arXiv subjects

Qin Li

Publications and source records attributed to Qin Li.

At least 145 records · Page 8Linked to original sources

arXiv2022

A Deep Learning Approach to Generating Photospheric Vector Magnetograms of Solar Active Regions for SOHO/MDI Using SDO/HMI and BBSO Data

Solar activity is usually caused by the evolution of solar magnetic fields. Magnetic field parameters derived from photospheric vector magnetograms of solar active regions have been used to analyze and forecast eruptive events such as solar flares and coronal mass ejections. Unfortunately, the most recent solar cycle 24 was relatively weak with few large flares, though it is the only solar cycle in which consistent time-sequence vector magnetograms have been available through the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) since its launch in 2010. In this paper, we look into another major instrument, namely the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory (SOHO) from 1996 to 2010. The data archive of SOHO/MDI covers more active solar cycle 23 with many large flares. However, SOHO/MDI data only has line-of-sight (LOS) magnetograms. We propose a new deep learning method, named MagNet, to learn from combined LOS magnetograms, Bx and By taken by SDO/HMI along with H-alpha observations collected by the Big Bear Solar Observatory (BBSO), and to generate vector components Bx' and By', which would form vector magnetograms with observed LOS data. In this way, we can expand the availability of vector magnetograms to the period from 1996 to present. Experimental results demonstrate the good performance of the proposed method. To our knowledge, this is the first time that deep learning has been used to generate photospheric vector magnetograms of solar active regions for SOHO/MDI using SDO/HMI and H-alpha data.

astro-ph.SR↗

arXiv2022

A geometric construction of representations of the Berezin-Toeplitz quantization

For a Kähler manifold $X$ equipped with a prequantum line bundle $L$, we give a geometric construction of a family of representations of the Berezin-Toeplitz deformation quantization algebra $(C^\infty(X)[[\hbar]],\star_{BT})$ parametrized by points $z_0 \in X$. The key idea is to use peak sections to suitably localize the Hilbert spaces $H^{0}\left(X,L^{\otimes m}\right)$ around $z_{0}$ in the large volume limit.

math.QA↗

arXiv2022

Verifiable blind quantum computation with identity authentication for different types of clients

Quantum computing has considerable advantages in solving some problems over its classical counterpart. Currently various physical systems are developed to construct quantum computers but it is still challenging and the first use of quantum computers may adopt the cloud style. Blind quantum computing (BQC) provides a solution for clients with limited quantum capabilities to delegate their quantum computation to remote quantum servers while keeping input, output, and even algorithm private. In this paper, we propose three multi-party verifiable blind quantum computing (VBQC) protocols with identity authentication to handle clients with varying quantum capabilities in quantum networks, such as those who can just make measurements, prepare single qubits, or perform a few single-qubit gates. They are client-friendly and flexible since the clients can achieve BQC depending on their own quantum devices and resist both insider outsider attacks in quantum networks. Furthermore, all the three proposed protocols are verifiable, namely that the clients can verify the correctness of their calculations.

quant-ph↗

arXiv2022

Ancilla-driven blind quantum computation for clients with different quantum capabilities

Blind quantum computation (BQC) allows a client with limited quantum power to delegate his quantum computational task to a powerful server and still keep his input, output, and algorithm private. There are mainly two kinds of models about BQC, namely circuit-based and measurement-based models. In addition, a hybrid model called ancilla-driven universal blind quantum computing (ADBQC) was proposed by combining the properties of both circuit-based and measurement-based models, where all unitary operations on the register qubits can be realized with the aid of single ancillae coupled to the register qubits. However, in the ADBQC model, the quantum capability of the client is strictly limited to preparing single qubits. If a client can only perform single-qubit measurements or a few simple quantum gates, he may also want to delegate his computation to a remote server via ADBQC. This paper solves the problem and extends the existing model by proposing two types of ADBQC protocols for clients with different quantum capabilities, such as performing single-qubit measurements or single-qubit gates. Furthermore, in the proposed two ADBQC protocols, clients can detect whether servers are honest or not with a high probability by using corresponding verifiable techniques.

quant-ph↗

arXiv2022

Inferring Line-of-Sight Velocities and Doppler Widths from Stokes Profiles of GST/NIRIS Using Stacked Deep Neural Networks

