arXiv subjects

Yijia Tang

Publications and source records attributed to Yijia Tang.

8 recordsLinked to original sources

arXiv2026

Computation of entanglement for quantum states by a Consensus-Based Optimization method

The computation of quantum entanglement can be formulated as a high-dimensional nonconvex optimization problem with orthogonality constraints. In this work, we propose structure-preserving consensus-based optimization (CBO) methods for entanglement computation, with one approach based on a Hermitian formulation and the other evolving directly on the unitary manifold. To handle the variable dimension of the feasible set, we introduce a cross-dimensional interaction mechanism allowing exchange of information between particles of different sizes. Numerical experiments demonstrate that the proposed methods achieve accurate approximations.

quant-ph↗

arXiv2023

A Collaborative Jamming Algorithm Based on Multi-UAV Scheduling

In this paper, we consider the problem of multi-unmanned aerial vehicles' scheduling for cooperative jamming, where UAVs equipped with directional antennas perform collaborative jamming tasks against several targets of interest. To ensure effective jamming towards the targets, we formulate it as an non-convex optimization problem, aiming to minimize the communication performance of the targets by jointly optimizing UAVs' deployment and directional antenna orientations. Due to the unique structure of the problem, we derive an equivalent transformation by introducing a set of auxiliary matrices. Subsequently, we propose an efficient iterative algorithm based on the alternating direction method of multipliers, which decomposes the problem into multiple tractable subproblems solved in closed-form or by gradient projection method. Extensive simulations validate the efficacy of the proposed algorithm.

math.OC↗

arXiv2023

Solving stationary nonlinear Fokker-Planck equations via sampling

Solving the stationary nonlinear Fokker-Planck equations is important in applications and examples include the Poisson-Boltzmann equation and the two layer neural networks. Making use of the connection between the interacting particle systems and the nonlinear Fokker-Planck equations, we propose to solve the stationary solution by sampling from the $N$-body Gibbs distribution. This avoids simulation of the $N$-body system for long time and more importantly such a method can avoid the requirement of uniform propagation of chaos from direct simulation of the particle systems. We establish the convergence of the Gibbs measure to the stationary solution when the interaction kernel is bounded (not necessarily continuous) and the temperature is not very small. Numerical experiments are performed for the Poisson-Boltzmann equations and the two-layer neural networks to validate the method and the theory.

math.NA↗

arXiv2022

Some random batch particle methods for the Poisson-Nernst-Planck and Poisson-Boltzmann equations

We consider in this paper random batch interacting particle methods for solving the Poisson-Nernst-Planck (PNP) equations, and thus the Poisson-Boltzmann (PB) equation as the equilibrium, in the external unbounded domain. To justify the simulation in a truncated domain, an error estimate of the truncation is proved in the symmetric cases for the PB equation. Then, the random batch interacting particle methods are introduced which are $O(N)$ per time step. The particle methods can not only be considered as a numerical method for solving the PNP and PB equations, but also can be used as a direct simulation approach for the dynamics of the charged particles in solution. The particle methods are preferable due to their simplicity and adaptivity to complicated geometry, and may be interesting in describing the dynamics of the physical process. Moreover, it is feasible to incorporate more physical effects and interactions in the particle methods and to describe phenomena beyond the scope of the mean-field equations.

math.NA↗

arXiv2022

The Quadratic Wasserstein Metric With Squaring Scaling For Seismic Velocity Inversion

The quadratic Wasserstein metric has shown its power in measuring the difference between probability densities, which benefits optimization objective function with better convexity and is insensitive to data noise. Nevertheless, it is always an important question to make the seismic signals suitable for comparison using the quadratic Wasserstein metric. The squaring scaling is worth exploring since it guarantees the convexity caused by data shift. However, as mentioned in [Commun. Inf. Syst., 2019, 19:95-145], the squaring scaling may lose uniqueness and result in more local minima to the misfit function. In our previous work [J. Comput. Phys., 2018, 373:188-209], the quadratic Wasserstein metric with squaring scaling was successfully applied to the earthquake location problem. But it only discussed the inverse problem with few degrees of freedom. In this work, we will present a more in-depth study on the combination of squaring scaling technique and the quadratic Wasserstein metric. By discarding some inapplicable data, picking seismic phases, and developing a new normalization method, we successfully invert the seismic velocity structure based on the squaring scaling technique and the quadratic Wasserstein metric. The numerical experiments suggest that this newly proposed method is an efficient approach to obtain more accurate inversion results.

math.NA↗

arXiv2022

On the equilibrium of the Poisson-Nernst-Planck-Bikermann model equipping with the steric and correlation effects

The Poisson-Nernst-Planck-Bikermann (PNPB) model, in which the ions and water molecules are treated as different species with non-uniform sizes and valences with interstitial voids, can describe the steric and correlation effects in ionic solution neglected by the Poisson-Nernst-Planck and Poisson-Boltzmann theories with point charge assumption. In the PNPB model, the electric potential is governed by the fourth-order Poisson-Bikermann (4PBik) equation instead of the Poisson equation so that it can describe the correlation effect. What's more, the steric potential is included in the ionic and water fluxes as well as the equilibrium Fermi-like distributions which characterizes the steric effect quantitatively. In this work, after doing a nondimensionalization step, we analyze the self-adjointness and the kernel of the fourth-order operator of the 4PBik equation. Also, we show the positivity of the void volume function and the convexity of the free energy. Following these properties, the well-posedness of the PNPB model in equilibrium is given. Furthermore, because the PNPB model has an energy dissipated structure, we adopt a finite volume scheme which preserves the energy dissipated property at the semi-discrete level. After that, various numerical investigations are given to show the parameter dependence of the steric effect to the steady state.

math-ph↗

arXiv2021

Isomer: Transfer enhanced Dual-Channel Heterogeneous Dependency Attention Network for Aspect-based Sentiment Classification

Aspect-based sentiment classification aims to predict the sentiment polarity of a specific aspect in a sentence. However, most existing methods attempt to construct dependency relations into a homogeneous dependency graph with the sparsity and ambiguity, which cannot cover the comprehensive contextualized features of short texts or consider any additional node types or semantic relation information. To solve those issues, we present a sentiment analysis model named Isomer, which performs a dual-channel attention on heterogeneous dependency graphs incorporating external knowledge, to effectively integrate other additional information. Specifically, a transfer-enhanced dual-channel heterogeneous dependency attention network is devised in Isomer to model short texts using heterogeneous dependency graphs. These heterogeneous dependency graphs not only consider different types of information but also incorporate external knowledge. Experiments studies show that our model outperforms recent models on benchmark datasets. Furthermore, the results suggest that our method captures the importance of various information features to focus on informative contextual words.

cs.CL↗

arXiv2021

Random batch particle methods for the homogeneous Landau equation

We consider in this paper random batch particle methods for efficiently solving the homogeneous Landau equation in plasma physics. The methods are stochastic variations of the particle methods proposed by Carrillo et al. [J. Comput. Phys.: X 7: 100066, 2020] using the random batch strategy. The collisions only take place inside the small but randomly selected batches so that the computational cost is reduced to $O(N)$ per time step. Meanwhile, our methods can preserve the conservation of mass, momentum, energy and the decay of entropy. Several numerical examples are performed to validate our methods.

math.NA↗