arXiv subjects

Quanling Deng

Publications and source records attributed to Quanling Deng.

At least 19 recordsLinked to original sources

arXiv2026

Season-Aware Hybrid Convolutional-Transformer for Antarctic Sea Ice Concentration Forecasting

Antarctic sea ice concentration (SIC) forecasting is an important yet challenging task due to the coexistence of complex spatial structure, long-range temporal dependencies, and strong seasonal variability. Conventional convolution-based models are effective at capturing local spatial patterns, but often have limited ability to model long-term temporal evolution. To address these challenges, we build on a hybrid Convolutional-Transformer forecasting framework for monthly Antarctic SIC forecasting. This framework combines convolutional encoding for spatial feature extraction with factorised self-attention for spatio-temporal dependency modelling. We further introduce two seasonal prior mechanisms: a month-aware positional encoding that injects calendar-month information into the token representation, and a seasonal temporal bias that encourages attention to periodically related historical states. Experimental results show that the proposed framework achieves better performance than convolutional and recurrent baselines across both classification and regression metrics. Ablation studies further indicate that the seasonal prior mechanisms provide consistent additional gains in both short- and long-horizon prediction. These results demonstrate the value of combining convolutional structures, attention mechanisms, and periodic prior information for Antarctic SIC forecasting.

cs.LG↗

arXiv2026

Particle, kinetic and hydrodynamic models for sea ice floes. Part II: Rotating floes with environmental forces

This paper builds on the multiscale modeling framework introduced in Part I (Deng and Ha, Physica D: Nonlinear Phenomena 483 (2025) 134951) for sea-ice floe dynamics with non-rotating floes to the case with rotational floes, nonlinear contact interactions, Coriolis force and ocean tilt. Building on the particle-kinetic-hydrodynamic hierarchy developed for non-rotating floes, we generalize the particle model to describe ice floes as rigid bodies characterized by position, linear velocity, angular velocity, size, and moment of inertia. The interaction rules now include nonlinear contact forces and torques arising from short-range compression, restitution, and tangential friction laws, together with both oceanic and atmospheric drags that couple translational and rotational motions. These particle descriptions lead to an enriched Vlasov-type kinetic equation posed on an extended phase space, whose moments yield a hydrodynamic system for mass, momentum, and angular-momentum balances. Compared with Part I, the resulting macroscopic equations feature additional hydrodynamic and stress contributions, rotational transport, and dissipative mechanisms stemming from nonlinear collisions. The proposed framework provides a more accurate description of sea-ice floe dynamics and offers a systematic pathway toward multiscale modeling of sea-ice rheology under complex environmental forcing.

math-ph↗

arXiv2026

Domain-Decomposed Lagrangian Data Assimilation for Drifting Sea-Ice Floe Dynamics

Sea ice dynamics are crucial to the global climate system, yet traditional continuum (e.g., viscous-plastic) models often fail to represent the discrete floe interactions that dominate in the marginal ice zone. Lagrangian discrete element methods (DEMs) resolve floe-scale physics more realistically, but their high particle counts make ensemble data assimilation (DA) more expensive. We consider a highly-simplified floe model and propose a scalable, domain-decomposed DA framework that couples Lagrangian particle observations with an ensemble transform Kalman filter (ETKF) to recover the underlying ocean flow field in a multiscale setting. The Eulerian domain is first partitioned into subdomains. We then impose an ETKF in each subdomain to recover the local fine-scale ocean features. A Gaussian-weighted blending step then reconstructs a globally consistent flow field across subdomain boundaries. Numerical experiments demonstrate consistently better skill scores that are characterised by normalised root mean square error (NRMSE) and pattern correlation coefficients (PCC), compared to the global and expensive DA baseline. Results suggest that the domain-decomposed DA method is an alternative, scalable approach for particle-based sea-ice floe dynamics and ocean flow recovery.

cs.CE↗

arXiv2025

HoSGFEM: High-order stable generalized finite element method for elliptic interface problem

