arXiv subjects

Yiwen Lin

Publications and source records attributed to Yiwen Lin.

16 recordsLinked to original sources

arXiv2026

Inverse scattering for three-dimensional random obstacles with multi-frequency data

In many practical scenarios the shapes of scatterers exhibit uncertain geometric variations arising from diverse physical or environmental factors. For inverse scattering problems which are inherently ill-posed, the presence of such geometric uncertainties may have a non-negligible impact on the recovery process. With the aim of recovering both obstacle geometry and statistics of the shape uncertainties, in this paper we study an inverse acoustic scattering problem for three-dimensional smooth star-shaped obstacles with random isotropic fluctuations. We propose an efficient Monte Carlo-based multi-frequency recursive linearization algorithm in which the far-field operator is linearized with respect to the geometry parameters and frequency continuation is employed to recover the unknown geometry from coarse to fine scales. Based on the reconstructed samples, we further estimate the reference geometry and key statistics of the shape fluctuation field including Karhunen--Lo\`eve eigenvalues, covariance hyper-parameters for Gaussian perturbations and covariance structure, representative marginal distributions for non-Gaussian perturbations. We also prove that the probability law of the far-field data uniquely determines the radial function in distribution which implies uniqueness of the reference shape and related statistics. Numerical experiments demonstrate the effectiveness of the proposed method in recovering both the scatterer shapes and the associated statistical information under Gaussian and non-Gaussian random variations.

math.NA↗

arXiv2026

Inverse acoustic scattering for random obstacles with multi-frequency data

We study an inverse random obstacle scattering problems in $\mathbb{R}^2$ where the scatterer is formulated by a Gaussian process defined on the angular parameter domain. Equipped with a modified covariance function which is mathematically well-defined and physically consistent, the Gaussian process admits a parameterization via Karhunen--Lo\`eve (KL) expansion. Based on observed multi-frequency data, we develop a two-stage inversion method: the first stage reconstructs the baseline shape of the random scatterer and the second stage estimates the statistical characteristics of the boundary fluctuations, including KL eigenvalues and covariance hyperparameters. We further provide theoretical justifications for the modeling and inversion pipeline, covering well-definedness of the Gaussian-process model, convergence for the two-stage procedure and a brief discussion on uniqueness. Numerical experiments demonstrate stable recovery of both geometric and statistical information for obstacles with simple and more complex shapes.

math.NA↗

arXiv2025

Random Regularity of the Vlasov-Poisson System with Random Initial Inputs in the Quasineutral Regime

The Vlasov-Poisson system is widely used in plasma physics and other related fields. In this paper, we study the Vlasov-Poisson system with initial uncertainty in the quasineutral regime. First, we prove the uniform convergence in the Wasserstein distance between the uncertain Vlasov-Poisson system in the quasineutral regime and its quasineutral limit system with random initial inputs. This is achieved by deriving an upper bound for the Wasserstein distance and rigorously estimating each component of this bound. Furthermore, by defining a new norm with respect to the quasineutral parameter and estimating the distribution function as well as the electric field in this norm using a variable substitution, we establish the random regularity of the solutions in the quasineutral regime. This work develops a novel framework for quantifying the propagation of the initial uncertainty of the Vlasov-Poisson system in the quasineutral regime, providing a theoretical basis for designing high-performance numerical algorithms.

math.AP↗

arXiv2025

Efficient numerical methods for the uncertain Boltzmann equation based on a hybrid solver

In this work, we propose and compare several approaches to solve the Boltzmann equation with uncertain parameters, including multi-level Monte Carlo and multi-fidelity methods that employ an asymptotic-preserving-hybrid (APH) scheme (Filbet and Rey, 2015) for the deterministic Boltzmann model. By constructing a hierarchy of models from finer to coarser meshes in phase space for the APH scheme and adopting variance reduction techniques, the MLMC method is able to allocate computational resources across different hierarchies quasi-optimally. On the other hand, in the bi-fidelity method we choose the APH scheme for the Boltzmann equation as the high-fidelity solver, and a finite volume scheme for the compressible Euler system as the low-fidelity model. Since both methods are non-intrusive, they can preserve the physical properties of the deterministic solver. Extensive numerical experiments demonstrate that our APH-based MLMC and multi-fidelity methods are significantly faster than standard approaches, while maintaining accuracy. We also provide practical guidelines for selection between APH-based MLMC and multi-fidelity approaches, based on solution smoothness and computational resource availability.

