We develop novel asymptotic-preserving (AP) deterministic particle methods for collisional plasma models, including both Landau–Fokker–Planck and Dougherty collision operators, under hydrodynamic scaling. Our schemes treat the non-stiff transport part explicitly and the stiff collision operators fully implicitly through the energy-conserving Jordan–Kinderlehrer–Otto (JKO) schemes by exploiting their gradient flow structures. This approach extends our previous work on the space-homogeneous Landau equation [arXiv:2409.12296] and introduces a new treatment of the Dougherty operator via a projected gradient flow formulation. We identify the crucial role of Jacobian log-determinant evaluation in stiff regimes and introduce an inner-time quadrature strategy that improves both accuracy and efficiency. Furthermore, we uncover intriguing connections with score-based transport modeling, showing that both explicit and implicit score matching arise as special cases of our unified variational framework and exhibit limitations in the stiff regime. We also develop practical large-scale implementations via neural network parameterization and efficient training strategies. Various numerical examples demonstrate the structure-preserving and AP properties of our schemes for general initial data.

Abstract Inspired by the gradient flow viewpoint of the Landau equation and the corresponding dynamic formulation of the Landau metric in Carrillo et al. (2024a), we develop a novel implicit particle method for the Landau equation in the framework of the Jordan–Kinderlehrer–Otto scheme. We first reformulate the Landau metric in a computationally friendly form, and then translate it into the Lagrangian viewpoint using the flow map. A key observation is that, while the flow map evolves according to a rather complicated integral equation, the unknown component is simply a score function of the corresponding density plus an additional term in the null space of the collision kernel. This insight guides us in designing and training the neural network for the flow map. Additionally, the objective function is in a double summation form, making it highly suitable for stochastic methods. Consequently, we have designed a tailored version of stochastic gradient descent that maintains particle interactions and significantly reduces the computational complexity. Compared to other deterministic particle methods, the proposed method enjoys exact entropy dissipation and unconditional stability, thereby making it suitable for large-scale plasma simulations over extended time periods.

The central object in wave turbulence theory is the wave kinetic equation (WKE), which is an evolution equation for wave action density and acts as the wave analog of the Boltzmann kinetic equations for particle interactions. Despite recent exciting progress in the theoretical aspects of the WKE, numerical developments have lagged behind. In this paper, we introduce a fast Fourier spectral method for solving the WKE. The key idea lies in reformulating the high-dimensional nonlinear wave kinetic operator as a spherical integral, analogous to the classical Boltzmann collision operator. The conservation of mass and momentum leads to a double convolution structure in Fourier space, which can be efficiently handled by the fast Fourier transform (FFT), reducing the computational cost from O(N-3d) to O(MN(d)log N) with N-frequency nodes and M << N2d-1 in d dimensions. We demonstrate the accuracy and efficiency of the proposed method through several numerical tests in both 2D and 3D, revealing and conjecturing some interesting and unique features of this equation.

Terrestrial laser scanning (TLS), also referred to as terrestrial LiDAR, has become an essential close-range remote sensing technique for high-precision engineering surveying, deformation monitoring, industrial inspection, and cultural heritage documentation. The geometric reliability of TLS point clouds strongly depends on the effective compensation of instrumental systematic errors through in situ self-calibration. However, conventional target-based self-calibration often suffers from strong coupling between calibration parameters and exterior orientation parameters, whereas recently developed coplanarity-constrained formulations generally require highly redundant target networks, limiting their field efficiency. To address this limitation, this study proposes a variance inflation factor (VIF)-driven minimal network design strategy for efficient in situ geometric self-calibration of TLS systems. Unlike the commonly used geometric dilution of precision, VIF provides a dimensionless statistical alternative that effectively resolves the dimensional inconsistency inherent in traditional GDOP when handling mixed angular and distance parameters. A differential evolution algorithm is employed to search for hybrid calibration networks that minimize parameter coupling while preserving the physical interpretability of the National Institute of Standards and Technology (NIST) 10-parameter instrumental error model. Five digital twin simulation experiments and a physical validation experiment using a Faro Focus 350 scanner were conducted to evaluate the proposed method. The results show that the optimized network substantially reduces the number of required targets while maintaining high calibration accuracy. The final configuration, which combines VIF-optimized target placement with a dual-station height-difference constraint, reduces the condition number of the normal equations to below 60 and yields a mean system VIF close to 10. The maximum parameter correlation coefficient among the key calibration parameters is constrained to approximately 0.75, indicating near-optimal parameter decoupling under the limited field-of-view geometry of the instrument. These findings demonstrate that the proposed VIF-driven network design provides a highly effective strategy for field-efficient TLS self-calibration and improves the geometric reliability of terrestrial LiDAR point clouds in high-precision remote sensing applications.

