Gauss Newton method for solving variational problems of PDEs with neural network discretizaitons

The numerical solution of differential equations using machine learning-based approaches has gained significant popularity. Neural network-based discretization has emerged as a powerful tool for solving differential equations by parameterizing a set of functions. Various approaches, such as the deep Ritz method and physics-informed neural networks, have been developed for numerical solutions. Training algorithms, including gradient descent and greedy algorithms, have been proposed to solve the resulting optimization problems. In this paper, we focus on the variational formulation of the problem and propose a Gauss- Newton method for computing the numerical solution. We provide a comprehensive analysis of the superlinear convergence properties of this method, along with a discussion on semi-regular zeros of the vanishing gradient. Numerical examples are presented to demonstrate the efficiency of the proposed Gauss-Newton method

SPColor: Semantic Prior Guided Exemplar-based Image Colorization

Exemplar-based image colorization aims to colorize a target grayscale image based on a color reference image, and the key is to establish accurate pixel-level semantic correspondence between these two images. Previous methods search for correspondence across the entire reference image, and this type of global matching is easy to get mismatch. We summarize the difficulties in two aspects: (1) When the reference image only contains a part of objects related to target image, improper correspondence will be established in unrelated regions. (2) It is prone to get mismatch in regions where the shape or texture of the object is easily confused. To overcome these issues, we propose SPColor, a semantic prior guided exemplar-based image colorization framework. Different from previous methods, SPColor first coarsely classifies pixels of the reference and target images to several pseudo-classes under the guidance of semantic prior, then the correspondences are only established locally between the pixels in the same class via the newly designed semantic prior guided correspondence network. In this way, improper correspondence between different semantic classes is explicitly excluded, and the mismatch is obviously alleviated. Besides, to better reserve the color from reference, a similarity masked perceptual loss is designed. Noting that the carefully designed SPColor utilizes the semantic prior provided by an unsupervised segmentation model, which is free for additional manual semantic annotations. Experiments demonstrate that our model outperforms recent state-of-the-art methods both quantitatively and qualitatively on public dataset

New Bismuth Sodium Titanate Based Ceramics and Their Applications

Ferroelectric materials are widely investigated due to their excellent properties and versatile applications. At present, the dominant materials are lead-containing materials, such as Pb (Zr,Ti)O3 solid solutions. However, the use of lead gives rise to environmental concerns, which is the driving force for the development of alternative lead-free ferroelectric materials. (Bi0.5Na0.5)TiO3-based ceramics are considered to be one of the most promising lead-free materials to replace lead-containing ferroelectric ceramics due to their excellent ferroelectric properties, relaxation characteristics, and high Curie point. After decades of efforts, great progress has been made in the phase structure characterization and properties improvement of BNT based ceramics. However, most of the studies on BNT system mainly focuses on its piezoelectric properties and application of piezoelectric sensors and strain actuators, little attention is paid to its ferroelectric properties and related applications. In this chapter, new BNT-based ceramics via composition modification and special focuses on the ferroelectric properties, phase transition behaviors under external fields and related applications, such as application in energy storage, pulsed power supply and pyroelectric detection were proposed

Exemplar-based Video Colorization with Long-term Spatiotemporal Dependency

Exemplar-based video colorization is an essential technique for applications like old movie restoration. Although recent methods perform well in still scenes or scenes with regular movement, they always lack robustness in moving scenes due to their weak ability in modeling long-term dependency both spatially and temporally, leading to color fading, color discontinuity or other artifacts. To solve this problem, we propose an exemplar-based video colorization framework with long-term spatiotemporal dependency. To enhance the long-term spatial dependency, a parallelized CNN-Transformer block and a double head non-local operation are designed. The proposed CNN-Transformer block can better incorporate long-term spatial dependency with local texture and structural features, and the double head non-local operation further leverages the performance of augmented feature. While for long-term temporal dependency enhancement, we further introduce the novel linkage subnet. The linkage subnet propagate motion information across adjacent frame blocks and help to maintain temporal continuity. Experiments demonstrate that our model outperforms recent state-of-the-art methods both quantitatively and qualitatively. Also, our model can generate more colorful, realistic and stabilized results, especially for scenes where objects change greatly and irregularly

Boosting the thermoelectric performance of p-type heavily Cu-doped polycrystalline SnSe via inducing intensive crystal imperfections and defect phonon scattering

