetric inductors-capacitors (LC) resonators, this paper has proposed non-reciprocal transmission configurations by PT-symmetry breaking. In the configuration, the coupled capacitance between the two coupled LC resonators can be adjusted so that the transmission frequency is tunable. At the same time, the resonant frequency and transmission frequency have been discriminated to optimize the non-reciprocal transmission. The configuration has been implemented by utilizing discrete components on a printed circuit board (PCB). It demonstrates that the center operation frequency of 14.05 MHz with the bandwidth 4 MHz, the insertion loss 0.32 dB, and the isolation 11 dB is adjusted to the center operation frequency of 14.95 MHz with the bandwidth 4.6 MHz, the insertion loss 0.716 dB, and the isolation 14.5 dB.
允许信号仅在一个方向上传输的非互易设备对于全双工通信是重要的。由于小型化系统的要求,近年来人们对非磁性非互易器件越来越感兴趣。基于奇偶时间(PT)对称电感器-电容器(LC)谐振器,提出了PT对称破缺的非互易传输配置。在该配置中,可以调节两个耦合LC谐振器之间的耦合电容,使得传输频率是可调谐的。同时,对谐振频率和传输频率进行了区分,以优化非互易传输。该配置是通过利用印刷电路板(PCB)上的分立元件来实现的。结果表明,将带宽为4MHz、插入损耗为0.32dB、隔离度为11dB的中心工作频率14.05MHz调整为带宽为4.6MHz、插入损耗0.716dB、隔离性为14.5dB的中心操作频率14.95MHz。
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引用次数: 0
Bending of electric field lines and light-ray trajectories in a static gravitational field 静电引力场中电场线和光线轨迹的弯曲
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-06-01 DOI: 10.1088/2399-6528/acdc83
A. Singal
It is well known that the light-ray trajectories follow a curved path in a gravitational field. This has been confirmed observationally where light rays coming from distant astronomical objects are seen to get bent in Sun’s gravitational field. We explore here the bending of electric field lines due to gravity. We determine, from a theoretical perspective, not only the exact shapes of the bent trajectories of light rays, emitted isotropically by a source supported in a gravitational field, but also demonstrate that the electric field lines of a charge, supported in a gravitational field, follow exactly the trajectories of light rays emitted isotropically from a source at the charge location. From a detailed examination of the electrostatic field of a charge accelerated uniformly in the instantaneous rest frame, exploiting the strong principle of equivalence, we determine the bending of the electric field lines of a charge in a gravitational field. The fraction of electric field lines crossing a surface, stationary above or below the charge in the gravitational field, are shown to be exactly similar to the fraction of light-ray trajectories intersecting that surface, emanating from a source lying at the charge location. On the other hand, for a freely falling charge in the gravitational field there is no such bending of electric field lines. The field lines continue to extend in radial straight lines from the instantaneous ‘present’ position of the charge, as do the trajectories of light rays spreading away from the instantaneous position of a freely falling source in the gravitational field. The electric field configuration of a freely falling charge in the gravitational field is shown to be exactly the same as that of a charge moving uniformly in an inertial frame with velocity equal to the instantaneous ‘present’ velocity of the freely falling charge.
众所周知,光线轨迹在引力场中遵循弯曲路径。这一点在观测中得到了证实,来自遥远天体的光线在太阳引力场中弯曲。我们在这里探索电场线由于重力而弯曲的现象。从理论角度来看,我们不仅确定了由引力场中支撑的光源各向同性发射的光线弯曲轨迹的确切形状,而且证明了在引力场中支持的电荷的电场线完全遵循从电荷位置的光源各向异性发射的光线轨迹。通过对在瞬时静止框架中均匀加速的电荷的静电场的详细检查,利用强等效原理,我们确定了电荷在引力场中的电场线的弯曲。穿过重力场中电荷上方或下方静止的表面的电场线的分数与从位于电荷位置的源发出的与该表面相交的光线轨迹的分数完全相似。另一方面,对于重力场中自由下落的电荷,电场线不存在这种弯曲。磁力线继续从电荷的瞬时“当前”位置以径向直线延伸,从引力场中自由下落源的瞬时位置传播的光线轨迹也是如此。自由下落电荷在引力场中的电场配置与在惯性系中均匀移动的电荷的电场配置完全相同,其速度等于自由下落电荷的瞬时“当前”速度。
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引用次数: 0
Temperature-induced hysteresis in amplification and attenuation of surface-plasmon-polariton waves 表面等离子体激元波放大和衰减过程中的温度滞后现象
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-05-31 DOI: 10.1088/2399-6528/acda7a
T. Mackay, T. Son, A. Haché, A. Lakhtakia
The propagation of surface-plasmon-polariton (SPP) waves at the planar interface of a metal and a dielectric material was investigated for a dielectric material with strongly temperature-dependent constitutive properties. The metal was silver and the dielectric material was vanadium multioxide impregnated with a combination of active dyes. Depending upon the volume fraction of vanadium multioxide, either attenuation or amplification of the SPP waves may be achieved; the degree of attenuation or amplification is strongly dependent on both the temperature and whether the temperature is increasing or decreasing. At intermediate volume fractions of vanadium multioxide, for a fixed temperature, a SPP wave may experience attenuation if the temperature is increasing but experience amplification if the temperature is decreasing.