The Generalized Finite Element Method (GFEM) is an effective unfitted numerical method for handling interface problems. By augmenting the standard FEM space with an appropriate enrichment space, GFEM can accurately capture C^0 solutions across the interfaces. While numerous GFEMs for interface problems have been studied, establishing a stable high-order GFEM with optimal convergence rates and robust system conditioning remains a challenge. The highest known order of two was established by Zhang and Babu\v{s}ka (SGFEM2, Comput. Methods Appl. Mech. Engrg. 363 (2020), 112889). In this paper, we propose a unified enrichment space construction and establish arbitrary high-order stable GFEMs (HoSGFEM) for elliptic interface problems. The main idea distinguishes itself from Zhang and Babu\v{s}ka's SGFEM2 substantially and it is twofold: a) we construct dimensionality-reduced auxiliary locally supported piecewise polynomials that satisfy the partition of unity property for elements containing interfaces; b) we construct the enrichment scheme based on d{1,(x-x_c^e),...,(y-y_c^e)^{p-1}} (d is the distance function; (x_c^e, y_c^e) is the center of the element containing interface, thus element-based) for arbitrary p-th order elements instead of d, d{1,x,y} or d{1,x,y,x^2,xy,y^2} (global functions) for p=1,2 in the literature. This idea results in an enrichment space that has a large angle with the standard FEM space, leading to the stability of the method with system condition number growing in order O(h^{-2}). We establish optimal convergence rates for HoSGFEM solutions under the proposed construction. Various numerical experiments with both straight and curved interfaces demonstrate the optimal convergence, FEM-comparable system condition number with O(h^{-2}) growth, and robustness as element boundaries approach interfaces.

math.NA↗

arXiv2025

An Eulerian Data Assimilation Method for Two-Layer Quasi-Geostrophic Model in Physical Domain

Data assimilation (DA) integrates observational data with numerical models to improve the prediction of complex physical systems. However, traditional DA methods often struggle with nonlinear dynamics and multi-scale variability, particularly when implemented directly in the physical domain. To address these challenges, this work develops an Eulerian Data Assimilation (EuDA) method with the Conditional Gaussian Nonlinear System (CGNS). The proposed approach enables the treatment of systems with non-periodic boundaries and provides a more intuitive representation of localized and time-dependent phenomena. The work considers a simplified physical domain inspired by sea-ice floe trajectories and ocean eddy recovery in the Arctic regions, where the dynamics are modeled by a two-layer quasi-geostrophic (QG) system. The QG equations are numerically solved using forward-Euler time stepping and centered finite-difference schemes. CGNS provides a nonlinear filter as it offers an analytical and continuous formulation for filtering a nonlinear system. Model performance is assessed using normalized root mean square error (RMSE) and pattern correlation (Corr) of the posterior mean. The results show that both metrics improve monotonically with refining timesteps, while RMSE converges to approximately 0.1, which is the noise strength, and Corr increases from 0.64 to 0.92 as the grid resolution becomes finer. Lastly, a coupled scenario with sea-ice particles advected by the two-layer QG flow under a linear drag force is examined, demonstrating the flexibility of the EuDA-CGNS framework in capturing coupled ice-ocean interactions. These findings demonstrate the effectiveness of exploiting the two-layer QG model in the physical domain to capture multiscale flow features.

cs.CE↗

arXiv2025

Particle, kinetic and hydrodynamic models for sea ice floes. Part I: Non-rotating floes

We introduce a comprehensive modeling framework for the dynamics of sea ice floes using particle, kinetic, and hydrodynamic approaches. Building upon the foundational work of Ha and Tadmor on the Cucker-Smale model for flocking, we derive a Vlasov-type kinetic formulation and a corresponding hydrodynamic description. The particle model incorporates essential physical properties of sea ice floes, including size, position, velocity, and interactions governed by Newtonian mechanics. By extending these principles, the kinetic model captures large-scale features through the phase-space distribution, and we also present a hydrodynamic model using the velocity moments and a suitable closure condition. In this paper, as an idea-introductory step, we assume that ice floes are non-rotating and focus on the linear velocity dynamics. Our approach highlights the role of contact forces, ocean drag effects, and conservation laws in the multiscale description of sea ice dynamics, offering a potential pathway for the improved understanding and prediction of sea ice behaviors in changing climatic conditions.