math.NA↗

arXiv2025

An inverse random diffraction grating problem for the Helmholtz equation

This paper investigates the inverse scattering problem of time-harmonic plane waves incident on a perfectly reflecting random periodic structure. To simulate random perturbations arising from manufacturing defects and surface wear in real-world grating profiles, we propose a stochastic surface modeling framework motivated by the discretization of the Wiener process. Our approach introduces randomness at discrete nodes and then applies linear interpolation to construct the surface, marking a novel attempt to incorporate the concepts of the Wiener process into random surface representation. Under this framework, each realization of the random surface generates a Lipschitz-continuous diffraction grating, mathematically represented as a sum of a baseline profile and a weighted linear combination of local `tent' basis functions, meanwhile preserving key statistics of the random surface. Building on this representation, we introduce the Recursive Parametric Smoothing Strategy (RPSS) to invert the key statistics of our random surfaces. Combined with Monte Carlo sampling and a wavenumber continuation strategy, our reconstruction scheme demonstrates effectiveness across multiple benchmark scenarios. Several numerical results are presented along with some discussions in the end on reconstruction mechanisms and future extensions.

math.NA↗

arXiv2024

On the mean-field limit of the Cucker-Smale model with Random Batch Method

In this work, we focus on the mean-field limit of the Random Batch Method (RBM) for the Cucker-Smale model. Different from the classical mean-field limit analysis, the chaos in this model is imposed at discrete time and is propagated to discrete time flux. We approach separately the limits of the number of particles $N\to\infty$ and the discrete time interval $\tau\to 0$ with respect to the RBM, by using the flocking property of the Cucker-Smale model and the observation in combinatorics. The Wasserstein distance is used to quantify the difference between the approximation limit and the original mean-field limit. Also, we combine the RBM with generalized Polynomial Chaos (gPC) expansion and proposed the RBM-gPC method to approximate stochastic mean-field equations, which conserves positivity and momentum of the mean-field limit with random inputs.

math.NA↗

arXiv2024

On a class of multi-fidelity methods for the semiclassical Schr\"odinger equation with uncertainties

In this paper, we study the semiclassical Schr\"odinger equation with random parameters and develop several robust multi-fidelity methods. We employ the time-splitting Fourier pseudospectral (TSFP) method for the high-fidelity solver, and consider different low-fidelity solvers including the meshless method like frozen Gaussian approximation (FGA) and the level set (LS) method for the semiclassical limit of the Schr\"odinger equation. With a careful choice of the low-fidelity model, we obtain an error estimate for the bi-fidelity method. We conduct numerous numerical experiments and validate the accuracy and efficiency of our proposed multi-fidelity methods, by comparing the performance of a class of bi-fidelity and tri-fidelity approximations.

math.NA↗

arXiv2024

Catalyzing Equity in STEM Teams: Harnessing Generative AI for Inclusion and Diversity

Collaboration is key to STEM, where multidisciplinary team research can solve complex problems. However, inequality in STEM fields hinders their full potential, due to persistent psychological barriers in underrepresented students' experience. This paper documents teamwork in STEM and explores the transformative potential of computational modeling and generative AI in promoting STEM-team diversity and inclusion. Leveraging generative AI, this paper outlines two primary areas for advancing diversity, equity, and inclusion. First, formalizing collaboration assessment with inclusive analytics can capture fine-grained learner behavior. Second, adaptive, personalized AI systems can support diversity and inclusion in STEM teams. Four policy recommendations highlight AI's capacity: formalized collaborative skill assessment, inclusive analytics, funding for socio-cognitive research, human-AI teaming for inclusion training. Researchers, educators, policymakers can build an equitable STEM ecosystem. This roadmap advances AI-enhanced collaboration, offering a vision for the future of STEM where diverse voices are actively encouraged and heard within collaborative scientific endeavors.

cs.CY↗

arXiv2023

Error estimates of a bi-fidelity method for a multi-phase Navier-Stokes-Vlasov-Fokker-Planck system with random inputs

Uniform error estimates of a bi-fidelity method for a kinetic-fluid coupled model with random initial inputs in the fine particle regime are proved in this paper. Such a model is a system coupling the incompressible Navier-Stokes equations to the Vlasov-Fokker-Planck equations for a mixture of the flows with distinct particle sizes. The main analytic tool is the hypocoercivity analysis for the multi-phase Navier-Stokes-Vlasov-Fokker-Planck system with uncertainties, considering solutions in a perturbative setting near the global equilibrium. This allows us to obtain the error estimates in both kinetic and hydrodynamic regimes.

math.AP↗

arXiv2023

On uniqueness of elastic scattering from a cavity

The paper considers direct and inverse elastic scattering from a cavity in homogeneous medium with Dirichlet and Neumann boundary conditions. For direct scattering, existence and uniqueness are derived by variation approach. For inverse scattering, Fr$\acute{\rm e}$chet derivatives of the solution operators are investigated, which give local stability for Dirichlet case.