Obtaining high-quality magnetic and velocity fields through Stokes inversion is crucial in solar physics. In this paper, we present a new deep learning method, named Stacked Deep Neural Networks (SDNN), for inferring line-of-sight (LOS) velocities and Doppler widths from Stokes profiles collected by the Near InfraRed Imaging Spectropolarimeter (NIRIS) on the 1.6 m Goode Solar Telescope (GST) at the Big Bear Solar Observatory (BBSO). The training data of SDNN is prepared by a Milne-Eddington (ME) inversion code used by BBSO. We quantitatively assess SDNN, comparing its inversion results with those obtained by the ME inversion code and related machine learning (ML) algorithms such as multiple support vector regression, multilayer perceptrons and a pixel-level convolutional neural network. Major findings from our experimental study are summarized as follows. First, the SDNN-inferred LOS velocities are highly correlated to the ME-calculated ones with the Pearson product-moment correlation coefficient being close to 0.9 on average. Second, SDNN is faster, while producing smoother and cleaner LOS velocity and Doppler width maps, than the ME inversion code. Third, the maps produced by SDNN are closer to ME's maps than those from the related ML algorithms, demonstrating the better learning capability of SDNN than the ML algorithms. Finally, comparison between the inversion results of ME and SDNN based on GST/NIRIS and those from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory in flare-prolific active region NOAA 12673 is presented. We also discuss extensions of SDNN for inferring vector magnetic fields with empirical evaluation.

astro-ph.SR↗

arXiv2022

Monte Carlo Gradient in Optimization Constrained by Radiative Transport Equation

Can Monte Carlo (MC) solvers be directly used in gradient-based methods for PDE-constrained optimization problems? In these problems, a gradient of the loss function is typically presented as a product of two PDE solutions, one for the forward equation and the other for the adjoint. When MC solvers are used, the numerical solutions are Dirac measures. As such, one immediately faces the difficulty in explaining the multiplication of two measures. This suggests that MC solvers are naturally incompatible with gradient-based optimization under PDE constraints. In this paper, we study two different strategies to overcome the difficulty. One is to adopt the Discrete-Then-Optimize technique and conduct the full optimization on the algebraic system, avoiding the Dirac measures. The second strategy stays within the Optimize-Then-Discretize framework. We propose a correlated simulation where, instead of using MC solvers separately for both forward and adjoint problems, we recycle the samples in the forward simulation in the adjoint solver. This frames the adjoint solution as a test function, and hence allows a rigorous convergence analysis. The investigation is presented through the lens of the radiative transfer equation, either in the inverse setting from optical imaging or in the optimal control framework. We detail the algorithm development, convergence analysis, and complexity cost. Numerical evidence is also presented to demonstrate the claims.

math.NA↗

arXiv2022

Computation of optimal beams in weak turbulence

When an optical beam propagates through a turbulent medium such as the atmosphere or ocean, the beam will become distorted. It is then natural to seek the best or optimal beam that is distorted least, under some metric such as intensity or scintillation. We seek to maximize the light intensity at the receiver using the paraxial wave equation with weak-fluctuation as the model. In contrast to classical results that typically confine original laser beams to be from a special class, we allow the beam to be general, which leads to an eigenvalue problem of a large-sized matrix with each entry being a multi-dimensional integral. This is an expensive and sometimes infeasible computational task in many practically reasonable settings. To overcome this, we utilize an asymptotic expansion and transform the derivation to Fourier space, which allows us to incorporate some optional turbulence assumptions, such as homogeneous-statistics assumption, small-length-scale cutoff assumption, and Markov assumption, to reduce the dimension of the numerical integral. The proposed methods provide a computational strategy that is numerically feasible, and results are demonstrated in several numerical examples.

physics.comp-ph↗

arXiv2022

High-frequency limit of the inverse scattering problem: asymptotic convergence from inverse Helmholtz to inverse Liouville

We investigate the asymptotic relation between the inverse problems relying on the Helmholtz equation and the radiative transfer equation (RTE) as physical models, in the high-frequency limit. In particular, we evaluate the asymptotic convergence of a generalized version of inverse scattering problem based on the Helmholtz equation, to the inverse scattering problem of the Liouville equation (a simplified version of RTE). The two inverse problems are connected through the Wigner transform that translates the wave-type description on the physical space to the kinetic-type description on the phase space, and the Husimi transform that models data localized both in location and direction. The finding suggests that impinging tightly concentrated monochromatic beams can indeed provide stable reconstruction of the medium, asymptotically in the high-frequency regime. This fact stands in contrast with the unstable reconstruction for the classical inverse scattering problem when the probing signals are plane-waves.

math.NA↗

arXiv2022

Improvements to enhance robustness of third-order scale-independent WENO-Z schemes