math.DS↗

arXiv2024

Exact Eigenvalues and Eigenvectors for Some n-Dimensional Matrices

Building on previous work that provided analytical solutions to generalised matrix eigenvalue problems arising from numerical discretisations, this paper develops exact eigenvalues and eigenvectors for a broader class of $n$-dimensional matrices, focusing on non-symmetric and non-persymmetric matrices. These matrices arise in one-dimensional Laplacian eigenvalue problems with mixed boundary conditions and in a few quantum mechanics applications where standard Toeplitz-plus-Hankel matrix forms do not suffice. By extending analytical methodologies to these broader matrix categories, the study not only widens the scope of applicable matrices but also enhances computational methodologies, leading to potentially more accurate and efficient solutions in physics and engineering simulations.

math.SP↗

arXiv2024

EXAGREE: Mitigating Explanation Disagreement with Stakeholder-Aligned Models

Conflicting explanations, arising from different attribution methods or model internals, limit the adoption of machine learning models in safety-critical domains. We turn this disagreement into an advantage and introduce EXplanation AGREEment (EXAGREE), a two-stage framework that selects a Stakeholder-Aligned Explanation Model (SAEM) from a set of similar-performing models. The selection maximizes Stakeholder-Machine Agreement (SMA), a single metric that unifies faithfulness and plausibility. EXAGREE couples a differentiable mask-based attribution network (DMAN) with monotone differentiable sorting, enabling gradient-based search inside the constrained model space. Experiments on six real-world datasets demonstrate simultaneous gains of faithfulness, plausibility, and fairness over baselines, while preserving task accuracy. Extensive ablation studies, significance tests, and case studies confirm the robustness and feasibility of the method in practice.

cs.LG↗

arXiv2024

Practical Attribution Guidance for Rashomon Sets

Different prediction models might perform equally well (Rashomon set) in the same task, but offer conflicting interpretations and conclusions about the data. The Rashomon effect in the context of Explainable AI (XAI) has been recognized as a critical factor. Although the Rashomon set has been introduced and studied in various contexts, its practical application is at its infancy stage and lacks adequate guidance and evaluation. We study the problem of the Rashomon set sampling from a practical viewpoint and identify two fundamental axioms - generalizability and implementation sparsity that exploring methods ought to satisfy in practical usage. These two axioms are not satisfied by most known attribution methods, which we consider to be a fundamental weakness. We use the norms to guide the design of an $\epsilon$-subgradient-based sampling method. We apply this method to a fundamental mathematical problem as a proof of concept and to a set of practical datasets to demonstrate its ability compared with existing sampling methods.

cs.LG↗

arXiv2024

Generalised Soft Finite Element Method for Elliptic Eigenvalue Problems

The recently proposed soft finite element method (SoftFEM) reduces the stiffness (condition numbers), consequently improving the overall approximation accuracy. The method subtracts a least-square term that penalizes the gradient jumps across mesh interfaces from the FEM stiffness bilinear form while maintaining the system's coercivity. Herein, we present two generalizations for SoftFEM that aim to improve the approximation accuracy and further reduce the discrete systems' stiffness. Firstly and most naturally, we generalize SoftFEM by adding a least-square term to the mass bilinear form. Superconvergent results of rates $h^6$ and $h^8$ for eigenvalues are established for linear uniform elements; $h^8$ is the highest order of convergence known in the literature. Secondly, we generalize SoftFEM by applying the blended Gaussian-type quadratures. We demonstrate further reductions in stiffness compared to traditional FEM and SoftFEM. The coercivity and analysis of the optimal error convergences follow the work of SoftFEM. Thus, this paper focuses on the numerical study of these generalizations. For linear and uniform elements, analytical eigenpairs, exact eigenvalue errors, and superconvergent error analysis are established. Various numerical examples demonstrate the potential of generalized SoftFEMs for spectral approximation, particularly in high-frequency regimes.

