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Liqun Cao

Publications and source records attributed to Liqun Cao.

12 recordsLinked to original sources

Lean Learning Beyond Clouds: Efficient Discrepancy-Conditioned Optical-SAR Fusion for Semantic Segmentation

Cloud occlusion severely degrades the semantic integrity of optical remote sensing imagery. While incorporating Synthetic Aperture Radar (SAR) provides complementary observations, achieving efficient global modeling and reliable cross-modal fusion under cloud interference remains challenging. Existing methods rely on dense global attention to capture long-range dependencies, yet such aggregation indiscriminately propagates cloud-induced noise. Improving robustness typically entails enlarging model capacity, which further increases computational overhead. Given the large-scale and high-resolution nature of remote sensing applications, such computational demands hinder practical deployment, leading to an efficiency-reliability trade-off. To address this dilemma, we propose EDC, an efficiency-oriented and discrepancy-conditioned optical-SAR semantic segmentation framework. A tri-stream encoder with Carrier Tokens enables compact global context modeling with reduced complexity. To prevent noise contamination, we introduce a Discrepancy-Conditioned Hybrid Fusion (DCHF) mechanism that selectively suppresses unreliable regions during global aggregation. In addition, an auxiliary cloud removal branch with teacher-guided distillation enhances semantic consistency under occlusion. Extensive experiments demonstrate that EDC achieves superior accuracy and efficiency, improving mIoU by 0.56\% and 0.88\% on M3M-CR and WHU-OPT-SAR, respectively, while reducing the number of parameters by 46.7\% and accelerating inference by 1.98$\times$. Our implementation is available at https://github.com/mengcx0209/EDC.

cs.CV

A fourth-order multi-scale computational method and its convergence analysis for composite Kirchhoff plates with microscopic periodic configurations

The Kirchhoff plate model plays a vital role in modeling, computing and analyzing the mechanical behaviors of thin plate structures. This study propose a novel fourth-order multi-scale (FOMS) computational method for high-accuracy and efficient simulation of composite Kirchhoff plates with highly periodic heterogeneities. At first, two-scale asymptotic expansion theory is employed to establish the high-accuracy fourth-order multi-scale computation model with novel fourth-order correctors for composite Kirchhoff plates, which are governed by fourth-order partial differential equation (PDE) with periodically oscillatory and highly discontinuous coefficients. Then, the locally point-wise error analysis is derived to theoretically illustrate the local balance preserving of fourth-order multi-scale model enabling high-accuracy multi-scale computation. Furthermore, a global error estimation with an explicit order for fourth-order multi-scale solutions is first demonstrated under appropriate assumptions. In contrast to the second- and third-order multi-scale solutions, only the fourth-order one is capable of providing an explicit error order estimate. Additionally, an efficient numerical algorithm is developed to conduct high-accuracy simulation for heterogeneous plate structures. Extensive numerical examples are provided to confirm the theoretical results for the computational convergence and accuracy of the proposed method. This work offers a higher-order (fourth-order) multi-scale computational framework that enables robust simulation and high-accuracy analysis to composite Kirchhoff plates.

math.NA

Parabolic hysteresis problems revisited: Finite element error analysis and convergent Newton-type solvers

Numerical investigations of partial differential equations with hysteresis have largely focused on simulations, leaving numerical error analysis unexplored and relying mainly on derivative-free nonlinear solvers. This work establishes rigorous finite element error estimates for the backward Euler fully discrete scheme applied to semilinear and quasilinear parabolic equations involving continuous hysteresis operators. To efficiently handle the inherent nonsmoothness of the resulting nonlinear algebraic systems, we develop a damped smoothing Newton solver under a general condition on the smoothing approximation, ensuring global convergence together with local Q-quadratic convergence. Numerical experiments confirm the theoretical convergence rates for semilinear problems, while showing higher-than-predicted orders for quasilinear ones. The robustness and efficiency of the proposed solver are further demonstrated in comparison with existing methods.

math.NA

Optimal-rate error estimates and a twice decoupled solver for a backward Euler finite element scheme of the Doyle-Fuller-Newman model of lithium-ion cells

We investigate the convergence of a backward Euler finite element discretization applied to a multi-domain and multi-scale elliptic-parabolic system, derived from the Doyle-Fuller-Newman model for lithium-ion cells. We establish optimal-order error estimates for the solution in the norms $l^2(H^1)$ and $l^2(L^2(H^q_r))$, $q=0,1$. To improve computational efficiency, we propose a novel solver that accelerates the solution process and controls memory usage. Numerical experiments with realistic battery parameters validate the theoretical error rates and demonstrate the significantly superior performance of the proposed solver over existing solvers.

math.NA

Optimal convergence in finite element semi-discrete error analysis of the Doyle-Fuller-Newman model beyond 1D with a novel projection operator

We present a finite element semi-discrete error analysis for the Doyle-Fuller-Newman model, which is the most popular model for lithium-ion batteries. Central to our approach is a novel projection operator designed for the pseudo-($N$+1)-dimensional equation, offering a powerful tool for multiscale equation analysis. Our results bridge a gap in the analysis for dimensions $2 \le N \le 3$ and achieve optimal convergence rates of $h+(Δr)^2$. Additionally, we perform a detailed numerical verification, marking the first such validation in this context. By avoiding the change of variables, our error analysis can also be extended beyond isothermal conditions.