High-fidelity sound speed profiles (SSPs) are essential for accurate underwater acoustic applications, but their high resolution imposes significant computational, storage, and transmission burdens. This necessitates SSP simplification, a process that reduces the number of data points while preserving essential acoustic propagation characteristics. This paper introduces the Travel-Time-Weighted Adaptive Simplification (TTWAS) algorithm, a novel, physics-informed method for SSP layering. Unlike conventional geometry-based techniques, TTWAS is derived directly from the acoustic ray travel-time equation. The method establishes a depth-dependent weighting function that quantifies the sensitivity of travel time to local sound speed errors, transforming the simplification problem into a tractable weighted least-squares (WLS) optimization. An optimal piecewise-linear structure is then determined globally and efficiently using a dynamic programming algorithm accelerated by a divide-and-conquer strategy. The final number of layers is determined automatically using the Bayesian Information Criterion (BIC), eliminating the need for user-specified complexity parameters. Experiments on a diverse dataset of sound speed profiles demonstrate that TTWAS outperforms established geometric methods, reducing the mean Root Mean Square Horizontal Range Error (RMSHRE) by over 70% and achieving an average accuracy of 2.7 mm. This level of precision is critical for high-fidelity underwater acoustic ray tracing, enabling significant improvements in positioning and navigation accuracy. By shifting the paradigm from geometry-centric to physics-centric simplification, our work yields compact and physically faithful models suitable for high-precision underwater acoustic applications.

This paper focuses on execution efficiency for Combined Uncertainty and Bathymetry Estimator (CUBE) algorithm. By analyzing the key steps of the algorithm, this paper shows how to improve algorithm efficiency by using Octree index and Graphics Processing Unit (GPU) parallel computing. The former is used to establish rules grids and neighborhood searches, while the latter is used to calculate the filtering calculation task in parallel. The combination of the two improves the overall execution efficiency of the algorithm. This paper designs experiment to test efficiency of the algorithm when processing the Multi-Beam Echo Sounder (MBES) data, and compare with the CUBE filter module of CARIS HIPS software. The experimental results show that the algorithm used in this paper can increase the filtering speed by about 13.8 times when dealing with ten million levels of data, and the efficiency of this algorithm in processing millions of MBES data is significantly better than the efficiency of CARIS HIPS software; The algorithm has better denoising effect than CARIS HIPS software in some cases.

We construct an efficient primal-dual forward-backward (PDFB) splitting method for computing a class of minimizing movement schemes with nonlinear mobility transport distances, and apply it to computing Wasserstein-like gradient flows. This approach introduces a novel saddle point formulation for the minimizing movement schemes, leveraging a support function form from the Benamou-Brenier dynamical formulation of optimal transport. The resulting framework allows for flexible computation of Wasserstein-like gradient flows by solving the corresponding saddle point problem at the fully discrete level, and can be easily extended to handle general nonlinear mobilities. We also provide a detailed convergence analysis of the PDFB splitting method, along with practical remarks on its implementation and application. The effectiveness of the method is demonstrated through several challenging numerical examples.