math.NA↗

arXiv2024

LEMDA: A Lagrangian-Eulerian Multiscale Data Assimilation Framework

Lagrangian trajectories are widely used as observations for recovering the underlying flow field via Lagrangian data assimilation (DA). However, the strong nonlinearity in the observational process and the high dimensionality of the problems often cause challenges in applying standard Lagrangian DA. In this paper, a Lagrangian-Eulerian multiscale DA (LEMDA) framework is developed. It starts with exploiting the Boltzmann kinetic description of the particle dynamics to derive a set of continuum equations, which characterize the statistical quantities of particle motions at fixed grids and serve as Eulerian observations. Despite the nonlinearity in the continuum equations and the processes of Lagrangian observations, the time evolutions of the posterior distribution from LEMDA can be written down using closed analytic formulae. This offers an exact and efficient way of carrying out DA, which avoids using ensemble approximations and the associated tunings. The analytically solvable properties also facilitate the derivation of an effective reduced-order Lagrangian DA scheme that further enhances computational efficiency. The Lagrangian DA within the framework has advantages when a moderate number of particles is used, while the Eulerian DA can effectively save computational costs when the number of particle observations becomes large. The Eulerian DA is also valuable when particles collide, such as using sea ice floe trajectories as observations. LEMDA naturally applies to multiscale turbulent flow fields, where the Eulerian DA recovers the large-scale structures, and the Lagrangian DA efficiently resolves the small-scale features in each grid cell via parallel computing. Numerical experiments demonstrate the skilful results of LEMDA and its two components.

physics.flu-dyn↗

arXiv2023

Particle-Continuum Multiscale Modeling of Sea Ice Floes

Sea ice profoundly influences the polar environment and the global climate. Traditionally, Sea ice has been modeled as a continuum under Eulerian coordinates to describe its large-scale features, using, for instance, viscous-plastic rheology. Recently, Lagrangian particle models, also known as the discrete element method (DEM) models, have been utilized for characterizing the motion of individual sea ice fragments (called floes) at scales of 10 km and smaller, especially in marginal ice zones. This paper develops a multiscale model that couples the particle and the continuum systems to facilitate an effective representation of the dynamical and statistical features of sea ice across different scales. The multiscale model exploits a Boltzmann-type system that links the particle movement with the continuum equations. For the small-scale dynamics, it describes the motion of each sea ice floe. Then, as the large-scale continuum component, it treats the statistical moments of mass density and linear and angular velocities. The evolution of these statistics affects the motion of individual floes, which in turn provides bulk feedback that adjusts the large-scale dynamics. Notably, the particle model characterizing the sea ice floes is localized and fully parallelized, in a framework that is sometimes called superparameterization, which significantly improves computation efficiency. Numerical examples demonstrate the effective performance of the multiscale model. Additionally, the study demonstrates that the multiscale model has a linear-order approximation to the truth model.

math.NA↗

arXiv2023

Physics-Informed Neural Networks for Discovering Localised Eigenstates in Disordered Media

The Schrödinger equation with random potentials is a fundamental model for understanding the behaviour of particles in disordered systems. Disordered media are characterised by complex potentials that lead to the localisation of wavefunctions, also called Anderson localisation. These wavefunctions may have similar scales of eigenenergies which poses difficulty in their discovery. It has been a longstanding challenge due to the high computational cost and complexity of solving the Schrödinger equation. Recently, machine-learning tools have been adopted to tackle these challenges. In this paper, based upon recent advances in machine learning, we present a novel approach for discovering localised eigenstates in disordered media using physics-informed neural networks (PINNs). We focus on the spectral approximation of Hamiltonians in one dimension with potentials that are randomly generated according to the Bernoulli, normal, and uniform distributions. We introduce a novel feature to the loss function that exploits known physical phenomena occurring in these regions to scan across the domain and successfully discover these eigenstates, regardless of the similarity of their eigenenergies. We present various examples to demonstrate the performance of the proposed approach and compare it with isogeometric analysis.

cond-mat.dis-nn↗

arXiv2023

Exploring the cloud of feature interaction scores in a Rashomon set

Interactions among features are central to understanding the behavior of machine learning models. Recent research has made significant strides in detecting and quantifying feature interactions in single predictive models. However, we argue that the feature interactions extracted from a single pre-specified model may not be trustworthy since: a well-trained predictive model may not preserve the true feature interactions and there exist multiple well-performing predictive models that differ in feature interaction strengths. Thus, we recommend exploring feature interaction strengths in a model class of approximately equally accurate predictive models. In this work, we introduce the feature interaction score (FIS) in the context of a Rashomon set, representing a collection of models that achieve similar accuracy on a given task. We propose a general and practical algorithm to calculate the FIS in the model class. We demonstrate the properties of the FIS via synthetic data and draw connections to other areas of statistics. Additionally, we introduce a Halo plot for visualizing the feature interaction variance in high-dimensional space and a swarm plot for analyzing FIS in a Rashomon set. Experiments with recidivism prediction and image classification illustrate how feature interactions can vary dramatically in importance for similarly accurate predictive models. Our results suggest that the proposed FIS can provide valuable insights into the nature of feature interactions in machine learning models.