研究了具有强温度相关本构特性的介电材料的表面等离子体激元(SPP)波在金属和介电材料平面界面上的传播。金属是银,介电材料是用活性染料的组合浸渍的钒多氧化物。根据钒多氧化物的体积分数,可以实现SPP波的衰减或放大;衰减或放大的程度强烈地取决于温度以及温度是增加还是减少。在钒多氧化物的中等体积分数下,对于固定温度,如果温度升高,SPP波可能会衰减,但如果温度降低,则会放大。
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引用次数: 0
Towards the construction of an accurate kinetic energy density functional and its functional derivative through physics-informed neural networks 通过物理信息神经网络构建精确的动能密度泛函及其泛函导数
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-05-25 DOI: 10.1088/2399-6528/acd90e
L. Rincón, L. Seijas, R. Almeida, F. Javier Torres
One of the primary obstacles in the development of orbital–free density functional theory is the lack of an accurate functional for the Kohn–Sham non-interacting kinetic energy, which, in addition to its accuracy, must also render a good approximation for its functional derivative. To address this critical issue, we propose the construction of a kinetic energy density functional throught physical- informed neural network, where the neural network’s loss function is designed to simultaneously reproduce the atom’s shell structures, and also, an analytically calculated functional derivative. As a proof-of-concept, we have tested the accuracy of the kinetic energy potential by optimizing electron densities for atoms from Li to Xe.
轨道-自由密度泛函理论发展的主要障碍之一是缺乏Kohn–Sham非相互作用动能的精确泛函,除了其准确性外,还必须为其泛函导数提供良好的近似。为了解决这个关键问题,我们建议通过物理知情神经网络构建动能密度泛函,其中神经网络的损失函数被设计为同时再现原子的壳层结构,以及分析计算的泛函导数。作为概念的证明,我们通过优化从Li到Xe原子的电子密度来测试动能势的准确性。
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引用次数: 1
Diode pumped compact single frequency cw ruby laser 二极管泵浦紧凑型单频连续红宝石激光器
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-05-19 DOI: 10.1088/2399-6528/acd746
W. Luhs, B. Wellegehausen
Investigations on 405 nm diode-pumped cw ruby lasers operated in less than 3 mm plane-parallel resonators are reported. With 2.5 mm long ruby crystals TEM00 emission with output powers up to 40 mW are achieved. With an uncoated thin etalon of 0.13 mm thickness, single frequency emission on both ruby lines R1 and R2 is possible. With the piezoelectric shifting of one resonator mirror and corresponding tilting of the etalon, single frequency tuning of up to 400 GHz has been achieved. Details of the laser system are presented, and potential applications will be discussed.
报道了405nm二极管泵浦连续红宝石激光器在小于3mm平面并联谐振器中的工作情况。用2.5毫米长的红宝石晶体实现了输出功率高达40毫瓦的TEM00发射。使用0.13mm厚度的未涂覆的薄标准具,在红宝石线R1和R2上的单频发射是可能的。通过一个谐振镜的压电位移和标准具的相应倾斜,已经实现了高达400GHz的单频调谐。介绍了激光系统的细节,并将讨论潜在的应用。
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引用次数: 0
Sustainable development on production and characterization of metal matrix composites using stir casting 搅拌铸造金属基复合材料的可持续发展及性能研究
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-05-19 DOI: 10.1088/2399-6528/acd748
R. Rajan, S. Ramesh, S. B. Boppana, P. Krishnan
In this study, four different combinations of aluminium metal matrix composites (AMCs) were produced using a computerized stir casting process. The feasibility of using car Scrap Aluminium Engine Head (SAEH) as matrix material, Fresh Alumina Catalyst (FAC) and Spent Alumina Catalyst (SAC) from petrochemical industries as reinforcement material were investigated. The physical and mechanical properties of the cast samples were tested through density, hardness, tensile, compression, and impact test. Microstructural investigations were carried out using an optical microscope, scanning electron microscope (SEM), energy dispersive X-ray spectroscopy (EDS), and X-ray diffraction (XRD). Differential thermal analysis (DTA) and Thermo gravimetric analysis (TGA) were also conducted to justify the results obtained. The results indicated that SAEH reinforced with 5 wt% SAC exhibited lower porosity (2.6%) and higher Brinell hardness (71.5 BHN), Vickers hardness (307.1 VHN), tensile strength (217 MPa), and compressive strength (426 MPa) than other composites. Additionally, this composite showed the highest impact strength (0.02375 J mm−2) and DTA value (568.5 μV mg−1). The TGA result showed that all composites had high thermal stability, with the SAC-reinforced composites having the highest thermal stability (100.13%).
在这项研究中,使用计算机搅拌铸造工艺生产了四种不同组合的铝金属基复合材料(AMC)。研究了以汽车废铝发动机缸盖(SAEH)为基体材料,以石化工业的新鲜氧化铝催化剂(FAC)和废氧化铝催化剂(SAC)为增强材料的可行性。通过密度、硬度、拉伸、压缩和冲击试验测试了铸造样品的物理力学性能。使用光学显微镜、扫描电子显微镜(SEM)、能谱仪(EDS)和X射线衍射仪(XRD)进行了微观结构研究。还进行了差热分析(DTA)和热重分析(TGA)来证明所获得的结果。结果表明,与其他复合材料相比,用5wt%SAC增强的SAEH表现出更低的孔隙率(2.6%)和更高的布氏硬度(71.5BHN)、维氏硬度(307.1VHN)、拉伸强度(217MPa)和压缩强度(426MPa)。此外,该复合材料显示出最高的冲击强度(0.02375 J mm−2)和DTA值(568.5μV mg−1)。TGA结果表明,所有复合材料都具有较高的热稳定性,其中SAC增强复合材料具有最高的热稳定性(100.13%)。
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引用次数: 2
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Journal of Physics Communications
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