Over three decades of research has been undertaken on point cloud registration algorithms, resulting in mature theoretical frameworks and methodologies. However, among the numerous registration techniques used, the impact of point cloud scanning quality on registration outcomes has rarely been addressed. In most engineering and industrial measurement applications, the accuracy and density of LiDAR point clouds are highly dependent on laser scanners, leading to significant variability that critically affects registration quality. Key factors influencing point cloud accuracy include scanning distance, incidence angle, and the surface characteristics of the target. Notably, in short-range scanning scenarios, incidence angle emerges as the dominant error source. Building on this insight, this study systematically investigates the relationship between scanning incidence angles and point cloud quality. We propose an incident-angle-dependent weighting function for point cloud observations, and further develop an improved weighted Iterative Closest Point (ICP) registration algorithm. Experimental results demonstrate that the proposed method achieves approximately 30% higher registration accuracy compared to traditional ICP algorithms and a 10% improvement over Faro SCENE’s proprietary solution.

Viscous fingering, a classic hydrodynamic instability, is governed by the the competition between destabilising viscosity ratios and stabilising surface tension or thermal diffusion. We show that the channel confinement can induce ‘diffusion’-like stabilising effects on viscous fingering even in the absence of interfacial tension and thermal diffusion, when a clear oil invades the mixture of the same oil and non-colloidal particles. The key lies in the generation of long-range dipolar disturbance flows by highly confined particles that form a monolayer inside a Hele-Shaw cell. We develop a coarse-grained model whose results correctly predict universal fingering dynamics that is independent of particle concentrations. This new mechanism offers insights into manipulating and harnessing collective motion in non-equilibrium systems.

Jump processes in stable stochastic differential equations (SDEs) with jumps disrupt their stable state, leading to large fluctuations that hinder parameter estimation. Regularization methods alone are often insufficient to handle the large fluctuations during non-stationary phases of SDEs. This paper proposes a more robust estimation method for SDEs with jumps by smoothing the impact of jump disturbances in the data. The proposed method utilizes quadratic variation to detect the starting points when the stable stochastic process enters a stable state and the recovery points from jump shocks. Based on this detection, a novel OU bridge replacement for regularized parameter estimation is employed to smooth out the jump disturbance segments in the original data. Repeated experimental results demonstrate that these smoothing techniques can enhance the accuracy of parameter estimation for stable SDEs with jumps. We expect these methods to contribute to improved analysis of financial historical data.

Define a forward problem as ρ_y = G_#ρ_x, where the probability distribution ρ_x is mapped to another distribution ρ_y using the forward operator G. In this work, we investigate the corresponding inverse problem: Given ρ_y, how to find ρ_x? Depending on whether G is overdetermined or underdetermined, the solution can have drastically different behavior. In the overdetermined case, we formulate a variational problem min_ρ_x D( G_#ρ_x, ρ_y), and find that different choices of the metric D significantly affect the quality of the reconstruction. When D is set to be the Wasserstein distance, the reconstruction is the marginal distribution, while setting D to be a ϕ-divergence reconstructs the conditional distribution. In the underdetermined case, we formulate the constrained optimization min_{ G_#ρ_x=ρ_y} E[ρ_x]. The choice of E also significantly impacts the construction: setting E to be the entropy gives us the piecewise constant reconstruction, while setting E to be the second moment, we recover the classical least-norm solution. We also examine the formulation with regularization: min_ρ_x D( G_#ρ_x, ρ_y) + α𝖱[ρ_x], and find that the entropy-entropy pair leads to a regularized solution that is defined in a piecewise manner, whereas the W_2-W_2 pair leads to a least-norm solution where W_2 is the 2-Wasserstein metric.

This study presents a semi-infinite interval type-2 fuzzy multi-objective programming (SIIT2F-MOP) model for optimizing irrigation water management under uncertainty. The model integrates fuzzy sets, linear programming, and semi-infinite programming to address dynamic parameters. Applied to Zhangzhou City, Fujian, it optimizes water allocation for three crops across 11 districts and provides interval-based results. Combined with regional hydrological-characteristic methods, the model improves economic, yield, and water-saving benefits. At H3, alpha = 0.8, the results of the SIIT2F-MOP model under the three objectives of economic, crop yield, and water-saving are [686 930.9, 796 782.6] x 103 yuan, [394 613.7, 511 387.9] x 103 kg, and [7645.6, 148 567.6] x 103 m3, respectively. Compared with other methods, interval ranges decreased by up to 17.3%, 11.8%, and 8.6%, showing stronger performance under water-resource uncertainty. The analysis shows flexibility in assessing benefits and trade-offs under varied water-supply scenarios. The SIIT2F-MOP model supports evidence-based policy for sustainable agricultural and water-resource management.

