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Ego-velocity estimation from point cloud measurements of a millimeter-wave frequency-modulated continuous wave (mmWave FMCW) radar has become a crucial component of radar-inertial odometry (RIO) systems. Conventional approaches often perform poorly when the number of point cloud outliers exceeds that of inliers. In this paper, we propose CREVE, an acceleration-based inequality constraints filter that leverages additional measurements from an inertial measurement unit (IMU) to achieve robust ego-velocity estimations. To further enhance accuracy and robustness against sensor errors, we introduce a practical accelerometer bias estimation method and a parameter adaptation rule. The effectiveness of the proposed method is evaluated using five open-source drone datasets. Experimental results demonstrate that our algorithm significantly outperforms three existing state-of-the-art methods, achieving reductions in absolute trajectory error of approximately 53%, 84%, and 35% compared to them., Comment: 7 pages, conference

In this paper, we develop a systematic deep learning approach to solve two-dimensional (2D) stationary quantum droplets (QDs) and investigate their wave propagation in the 2D amended Gross-Pitaevskii equation with Lee-Huang-Yang correction and two kinds of potentials. Firstly, we use the initial-value iterative neural network (IINN) algorithm for 2D stationary quantum droplets of stationary equations. Then the learned stationary QDs are used as the initial value conditions for physics-informed neural networks (PINNs) to explore their evolutions in the some space-time region. Especially, we consider two types of potentials, one is the 2D quadruple-well Gaussian potential and the other is the PT-symmetric HO-Gaussian potential, which lead to spontaneous symmetry breaking and the generation of multi-component QDs. The used deep learning method can also be applied to study wave propagations of other nonlinear physical models., Comment: 17 pages, 12 figures (Proc. R. Soc. A, accepted for publication). arXiv admin note: text overlap with arXiv:2409.01124

We propose a new two-stage initial-value iterative neural network (IINN) algorithm for solitary wave computations of nonlinear wave equations based on traditional numerical iterative methods and physics-informed neural networks (PINNs). Specifically, the IINN framework consists of two subnetworks, one of which is used to fit a given initial value, and the other incorporates physical information and continues training on the basis of the first subnetwork. Importantly, the IINN method does not require any additional data information including boundary conditions, apart from the given initial value. Corresponding theoretical guarantees are provided to demonstrate the effectiveness of our IINN method. The proposed IINN method is efficiently applied to learn some types of solutions in different nonlinear wave equations, including the one-dimensional (1D) nonlinear Schr\"odinger equations (NLS) equation (with and without potentials), the 1D saturable NLS equation with PT -symmetric optical lattices, the 1D focusing-defocusing coupled NLS equations, the KdV equation, the two-dimensional (2D) NLS equation with potentials, the 2D amended GP equation with a potential, the (2+1)-dimensional KP equation, and the 3D NLS equation with a potential. These applications serve as evidence for the efficacy of our method. Finally, by comparing with the traditional methods, we demonstrate the advantages of the proposed IINN method., Comment: 25 pages, 17 figures

Ventilated acoustic resonator(VAR), a type of acoustic metamaterial, emerge as an alternative for sound attenuation in environments that require ventilation, owing to its excellent low-frequency attenuation performance and flexible shape adaptability. However, due to the non-linear acoustic responses of VARs, the VAR designs are generally obtained within a limited parametrized design space, and the design relies on the iteration of the numerical simulation which consumes a considerable amount of computational time and resources. This paper proposes an acoustic response-encoded variational autoencoder (AR-VAE), a novel variational autoencoder-based generative design model for the efficient and accurate inverse design of VAR even with non-parametrized designs. The AR-VAE matches the high-dimensional acoustic response with the VAR cross-section image in the dimension-reduced latent space, which enables the AR-VAE to generate various non-parametrized VAR cross-section images with the target acoustic response. AR-VAE generates non-parameterized VARs from target acoustic responses, which show a 25-fold reduction in mean squared error compared to conventional deep learning-based parameter searching methods while exhibiting lower average mean squared error and peak frequency variance. By combining the inverse-designed VARs by AR-VAE, multi-cavity VAR was devised for broadband and multitarget peak frequency attenuation. The proposed design method presents a new approach for structural inverse-design with a high-dimensional non-linear physical response.