Although there are many improvements to WENO3-Z that target the achievement of optimal order in the occurrence of the first-order critical point (CP1), they mainly address resolution performance, while the robustness of schemes is of less concern and lacks understanding accordingly. In light of our analysis considering the occurrence of critical points within grid intervals, we theoretically prove that it is impossible for a scale-independent scheme that has the stencil of WENO3-Z to fulfill the above order achievement, and current scale-dependent improvements barely fulfill the job when CP1 occurs at the middle of the grid cell. In order to achieve scale-independent improvements, we devise new smoothness indicators that increase the error order from 2 to 4 when CP1 occurs and perform more stably. Meanwhile, we construct a new global smoothness indicator that increases the error order from 4 to 5 similarly, through which new nonlinear weights with regard to WENO3-Z are derived and new scale-independents improvements, namely WENO-ZES2 and -ZES3, are acquired. Through 1D scalar and Euler tests, as well as 2D computations, in comparison with typical scale-dependent improvement, the following performances of the proposed schemes are demonstrated: The schemes can achieve third-order accuracy at CP1 no matter its location in the stencil, indicate high resolution in resolving flow subtleties, and manifest strong robustness in hypersonic simulations (e.g., the accomplishment of computations on hypersonic half-cylinder flow with Mach numbers reaching 16 and 19, respectively, as well as essentially non-oscillatory solutions of inviscid sharp double cone flow at M=9.59), which contrasts the comparative WENO3-Z improvement.

cs.CE↗

arXiv2022

Kapranov's $L_\infty$ structures, Fedosov's star products, and one-loop exact BV quantizations on Kähler manifolds

We study quantization schemes on a Kähler manifold and relate several interesting structures. We first construct Fedosov's star products on a Kähler manifold $X$ as quantizations of Kapranov's $L_\infty$-algebra structure. Then we investigate the Batalin-Vilkovisky (BV) quantizations associated to these star products. A remarkable feature is that they are all one-loop exact, meaning that the Feynman weights associated to graphs with two or more loops all vanish. This leads to a succinct cochain level formula in de Rham cohomology for the algebraic index.

math.QA↗

arXiv2022

Predicting Solar Energetic Particles Using SDO/HMI Vector Magnetic Data Products and a Bidirectional LSTM Network

Solar energetic particles (SEPs) are an essential source of space radiation, which are hazards for humans in space, spacecraft, and technology in general. In this paper we propose a deep learning method, specifically a bidirectional long short-term memory (biLSTM) network, to predict if an active region (AR) would produce an SEP event given that (i) the AR will produce an M- or X-class flare and a coronal mass ejection (CME) associated with the flare, or (ii) the AR will produce an M- or X-class flare regardless of whether or not the flare is associated with a CME. The data samples used in this study are collected from the Geostationary Operational Environmental Satellite's X-ray flare catalogs provided by the National Centers for Environmental Information. We select M- and X-class flares with identified ARs in the catalogs for the period between 2010 and 2021, and find the associations of flares, CMEs and SEPs in the Space Weather Database of Notifications, Knowledge, Information during the same period. Each data sample contains physical parameters collected from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. Experimental results based on different performance metrics demonstrate that the proposed biLSTM network is better than related machine learning algorithms for the two SEP prediction tasks studied here. We also discuss extensions of our approach for probabilistic forecasting and calibration with empirical evaluation.

astro-ph.SR↗

arXiv2022

Low-rank approximation for multiscale PDEs

Historically, analysis for multiscale PDEs is largely unified while numerical schemes tend to be equation-specific. In this paper, we propose a unified framework for computing multiscale problems through random sampling. This is achieved by incorporating randomized SVD solvers and manifold learning techniques to numerically reconstruct the low-rank features of multiscale PDEs. We use multiscale radiative transfer equation and elliptic equation with rough media to showcase the application of this framework.

math.NA↗

arXiv2022

A reduced order Schwarz method for nonlinear multiscale elliptic equations based on two-layer neural networks

Neural networks are powerful tools for approximating high dimensional data that have been used in many contexts, including solution of partial differential equations (PDEs). We describe a solver for multiscale fully nonlinear elliptic equations that makes use of domain decomposition, an accelerated Schwarz framework, and two-layer neural networks to approximate the boundary-to-boundary map for the subdomains, which is the key step in the Schwarz procedure. Conventionally, the boundary-to-boundary map requires solution of boundary-value elliptic problems on each subdomain. By leveraging the compressibility of multiscale problems, our approach trains the neural network offline to serve as a surrogate for the usual implementation of the boundary-to-boundary map. Our method is applied to a multiscale semilinear elliptic equation and a multiscale $p$-Laplace equation. In both cases we demonstrate significant improvement in efficiency as well as good accuracy and generalization performance.