We use the Wigner transformation and asymptotic analysis to systematically derive the semiclassical model for the Schro"\dinger equation in arbitrary spatial dimensions, with any periodic structure. Our particular emphasis lies in addressing the diabatic effect, i.e., the impact of Bloch band crossings. We consider both deterministic and random scenarios. In the former case, we derive a coupled Liouville system, revealing lower-order interactions among different Bloch bands. In the latter case, a coupled system of radiative transport equations emerges, with the scattering cross section induced by the random inhomogeneities. As a specific application, we deduce the effective dynamics of a wave packet in graphene with randomness.

We propose a novel score-based particle method for solving the Landau equation in plasmas, which seamlessly integrates learning with structure-preserving particle methods [1]. Building upon the Lagrangian viewpoint of the Landau equation, a central challenge stems from the nonlinear dependence of the velocity field on the density. Our primary innovation lies in recognizing that this nonlinearity is in the form of the score function, which can be approximated dynamically via techniques from score-matching. The resulting method inherits the conservation properties of the deterministic particle method while sidestepping the necessity for kernel density estimation in [1]. This streamlines computation and enhances scalability with dimensionality. Furthermore, we provide a theoretical estimate by demonstrating that the KL divergence between our approximation and the true solution can be effectively controlled by the score-matching loss. Additionally, by adopting the flow map viewpoint, we derive an update formula for exact density computation. Extensive examples have been provided to show the efficiency of the method, including a physically relevant case of Coulomb interaction.

Water shortages and supply pressures due to the special geographical environment pose significant challenges to the social and economic development of the Minjiang River Basin in Fujian Province, China. This study introduced a semi-infinite interval type-2 fuzzy multi-objective programming (SIIT2F-MOP) model to optimize the water resource system under conditions of uncertainty. Additionally, a novel multi-criteria decision analysis (MCDA) method, integrating the interval-based technique for order of preference by similarity to ideal solution (ITOPSIS), was developed to analyze and evaluate water allocation results using interval data instead of specific values. The SIIT2F-MOP model combines semi-infinite programming, multi-objective optimization, and interval type-2 fuzzy sets to address uncertainties and resolve conflicts among multiple decision-makers in water resource management. The innovations and contributions of this study are as follows: (i) prioritizing the restructuring of secondary industries while advancing manufacturing and modern service sectors can promote economic development and mitigate water shortages, and net system benefits increased by 7.2 %; (ii) evaluation of water allocation options using the ITOPSIS method demonstrates that industrial benefits account for 53.8 % of the optimal scenario; and (iii) the proposed model facilitates dynamic analysis of economic efficiency, equity in water distribution, and water scarcity within the water resource system. By integrating advanced optimization and decision-making techniques, this study contributes to sustainable resource management and supports risk control in the face of growing water demand.

The eddy current magneto-optical non-destructive testing (ECMO NDT) system offers advantages such as high detection speed, precision and resolution, making it widely used in the NDT of weakly conductive materials. In recent years, ECMO NDT technology based on digital lock-in amplifier (LIA) signal extraction has become increasingly mature. However, it is limited to revealing the surface contours of defects, while reconstructing the 3D morphology of defects remains a key research focus. In this work, we propose a method for reconstructing 3D images of material defects using polynomial fitting combined with cubic spline interpolation. The experiments were conducted on an ECMO NDT platform, which measured the amplitude and phase information of the eddy current magnetic field of the material. The 3D images of the defects were reconstructed based on the detected amplitude and phase information. The amplitude and phase data corresponding to the 3D shapes of different defects were treated as prior information for the fitting model. We incorporated the electromagnetic patterns derived from simulation phenomena, which describe the effect of defects on eddy currents, as constraints for the fitting process and introduced a regularization term to prevent model overfitting when prior data is limited. The cubic spline interpolation method was employed to enhance image resolution, allowing the system to reconstruct higher-resolution 3D images within a shorter detection time. Experimental results demonstrate that the reconstructed images of various defects in different materials are clear, providing detailed depth information. Compared to traditional 2D imaging methods that rely solely on the amplitude or phase of the eddy current, our method, which combines both amplitude and phase information, offers a more comprehensive representation of defect size and shape.

