Recently, the physics-informed neural networks (PINNs) have received more and more attention because of their ability to solve nonlinear partial differential equations via only a small amount of data ...to quickly obtain data-driven solutions with high accuracy. However, despite their remarkable promise in the early stage, their unbalanced back-propagation gradient calculation leads to drastic oscillations in the gradient value during model training, which is prone to unstable prediction accuracy. Based on this, we develop a gradient optimization algorithm, which proposes a new neural network structure and balances the interaction between different terms in the loss function during model training by means of gradient statistics, so that the newly proposed network architecture is more robust to gradient fluctuations. In this paper, we take the complex modified KdV equation as an example and use the gradient-optimized PINNs (GOPINNs) deep learning method to obtain data-driven rational wave solution and soliton molecules solution. Numerical results show that the GOPINNs method effectively smooths the gradient fluctuations and reproduces the dynamic behavior of these data-driven solutions better than the original PINNs method. In summary, our work provides new insights for optimizing the learning performance of neural networks and improves the prediction accuracy by a factor of 10 to 30 when solving the complex modified KdV equation.
Abstract
The intrinsic antiferromagnetic topological insulator MnBi
2
Te
4
provides an ideal platform for exploring exotic topological quantum phenomena. Recently, the Chern insulator and axion ...insulator phases have been realized in few-layer MnBi
2
Te
4
devices at low magnetic field regime. However, the fate of MnBi
2
Te
4
in high magnetic field has never been explored in experiment. In this work, we report transport studies of exfoliated MnBi
2
Te
4
flakes in pulsed magnetic fields up to 61.5 T. In the high-field limit, the Chern insulator phase with Chern number
C
= −1 evolves into a robust zero Hall resistance plateau state. Nonlocal transport measurements and theoretical calculations demonstrate that the charge transport in the zero Hall plateau state is conducted by two counter-propagating edge states that arise from the combined effects of Landau levels and large Zeeman effect in strong magnetic fields. Our result demonstrates the intricate interplay among intrinsic magnetic order, external magnetic field, and nontrivial band topology in MnBi
2
Te
4
.
The paraventricular nucleus of the hypothalamus (PVH), located in the ventral diencephalon adjacent to the third ventricle, is a highly conserved brain region present in species from zebrafish to ...humans. The PVH is composed of three main types of neurons, magnocellular, parvocellular, and long-projecting neurons, which play imperative roles in the regulation of energy balance and various endocrinological activities. In this review, we focus mainly on recent findings about the early development of the hypothalamus and the PVH, the functions of the PVH in the modulation of energy homeostasis and in the hypothalamus-pituitary system, and human diseases associated with the PVH, such as obesity, short stature, hypertension, and diabetes insipidus. Thus, the investigations of the PVH will benefit not only understanding of the development of the central nervous system but also the etiology of and therapy for human diseases.
Change detection based on heterogeneous images, such as optical images and synthetic aperture radar images, is a challenging problem because of their huge appearance differences. To combat this ...problem, we propose an unsupervised change detection method that contains only a convolutional autoencoder (CAE) for feature extraction and the commonality autoencoder for commonalities exploration. The CAE can eliminate a large part of redundancies in two heterogeneous images and obtain more consistent feature representations. The proposed commonality autoencoder has the ability to discover common features of ground objects between two heterogeneous images by transforming one heterogeneous image representation into another. The unchanged regions with the same ground objects share much more common features than the changed regions. Therefore, the number of common features can indicate changed regions and unchanged regions, and then a difference map can be calculated. At last, the change detection result is generated by applying a segmentation algorithm to the difference map. In our method, the network parameters of the commonality autoencoder are learned by the relevance of unchanged regions instead of the labels. Our experimental results on five real data sets demonstrate the promising performance of the proposed framework compared with several existing approaches.