In this paper, we propose a radar odometry structure that directly utilizes radar velocity measurements for dead reckoning while maintaining its ability to update estimations within the Kalman filter framework. Specifically, we employ the Doppler velocity obtained by a 4D Frequency Modulated Continuous Wave (FMCW) radar in conjunction with gyroscope data to calculate poses. This approach helps mitigate high drift resulting from accelerometer biases and double integration. Instead, tilt angles measured by gravitational force are utilized alongside relative distance measurements from radar scan matching for the filter's measurement update. Additionally, to further enhance the system's accuracy, we estimate and compensate for the radar velocity scale factor. The performance of the proposed method is verified through five real-world open-source datasets. The results demonstrate that our approach reduces position error by 62% and rotation error by 66% on average compared to the state-of-the-art radar-inertial fusion method in terms of absolute trajectory error., Comment: 9 pages, 5 figures, 1 table, IROS 2024

We propose a novel scheme for combining efficiently the truncated-unity functional renormalization group (TUFRG) and the mean-field theory. It follows a method of Wang, Eberlein and Metzner that uses only the two-particle irreducible part of the vertex as an input for the mean-field treatment. In the TUFRG, the neglect of fluctuation effects from other channels in the symmetry-broken regime is represented by applying the random phase approximation (RPA) in each individual channel, below the divergence scale. Then the Bethe-Salpeter equation for the four-point vertex is translated into the RPA matrix equations for the bosonic propagators that relates the singular and irreducible singular modes of the propagators. The universal symmetries for the irreducible singular modes are obtained from the antisymmetry of Grassmann variables. The mean-field equation based on these modes is derived by the saddle-point approximation in the framework of the path-integral formalism. By using our scheme, the power of the TUFRG, as an unbiased tool for identifying the many-body instabilities, could be elevated to a quantitative level, and its application would be extended to a quantitative analysis of the coexisting orders. As an illustration we employ this scheme to study the coexistence phase of the chiral superconductivity and the chiral spin-density wave, predicted near van Hove filling of the honeycomb lattice., Comment: 34 pages, 6 figures, 1 table

In this paper, we firstly extend the physics-informed neural networks (PINNs) to learn data-driven stationary and non-stationary solitons of 1D and 2D saturable nonlinear Schr\"odinger equations (SNLSEs) with two fundamental PT-symmetric Scarf-II and periodic potentials in optical fibers. Secondly, the data-driven inverse problems are studied for PT-symmetric potential functions discovery rather than just potential parameters in the 1D and 2D SNLSEs. Particularly, we propose a modified PINNs (mPINNs) scheme to identify directly the PT potential functions of the 1D and 2D SNLSEs by the solution data. And the inverse problems about 1D and 2D PT -symmetric potentials depending on propagation distance z are also investigated using mPINNs method. We also identify the potential functions by the PINNs applied to the stationary equation of the SNLSE. Furthermore, two network structures are compared under different parameter conditions such that the predicted PT potentials can achieve the similar high accuracy. These results illustrate that the established deep neural networks can be successfully used in 1D and 2D SNLSEs with high accuracies. Moreover, some main factors affecting neural networks performance are discussed in 1D and 2D PT Scarf-II and periodic potentials, including activation functions, structures of the networks, and sizes of the training data. In particular, twelve different nonlinear activation functions are in detail analyzed containing the periodic and non-periodic functions such that it is concluded that selecting activation functions according to the form of solution and equation usually can achieve better effect., Comment: 27 pages, 20 figures