math.AP↗

arXiv2023

A priori bounds for elastic scattering by deterministic and random unbounded rough surfaces

This paper investigates the elastic scattering by unbounded deterministic and random rough surfaces, which both are assumed to be graphs of Lipschitz continuous functions. For the deterministic case, an a priori bound explicitly dependent on frequencies is derived by the variational approach. For the scattering by random rough surfaces with a random source, well-posedness of the corresponding variation problem is proved. Moreover, a similar bound with explicit dependence on frequencies for the random case is also established based upon the deterministic result, Pettis measurability theorem and Bochner's integrability Theorem.

math.AP↗

arXiv2022

Asymptotic-preserving schemes for kinetic-fluid modeling of mixture flows with distinct particle sizes

We consider coupled models for particulate flows, where the disperse phase is made of particles with distinct sizes. We are thus led to a system coupling the incompressible Navier-Stokes equations to the multi-component Vlasov-Fokker-Planck equations. We design an asymptotic-preserving numerical scheme to approximate the system. The scheme is based on suitable implicit treatment of the stiff drag force term as well as the Fokker-Planck operator, and can be formally shown to capture the hydrodynamic limit with time step and mesh size independent of the Stokes number. Numerical examples illustrate the accuracy and asymptotic behavior of the scheme, with several interesting applications.

math.NA↗

arXiv2022

Stability for the Helmholtz equation in deterministic and random periodic structures

Stability results for the Helmholtz equations in both deterministic and random periodic structures are proved in this paper. Under the assumption of excluding resonances, by a variational method and Fourier analysis in the energy space, the stability estimate for the Helmholtz equation in a deterministic periodic structure is established. For the stochastic case, by introducing a variable transform, the variational formulation of the scattering problem in a random domain is reduced to that in a definite domain with random medium. Combining the stability result for the deteministic case with regularity and stochastic regularity of the scattering surface, Pettis measurability theorem and Bochner's Theorem further yield the stability result for the scattering problem by random periodic structures. Both stability estimates are explicit with respect to the wavenumber.

math.AP↗

arXiv2022

Discriminative Feature Learning through Feature Distance Loss

Ensembles of Convolutional neural networks have shown remarkable results in learning discriminative semantic features for image classification tasks. Though, the models in the ensemble often concentrate on similar regions in images. This work proposes a novel method that forces a set of base models to learn different features for a classification task. These models are combined in an ensemble to make a collective classification. The key finding is that by forcing the models to concentrate on different features, the classification accuracy is increased. To learn different feature concepts, a so-called feature distance loss is implemented on the feature maps. The experiments on benchmark convolutional neural networks (VGG16, ResNet, AlexNet), popular datasets (Cifar10, Cifar100, miniImageNet, NEU, BSD, TEX), and different training samples (3, 5, 10, 20, 50, 100 per class) show the effectiveness of the proposed feature loss. The proposed method outperforms classical ensemble versions of the base models. The Class Activation Maps explicitly prove the ability to learn different feature concepts. The code is available at: https://github.com/2Obe/Feature-Distance-Loss.git

cs.CV↗

arXiv2022

Energy estimates and hypocoercivity analysis for a multi-phase Navier-Stokes-Vlasov-Fokker-Planck system with uncertainty

This paper is concerned with a kineitc-fluid model with random initial inputs in the fine particle regime, which is a system coupling the incompressible Navier-Stokes equations and the Vlasov-Fokker-Planck equations that model dispersed particles of different sizes. A uniform regularity for random initial data near the global equilibrium is established in some suitable Sobolev spaces by using energy estimates, and we also prove the energy decays exponentially in time by hypocoercivity arguments, which means that the long time behavior of the solution is insensitive to the random perturbation in the initial data. For the generalized polynomial chaos stochastic Galerkin method (gPC-sG) for the model, with initial data near the global equilibrium and smooth enough in the physical and random spaces, we prove that the gPC-sG method has spectral accuracy, uniformly in time and the Knudsen number, and the error decays exponentially in time.

math.AP↗

arXiv2020

Inverse scattering by a random periodic structure

This paper develops an efficient numerical method for the inverse scattering problem of a time-harmonic plane wave incident on a perfectly reflecting random periodic structure. The method is based on a novel combination of the Monte Carlo technique for sampling the probability space, a continuation method with respect to the wavenumber, and the Karhunen-Lo$\grave{e}$ve expansion of the random structure, which reconstructs key statistical properties of the profile for the unknown random periodic structure from boundary measurements of the scattered fields away from the structure. Numerical results are presented to demonstrate the reliability and efficiency of the proposed method.

math.NA↗