ABSTRACT This study addresses the pivotal challenge of water resource allocation in urban environments by introducing a novel approach – a multi-objective chance-constrained fuzzy interval linear programming model integrated with principal component analysis (PCA). This innovative model aims to alleviate subjectivity in urban water management processes, particularly in adjusting water demands across various sectors. The proposed model incorporates correlation analysis to identify dimensionality-reducing factors of multitarget components, determining the proportion of each target component relative to the total components. Fuzzy sets are applied to irrigation water resource allocation quantity, segmented into six levels of fuzzy membership to analyze the stochasticity of water supply. Results demonstrate the model's efficacy, revealing that variations in risk probabilities impact water supply, necessitating positive water management strategies to enhance agricultural efficiency and negative strategies to mitigate the risk of inadequate water supply. Key findings emphasize the significance of agricultural water availability and the structure of irrigation water use in optimal resource allocation. Importantly, the study showcases the enhanced precision achieved through the proposed multi-objective chance-constrained fuzzy interval linear programming with PCA, thereby refining the optimization outcomes for water management under multifaceted objectives.

Inspired by the gradient flow viewpoint of the Landau equation and the corresponding dynamic formulation of the Landau metric in [arXiv:2007.08591], we develop a novel implicit particle method for the Landau equation in the framework of the JKO scheme. We first reformulate the Landau metric in a computationally friendly form, and then translate it into the Lagrangian viewpoint using the flow map. A key observation is that, while the flow map evolves according to a rather complicated integral equation, the unknown component is simply a score function of the corresponding density plus an additional term in the null space of the collision kernel. This insight guides us in designing and training the neural network for the flow map. Additionally, the objective function is in a double summation form, making it highly suitable for stochastic methods. Consequently, we design a tailored version of stochastic gradient descent that maintains particle interactions and significantly reduces the computational complexity. Compared to other deterministic particle methods, the proposed method enjoys exact entropy dissipation and unconditional stability, therefore making it suitable for large-scale plasma simulations over extended time periods.

We develop structure preserving schemes for a class of nonlinear mobility continuity equation. When the mobility is a concave function, this equation admits a form of gradient flow with respect to a Wasserstein-like transport metric. Our numerical schemes build upon such formulation and utilize modern large scale optimization algorithms. There are two distinctive features of our approach compared to previous ones. On one hand, the essential properties of the solution, including positivity, global bounds, mass conservation and energy dissipation are all guaranteed by construction. On the other hand, it enjoys sufficient flexibility when applies to a large variety of problems including different free energy functionals, general wetting boundary conditions and degenerate mobilities. The performance of our methods are demonstrated through a suite of examples.

A simplified kinetic description of rapid granular media leads to a nonlocal Vlasov-type equation with a convolution integral operator that is of the same form as the continuity equations for aggregation-diffusion macroscopic dynamics. While the singular behavior of these nonlinear continuity equations is well studied in the literature, the extension to the corresponding granular kinetic equation is highly nontrivial. The main question is whether the singularity formed in velocity direction will be enhanced or mitigated by the shear in phase space due to free transport. We present a preliminary study through a meticulous numerical investigation and heuristic arguments. We have numerically developed a structure-preserving method with adaptive mesh refinement that can effectively capture potential blow-up behavior in the solution for granular kinetic equations. We have analytically constructed a finite-time blow-up infinite mass solution and discussed how this can provide insights into the finite mass scenario.