cs.LG↗

arXiv2023

High-Order Enriched Finite Element Methods for Elliptic Interface Problems with Discontinuous Solutions

Elliptic interface problems whose solutions are $C^0$ continuous have been well studied over the past two decades. The well-known numerical methods include the strongly stable generalized finite element method (SGFEM) and immersed FEM (IFEM). In this paper, we study numerically a larger class of elliptic interface problems where their solutions are discontinuous. A direct application of these existing methods fails immediately as the approximate solution is in a larger space that covers discontinuous functions. We propose a class of high-order enriched unfitted FEMs to solve these problems with implicit or Robin-type interface jump conditions. We design new enrichment functions that capture the imposed discontinuity of the solution while keeping the condition number from fast growth. A linear enriched method in 1D was recently developed using one enrichment function and we generalized it to an arbitrary degree using two simple discontinuous one-sided enrichment functions. The natural tensor product extension to the 2D case is demonstrated. Optimal order convergence in the $L^2$ and broken $H^1$-norms are established. We also establish superconvergence at all discretization nodes (including exact nodal values in special cases). Numerical examples are provided to confirm the theory. Finally, to prove the efficiency of the method for practical problems, the enriched linear, quadratic, and cubic elements are applied to a multi-layer wall model for drug-eluting stents in which zero-flux jump conditions and implicit concentration interface conditions are both present.

math.NA↗

arXiv2023

Soft isogeometric analysis of the Bound States of a Quantum Three-Body Problem in 1D

The study of quantum three-body problems has been centered on low-energy states that rely on accurate numerical approximation. Recently, isogeometric analysis (IGA) has been adopted to solve the problem as an alternative but more robust (with respect to atom mass ratios) method that outperforms the classical Born-Oppenheimer (BO) approximation. In this paper, we focus on the performance of IGA and apply the recently-developed softIGA to reduce the spectral errors of the low-energy bound states. The main idea is to add high-order derivative-jump terms with a penalty parameter to the IGA bilinear forms. With an optimal choice of the penalty parameter, we observe eigenvalue error superconvergence. We focus on linear (finite elements) and quadratic elements and demonstrate the outperformance of softIGA over IGA through a variety of examples including both two- and three-body problems in 1D.

math.NA↗

arXiv2022

Spectral analysis of a family of nonsymmetric fractional elliptic operators

In this work, we investigate the spectral problem $Au = λu$ where $A$ is a fractional elliptic operator involving left- and right-sided Riemann-Liouville derivatives. These operators are nonlocal and nonsymmetric, however, share certain classic elliptic properties. The eigenvalues correspond to the roots of a class of certain special functions. Compared with classic Sturm-Liouville problems, the most challenging part is to set up the framework for analyzing these nonlocal operators, which requires developing new tools. We prove the existence of the real eigenvalues, find the range for all possible complex eigenvalues, explore the graphs of eigenfunctions, and show numerical findings on the distribution of eigenvalues on the complex plane.

math.AP↗

arXiv2022

SoftIGA: soft isogeometric analysis

We extend the softFEM idea to isogeometric analysis (IGA) to reduce the stiffness (consequently, the condition numbers) of the IGA discretized problem. We refer to the resulting approximation technique as softIGA. We obtain the resulting discretization by first removing the IGA spectral outliers to reduce the system's stiffness. We then add high-order derivative-jump penalization terms (with negative penalty parameters) to the standard IGA bilinear forms. The penalty parameter seeks to minimize spectral/dispersion errors while maintaining the coercivity of the bilinear form. We establish dispersion errors for both outlier-free IGA (OF-IGA) and softIGA elements. We also derive analytical eigenpairs for the resulting matrix eigenvalue problems and show that the stiffness and condition numbers of the IGA systems significantly improve (reduce). We prove a superconvergent result of order $h^{2p+4}$ for eigenvalues where $h$ characterizes the mesh size and $p$ specifies the order of the B-spline basis functions. To illustrate the main idea and derive the analytical results, we focus on uniform meshes in 1D and tensor-product meshes in multiple dimensions. For the eigenfunctions, softIGA delivers the same optimal convergence rates as the standard IGA approximation. Various numerical examples demonstrate the advantages of softIGA over IGA.

math.NA↗