math.NA↗

arXiv2022

Reconstructing the thermal phonon transmission coefficient at solid interfaces in the phonon transport equation

The ab initio model for heat propagation is the phonon transport equation, a Boltzmann-like kinetic equation. When two materials are put side by side, the heat that propagates from one material to the other experiences thermal boundary resistance. Mathematically, it is represented by the reflection coefficient of the phonon transport equation on the interface of the two materials. This coefficient takes different values at different phonon frequencies, between different materials. In experiments scientists measure the surface temperature of one material to infer the reflection coefficient as a function of phonon frequency. In this article, we formulate this inverse problem in an optimization framework and apply the stochastic gradient descent (SGD) method for finding the optimal solution. We furthermore prove the maximum principle and show the Lipschitz continuity of the Fréchet derivative. These properties allow us to justify the application of SGD in this setup.

math.NA↗

arXiv2022

Second-order diffusion limit for the phonon transport equation-asymptotics and numerics

We investigate the numerical implementation of the limiting equation for the phonon transport equation in the small Knudsen number regime. The main contribution is that we derive the limiting equation that achieves the second order convergence, and provide a numerical recipe for computing the Robin coefficients. These coefficients are obtained by solving an auxiliary half-space equation. Numerically the half-space equation is solved by a spectral method that relies on the even-odd decomposition to eliminate corner-point singularity. Numerical evidences will be presented to justify the second order asymptotic convergence rate.

math.NA↗

arXiv2022

Effective and Efficient Graph Learning for Multi-view Clustering

Despite the impressive clustering performance and efficiency in characterizing both the relationship between data and cluster structure, existing graph-based multi-view clustering methods still have the following drawbacks. They suffer from the expensive time burden due to both the construction of graphs and eigen-decomposition of Laplacian matrix, and fail to explore the cluster structure of large-scale data. Moreover, they require a post-processing to get the final clustering, resulting in suboptimal performance. Furthermore, rank of the learned view-consensus graph cannot approximate the target rank. In this paper, drawing the inspiration from the bipartite graph, we propose an effective and efficient graph learning model for multi-view clustering. Specifically, our method exploits the view-similar between graphs of different views by the minimization of tensor Schatten p-norm, which well characterizes both the spatial structure and complementary information embedded in graphs of different views. We learn view-consensus graph with adaptively weighted strategy and connectivity constraint such that the connected components indicates clusters directly. Our proposed algorithm is time-economical and obtains the stable results and scales well with the data size. Extensive experimental results indicate that our method is superior to state-of-the-art methods.

cs.LG↗

arXiv2021

Multiscale convergence of the inverse problem for chemotaxis in the Bayesian setting

Chemotaxis describes the movement of an organism, such as single or multi-cellular organisms and bacteria, in response to a chemical stimulus. Two widely used models to describe the phenomenon are the celebrated Keller-Segel equation and a chemotaxis kinetic equation. These two equations describe the organism movement at the macro- and mesoscopic level respectively, and are asymptotically equivalent in the parabolic regime. How the organism responds to a chemical stimulus is embedded in the diffusion/advection coefficients of the Keller-Segel equation or the turning kernel of the chemotaxis kinetic equation. Experiments are conducted to measure the time dynamics of the organisms' population level movement when reacting to certain stimulation. From this one infers the chemotaxis response, which constitutes an inverse problem. \\ In this paper we discuss the relation between both the macro- and mesoscopic inverse problems, each of which is associated to two different forward models. The discussion is presented in the Bayesian framework, where the posterior distribution of the turning kernel of the organism population is sought after. We prove the asymptotic equivalence of the two posterior distributions.

math.AP↗

arXiv2021

Bargmann-Fock sheaves on Kähler manifolds

Fedosov used flat sections of the Weyl bundle on a symplectic manifold to construct a star product $\star$ which gives rise to a deformation quantization. By extending Fedosov's method, we give an explicit, analytic construction of a sheaf of Bargmann-Fock modules over the Weyl bundle of a Kähler manifold $X$ equipped with a compatible Fedosov abelian connection, and show that the sheaf of flat sections forms a module sheaf over the sheaf of deformation quantization algebras defined $(C^\infty_X[[\hbar]], \star)$. This sheaf can be viewed as the $\hbar$-expansion of $L^{\otimes k}$ as $k \to \infty$, where $L$ is a prequantum line bundle on $X$ and $\hbar = 1/k$.

math.DG↗