In this paper, we study data-driven localized wave solutions and parameter discovery in the massive Thirring (MT) model via the deep learning in the framework of physics-informed neural networks (PINNs) algorithm. Abundant data-driven solutions including soliton of bright/dark type, breather and rogue wave are simulated accurately and analyzed contrastively with relative and absolute errors. For higher-order localized wave solutions, we employ the extended PINNs (XPINNs) with domain decomposition to capture the complete pictures of dynamic behaviors such as soliton collisions, breather oscillations and rogue-wave superposition. In particular, we modify the interface line in domain decomposition of XPINNs into a small interface zone and introduce the pseudo initial, residual and gradient conditions as interface conditions linked adjacently with individual neural networks. Then this modified approach is applied successfully to various solutions ranging from bright-bright soliton, dark-dark soliton, dark-antidark soliton, general breather, Kuznetsov-Ma breather and second-order rogue wave. Experimental results show that this improved version of XPINNs reduce the complexity of computation with faster convergence rate and keep the quality of learned solutions with smoother stitching performance as well. For the inverse problems, the unknown coefficient parameters of linear and nonlinear terms in the MT model are identified accurately with and without noise by using the classical PINNs algorithm., Comment: 24 pages, 12 figures; Chaos, Solitons & Fractals (accepted for publication)

We address symmetry breaking bifurcations (SBBs) in the ground-state (GS) and dipole-mode (DM) solitons of the 1D linearly coupled NLS equations, modeling the propagation of light in a dual-core planar waveguide with the Kerr nonlinearity and two types of PT-symmetric potentials. The PT-symmetric potential is employed to obtained different types of solutions. A supercritical pitchfork bifurcation occurs in families of symmetric solutions of both the GS and DM types. A novel feature of the system is interplay between breakings of the PT and inter-core symmetries. Stability of symmetric GS and DM modes and their asymmetric counterparts, produced by SBBs of both types, is explored via the linear-stability analysis and simulations. It is found that the instability of PT-symmetric solutions takes place prior to the inter-core symmetry breaking. Surprisingly, stable inter-core-symmetric GS solutions may remain stable while the PT symmetry is broken. Fully asymmetric GS and DM solitons are only partially stable. Moreover, we construct symmetric and asymmetric GS solitons under the action of a pure imaginary localized potential, for which the SBB is subcritical. These results exhibit that stable solitons can still be found in dissipative systems. Finally, excitations of symmetric and asymmetric GS solitons are investigated by making the potential's parameters or the system's coupling constant functions, showing that GS solitons can be converted from an asymmetric shape onto a symmetric one under certain conditions. These results may pave the way for the study of linear and nonlinear phenomena in a dual-core planar waveguide with PT potential and related experimental designs., Comment: 19 pages, 11 figures; Proc. R. Soc A (accepted)

We test the efficiency of applying Geometric Deep Learning to the problems in low-dimensional topology in a certain simple setting. Specifically, we consider the class of 3-manifolds described by plumbing graphs and use Graph Neural Networks (GNN) for the problem of deciding whether a pair of graphs give homeomorphic 3-manifolds. We use supervised learning to train a GNN that provides the answer to such a question with high accuracy. Moreover, we consider reinforcement learning by a GNN to find a sequence of Neumann moves that relates the pair of graphs if the answer is positive. The setting can be understood as a toy model of the problem of deciding whether a pair of Kirby diagrams give diffeomorphic 3- or 4-manifolds., Comment: 12 pages and appendix, 9 figures