The interplay of magnetism and topology is a key research subject in condensed matter physics, which offers great opportunities to explore emerging new physics, such as the quantum anomalous Hall ...(QAH) effect, axion electrodynamics, and Majorana fermions. However, these exotic physical effects have rarely been realized experimentally because of the lack of suitable working materials. Here, we predict a series of van der Waals layered MnBi2Te4-related materials that show intralayer ferromagnetic and interlayer antiferromagnetic exchange interactions. We find extremely rich topological quantum states with outstanding characteristics in MnBi2Te4, including an antiferromagnetic topological insulator with the long-sought topological axion states on the surface, a type II magnetic Weyl semimetal with one pair of Weyl points, as well as a collection of intrinsic axion insulators and QAH insulators in even- and odd-layer films, respectively. These notable predictions, if proven experimentally, could profoundly change future research and technology of topological quantum physics.The interplay of magnetism and topology is a key research subject in condensed matter physics, which offers great opportunities to explore emerging new physics, such as the quantum anomalous Hall (QAH) effect, axion electrodynamics, and Majorana fermions. However, these exotic physical effects have rarely been realized experimentally because of the lack of suitable working materials. Here, we predict a series of van der Waals layered MnBi2Te4-related materials that show intralayer ferromagnetic and interlayer antiferromagnetic exchange interactions. We find extremely rich topological quantum states with outstanding characteristics in MnBi2Te4, including an antiferromagnetic topological insulator with the long-sought topological axion states on the surface, a type II magnetic Weyl semimetal with one pair of Weyl points, as well as a collection of intrinsic axion insulators and QAH insulators in even- and odd-layer films, respectively. These notable predictions, if proven experimentally, could profoundly change future research and technology of topological quantum physics.
Exotic quantum phenomena have been demonstrated in recently discovered intrinsic magnetic topological insulator MnBi2Te4. At its two-dimensional limit, the quantum anomalous Hall effect and axion ...insulator state were observed in odd and even layers of MnBi2Te4, respectively. Here, we employ low-temperature scanning tunneling microscopy to study the electronic properties of MnBi2Te4. The quasiparticle interference patterns indicate that the electronic structures on the topmost layer of MnBi2Te4 are different from those of the expected out-of-plane A-type antiferromagnetic phase. The topological surface states may be embedded in deeper layers beneath the topmost surface. Such novel electronic structure is presumably related to the modification of crystalline structure during sample cleaving and reorientation of the magnetic moment of Mn atoms near the surface. Mn dopants substituted at the Bi site on the second atomic layer are observed. The electronic structures fluctuate at atomic scale on the surface, which can affect the magnetism of MnBi2Te4.
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•A fully unrecrystallized microstructure was achieved by the composite micro-alloying.•A novel low-Zn-Mg-content Al-7.61Zn-1.62 Mg-2.17Cu-0.12Zr-0.04Ti-0.28Y (wt.%) alloy was ...developed with a UTS of ∼ 700 MPa and 6.8 % elongation.•New insights into Al8Cu4Y phase in aluminum alloys were given.
Composite micro-alloying is an important technique for developing cost-effective, high-performance aluminum alloys. Here, the effect of combined addition of Zr, Ti and rare-earth Y on the microstructure and tensile properties of an Al-7.6Zn-1.6 Mg-2.1Cu (wt.%) alloy is systematically investigated by means of X-ray diffraction, optical microscopy, scanning electron microscopy, transmission electron microscopy and room-temperature unixal tensile tests. After adding 0.12 %Zr, 0.04 %Ti and 0.28 %Y, L12-Al3Zr/(Al,Zn)3Zr, AlMgZnTiCuFe and (Al,Zn)8Cu4Y phases were induced; the as-T6 treated microstructure of the base alloy changed from fully recrystallized to fully unrecrystallized, accompanied by strong 〈100〉 + 〈111〉 fiber textures along extrusion direction. As a result, the Al-Zn-Mg-Cu-Zr-Ti-Y alloy with low Zn and Mg contents exhibits an ultimate tensile strength of 692 MPa, yield strength of 647 MPa (∼36 % higher than the base alloy) and 6.8 % elongation. The main strengthening mechanisms responsible for this high yield strength are Orowan dislocation bypassing strengthening (∼449 MPa), fiber texture strengthening, and dispersion strengthening. Moreover, the synergistic strengthening effect of rare-earth Y and transitional element(s) Zr and/or Ti was revealed, which may be related to the formation(s) of nanoscale network-structured Al8Cu4Y and/or L12-Al3(Zr,Y) phase(s). The massive formation of the Al8Cu4Y network structure requires a narrow process window.
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