In this study, we, for the first time, report a high Cu solubility of 11.8% in single crystal SnSe microbelts synthesized via a facile solvothermal route. The pellets sintered from these heavily Cu-doped microbelts show a high power factor of 5.57 μW cm−1 K−2 and low thermal conductivity of 0.32 W m−1 K−1 at 823 K, contributing to a high peak ZT of ∼1.41. Through a combination of detailed structural and chemical characterizations, we found that with increasing the Cu doping level, the morphology of the synthesized Sn1−xCuxSe (x is from 0 to 0.118) transfers from rectangular microplate to microbelt. The high electrical transport performance comes from the obtained Cu+ doped state, and the intensive crystal imperfections such as dislocations, lattice distortions, and strains, play key roles in keeping low thermal conductivity. This study fills in the gaps of the existing knowledge concerning the doping mechanisms of Cu in SnSe systems, and provides a new strategy to achieve high thermoelectric performance in SnSe-based thermoelectric materials

High‐Voltage Aqueous Mg‐Ion Batteries Enabled by Solvation Structure Reorganization

Herein, an eco-friendly and high safety aqueous Mg-ion electrolyte (AME) with a wide electrochemical stability window (ESW) $≈$ 3.7 V, containing polyethylene glycol (PEG) and low-concentration salt (0.8 m Mg(TFSI)$_2$), is proposed by solvation structure reorganization of AME. The PEG agent significantly alters the Mg$^{2+}$ solvation and hydrogen bonds network of AMEs and forms the direct coordination of Mg$^{2+}$ and TFSI-, thus enhancing the physicochemical and electrochemical properties of electrolytes. As an exemplary material, V$_2$O$_5$ nanowires are tested in this new AME and exhibit initial high discharge/charge capacity of 359/326 mAh g$^{-1}$ and high capacity retention of 80% after 100 cycles. The high crystalline $α$-V$_2$O$_5$ shows two 2-phase transition processes with the formation of $ε$-Mg$_{0.6}$V$_2$O$_5$ and Mg-rich Mg$_x$V$_2$O$_5$ (x $≈$1.0) during the first discharge. Mg-rich Mg$_x$V$_2$O$_5$ (x $≈$ 1.0) phase formed through electrochemical Mg-ion intercalation at room temperature is for the first time observed via XRD. Meanwhile, the cathode electrolyte interphase (CEI) in aqueous Mg-ion batteries is revealed for the first time. MgF$_2$ originating from the decomposition of TFSI- is identified as the dominant component. This work offers a new approach for designing high-safety, low-cost, eco-friendly, and large ESW electrolytes for practical and novel aqueous multivalent batteries

Electrochemical performance and reaction mechanism investigation of V₂O₅ positive electrode material for aqueous rechargeable zinc batteries

The electrochemical performance and reaction mechanism of orthorhombic V$_2$O$_5$ in 1 M ZnSO$_4$ aqueous electrolyte are investigated. V$_2$O$_5$ nanowires exhibit an initial discharge and charge capacity of 277 and 432 mA h g$^{−1}$, respectively, at a current density of 50 mA g$^{−1}$. The material undergoes quick capacity fading during cycling under both low (50 mA g$^{−1}$) and high (200 mA g$^{−1}$) currents. V$_2$O$_5$ can deliver a higher discharge capacity at 200 mA g$^{−1}$ than that at 50 mA g$^{−1}$ after 10 cycles, which could be attributed to a different type of activation process under both current densities and distinct degrees of side reactions (parasitic reactions). Cyclic voltammetry shows several successive redox peaks during Zn ion insertion and deinsertion. In operando synchrotron diffraction reveals that V$_2$O$_5$ undergoes a solid solution and two-phase reaction during the 1st cycle, accompanied by the formation/decomposition of byproducts Zn$_3$(OH)$_2$V$_2$O$_7$·2(H$_2$O) and ZnSO$_4$Zn$_3$(OH)$_6$·5H$_2$O. In the 2nd insertion process, V$_2$O$_5$ goes through the same two-phase reaction as that in the 1st cycle, with the formation of the byproduct ZnSO$_4$Zn$_3$(OH)$_6$·5H$_2$O. The reduction/oxidation of vanadium is confirmed by in operando X-ray absorption spectroscopy. Furthermore, Raman, TEM, and X-ray photoelectron spectroscopy (XPS) confirm the byproduct formation and the reversible Zn ion insertion/deinsertion in the V$_2$O$_5$