In this paper, vortex solitons are produced for a variety of 2D spinning quantum droplets (QDs) in a PT-symmetric potential, modeled by the amended Gross-Pitaevskii equation with Lee-Huang-Yang corrections. In particular, exact QD states are obtained under certain parameter constraints, providing a guide to finding the respective generic family. In a parameter region of the unbroken PT symmetry, different families of QDs originating from the linear modes are obtained in the form of multipolar and vortex droplets at low and high values of the norm, respectively, and their stability is investigated. In the spinning regime, QDs become asymmetric above a critical rotation frequency, most of them being stable. The effect of the PT -symmetric potential on the spinning and nonspinning QDs is explored by varying the strength of the gain-loss distribution. Generally, spinning QDs trapped in the PT -symmetric potential exhibit asymmetry due to the energy flow affected by the interplay of the gain-loss distribution and rotation. Finally, interactions between spinning or nonspinning QDs are explored, exhibiting elastic collisions under certain conditions., Comment: 18 pages, 10 figures (to be published in Chaos)

Superconductivity is one of most intriguing quantum phenomena, and the quest for elemental superconductors with high critical temperature (Tc) is of great scientific significance due to their relatively simple material composition and the underlying mechanism. Here we report the experimental discovery of densely compressed scandium (Sc) becoming the first elemental superconductor with Tc breaking into 30 K range, which is comparable to the Tc values of the classic La-Ba-Cu-O or LaFeAsO superconductors. Our results show that Tconset of Sc increases from ~3 K at around 43 GPa to ~32 K at about 283 GPa (Tczero ~ 31 K), which is well above liquid neon temperature. Interestingly measured Tc shows no sign of saturation up to the maximum pressure achieved in our experiments, indicating that Tc might be even higher upon further compression., Comment: 17 pages, 4 figures, plus supplementary materials with 5 pages and 3 figures

We study the many-body instabilities of correlated electrons on the half-filled honeycomb lattice with enhanced exchange coupling. The system is described by an extended Hubbard model including the next-nearest-neighbor Coulomb repulsion ($V_2$) and the nearest-neighbor exchange interaction ($J$). We use the truncated unity functional renormalization group approach to determine a schematic ground-state phase diagram with higher resolution in the parameter space of $V_2$ and $J$. In the absence of the on-site repulsion and presence of sizable next-nearest-neighbor repulsion and enhanced nearest-neighbor exchange interaction, we encounter the quantum spin Hall phase, the spin-Kekul\'{e} phase, and the three-sublattice and the incommensurate charge-density-wave phases. We propose a scheme for combining consistently the truncated unity functional renormalization group and the mean-field approximation, which is distinct from the conventional one that directly uses the renormalization-group results as an input for the mean-field calculation. This scheme is used to study in detail the quantum spin Hall phase, presenting some characteristics like the bulk gap, the Chern number and the helical edge states., Comment: 17 pages, 6 figures, 1 table

Among the diverse platforms of quantum light sources, epitaxially grown semiconductor quantum dots (QDs) are one of the most attractive workhorses for realizing various quantum photonic technologies owing to their outstanding brightness and scalability. There exist various material systems for these QDs based on their appropriate emission bandwidth; however, only a few material systems have successfully grown single or low-density QDs, which are essential for quantum light sources. In most other material systems, it is difficult to realize low-density QDs, and the mesa-etching process is usually undergone in order to reduce their density. Nevertheless, the etching process irreversibly destroys the medium near the QD, which is detrimental to in-plane device integration. In this study, we apply a nondestructive luminescence picking method termed as nanoscale focus pinspot (NFP) using helium ion microscopy to reduce the luminous QD density while retaining the surrounding medium. Given that the NFP can precisely manipulate the luminescence at nanoscale resolution, a photonic device can be deterministically fabricated on the target QD matched from both spatial and spectral points of view. After applying the NFP, we extract only a single QD emission out of the high-density ensemble QD emission. Moreover, the photonic structure of a circular Bragg reflector is deterministically integrated with the selected QD, and the extraction efficiency of the QD emission has been improved 27 times. Furthermore, this technique does not destroy the medium and only controls the luminescence. Hence, it is highly applicable to various photonic structures, including photonic waveguides or photonic crystal cavities regardless of their materials., Comment: 16 pages, 5 figures