math.NA

Efficient algorithm and analysis for the Yang-Mills equations with temporal gauge

This paper discusses the finite element method for the Yang-Mills equations with temporal gauge. The new contributions reported in this paper are threefold: an efficient linearized strategy for the Lie bracket $[A, A]$ is introduced, the novel implicit scheme in time for the Yang-Mills equations based on the above linearized strategy is presented, which preserves the conservation of its discrete energy and the error estimates for the semi-discrete scheme and the linearized scheme are proved. Finally, numerical test studies are then carried out to confirm the theoretical results.

math.NA

Efficient multiscale algorithms for simulating nonlocal optical response of metallic nanostructure arrays

In this paper, we consider numerical simulations of the nonlocal optical response of metallic nanostructure arrays inside a dielectric host, which is of particular interest to the nanoplasmonics community due to many unusual properties and potential applications. Mathematically, it is described by Maxwell's equations with discontinuous coefficients coupled with a set of Helmholtz-type equations defined only on the domains of metallic nanostructures. To solve this challenging problem, we develop an efficient multiscale method consisting of three steps. First, we extend the system into the domain occupied by the dielectric medium in a novel way and result in a coupled system with rapidly oscillating coefficients. A rigorous analysis of the error between the solutions of the original system and the extended system is given. Second, we derive the homogenized system and define the multiscale approximate solution for the extended system by using the multiscale asymptotic method. Third, to fix the inaccuracy of the multiscale asymptotic method inside the metallic nanostructures, we solve the original system in each metallic nanostructure separately with boundary conditions given by the multiscale approximate solution. A fast algorithm based on the $LU$ decomposition is proposed for solving the resulting linear systems. By applying the multiscale method, we obtain the results that are in good agreement with those obtained by solving the original system directly at a much lower computational cost. Numerical examples are provided to validate the efficiency and accuracy of the proposed method.

math.NA

Neural Network Based in Silico Simulation of Combustion Reactions

Understanding and prediction of the chemical reactions are fundamental demanding in the study of many complex chemical systems. Reactive molecular dynamics (MD) simulation has been widely used for this purpose as it can offer atomic details and can help us better interpret chemical reaction mechanisms. In this study, two reference datasets were constructed and corresponding neural network (NN) potentials were trained based on them. For given large-scale reaction systems, the NN potentials can predict the potential energy and atomic forces of DFT precision, while it is orders of magnitude faster than the conventional DFT calculation. With these two models, reactive MD simulations were performed to explore the combustion mechanisms of hydrogen and methane. Benefit from the high efficiency of the NN model, nanosecond MD trajectories for large-scale systems containing hundreds of atoms were produced and detailed combustion mechanism was obtained. Through further development, the algorithms in this study can be used to explore and discovery reaction mechanisms of many complex reaction systems, such as combustion, synthesis, and heterogeneous catalysis without any predefined reaction coordinates and elementary reaction steps.

physics.chem-ph

Mathematical and numerical analysis of the time-dependent Maxwell--Schrödinger Equations in the Coulomb gauge

In this paper, we consider the initial-boundary value problem for the time-dependent Maxwell--Schrödinger equations in the Coulomb gauge. We first prove the global existence of weak solutions to the equations. Next we propose an energy-conserving fully discrete finite element scheme for the system and prove the existence and uniqueness of solutions to the discrete system. The optimal error estimates for the numerical scheme without any time-step restrictions are then derived. Numerical results are provided to support our theoretical analysis.

math.NA

Error estimates of the Crank-Nicolson Galerkin method for the time-dependent Maxwell-Schrödinger equations under the Lorentz gauge

In this paper we study the numerical method and the convergence for solving the time-dependent Maxwell-Schrödinger equations under the Lorentz gauge. An alternating Crank-Nicolson finite element method for solving the problem is presented and the optimal error estimate for the numerical algorithm is obtained by a mathematical inductive method. Numerical examples are then carried out to confirm the theoretical results.

math.NA

A Crank-Nicolson Finite Element Method and the Optimal Error Estimates for the modified Time-dependent Maxwell-Schrödinger Equations

In this paper we consider the initial-boundary value problem for the time-dependent Maxwell-Schrödinger equations, which arises in the interaction between the matter and the electromagnetic field for the semiconductor quantum devices. A Crank-Nicolson finite element method for solving the problem is presented. The optimal energy-norm error estimates for the numerical algorithm without any time-step restrictions are derived. Numerical tests are then carried out to confirm the theoretical results.

math.NA

Multiscale Approach and The Convergence for the time-dependent Maxwell-Schrödinger System in Heterogeneous Nanostructures

This paper discusses the multiscale approach and the convergence of the time-dependent Maxwell-Schrödinger system with rapidly oscillating discontinuous coefficients arising from the modeling of a heterogeneous nanostructure with a periodic microstructure. The homogenization method and the multiscale asymptotic method for the nonlinear coupled equations are presented. The efficient numerical algorithms based on the above methods are proposed. Numerical simulations are then carried out to validate the method presented in this paper.

math.NA