arXiv subjects

Wenjia Xie

Publications and source records attributed to Wenjia Xie.

16 recordsLinked to original sources

arXiv2026

How to Recover Oscillation-Free Pressure in Real Fluids: The RFQC Method and Its Liquid-Upwind Anomaly

From the perspective of continuum thermodynamics, we revisit the pressure oscillation problem in finite-volume methods for multiphase real fluids and clarify the physical counterpart of the Real Fluid Quasi-Conservative (RFQC) method. The pressure oscillation in conservative finite-volume methods originates from their implicit thermodynamic equilibrium assumption, whereas recovering an oscillation-free pressure requires additional physical information. The RFQC method achieves this by evolving the affine parameters xi and E0 of the isentropic internal-energy-pressure relation along pathlines, while the thermodynamic re-projection converts the deviation from the isentropic trajectory into an internal-energy error, thereby ensuring the thermodynamic consistency and numerical stability of the method. We then investigate the applicability limit of the RFQC method and identify a Liquid-upwind Anomaly (LUA) in extreme phase-change cases. For a Riemann problem involving liquid-vapor phase change, a numerical anomaly may occur if a liquid-upwind translational velocity is initially superimposed. Theoretical analysis reveals that this anomaly is initiated by the jump in the affine slope xi during phase change, which delays pressure rise in the downstream vapor cell. Concurrently, the re-projection removes the positive pressure increment, repeatedly generating large internal-energy errors and trapping the vapor cell in a cycle of delayed pressure recovery. The analysis indicates that the LUA is a start-up anomaly, which can be resolved by introducing a regularization strategy at the initial discontinuity. With the proposed regularization strategy, the RFQC method is equipped with enhanced accuracy and robustness for extreme thermodynamic flows, such as sonic phase-change jets.

math-ph↗

arXiv2026

Analysis and Numerics of a Stationary Drift-Diffusion Model for Electrical Discharge in MEMS

This work presents the analysis and numerical simulation of a stationary drift-diffusion model for electrical discharge in micro-electro-mechanical systems (MEMS). The model couples Poisson's equation for the electrostatic potential with continuity equations for positive ions and electrons, incorporating a Townsend-type impact ionization source term that depends exponentially on the electric field magnitude. We prove the existence of weak solutions under physically relevant assumptions and establish uniform bounds on the carrier densities. The proof relies on a regularization-approximation scheme with truncated nonlinearities, monotone operator theory (Browder-Minty), iterative energy estimates, and Stampacchia-type truncation arguments. We further develop a robust finite element solver to simulate the carrier density and electrostatic potential profiles for several geometries, including two-dimensional domains and a three-dimensional axisymmetric geometry.

math.AP↗

arXiv2026

An Oscillation-Free Real Fluid Quasi-Conservative Finite Volume Method for Transcritical and Phase-Change Flows

A new Real Fluid Quasi-Conservative (RFQC) finite volume method is developed to address the numerical simulation of real fluids involving shock waves in transcritical and phase-change flows. To eliminate the spurious pressure oscillations inherent in fully conservative schemes, we extend the classic quasi-conservative method, originally designed for two-phase flows, to real fluids governed by arbitrary equations of state (EoS). The RFQC method locally linearizes the real fluid EoS at each grid point and time step, constructing and evolving the frozen Grüneisen coefficient $Γ$ and the linearization remainder $E_0$ via two advection equations. At the end of each time step, the evolved $Γ$ and $E_0$ are utilized to reconstruct the oscillation-free pressure field, followed by a thermodynamic re-projection applied to the conserved variables. Theoretical analysis demonstrates that, in smooth regions, the energy conservation error introduced by the RFQC method is a second-order small term dominated by the time-step. In discontinuous regions, this error is determined by the entropy increase rate, thereby maintaining consistency with the inherent truncation error of shock-capturing methods. A series of numerical tests verifies that the method can robustly simulate complex flow processes with only minor energy conservation errors, including transcritical flows, phase transitions, and shock-interface interactions. The RFQC method is proven to be both accurate and robust in capturing shock waves and phase transitions.

physics.comp-ph↗

arXiv2026

Flash evaporation Riemann Problem: Formulation and its Exact Solution

Flash evaporation, a liquid-to-gas phase transition phenomenon in real fluids, is prevalent in aerospace propulsion systems. To elucidate the physical mechanisms of such complex flows and provide theoretical benchmarks for Computational Fluid Dynamics simulations, this paper formalizes the Flash evaporation Riemann problem (FeRP) characterized by the expansion branch crossing the saturation line, within the framework of Homogeneous Equilibrium and Vapor-Liquid Equilibrium assumptions. An exact solution framework that analytically resolves all thermodynamic derivatives of equilibrium two-phase fluids is established for arbitrary two-parameter equations of state. By evaluating the Landau fundamental derivative, the non-classical wave structures arising in the FeRP are analyzed, for which a stable iterative solution strategy incorporating the Chapman-Jouguet condition as an outer constraint is proposed. Furthermore, an exact solution for the FeRP based on Wood's mechanical equilibrium speed of sound is developed, enabling a comprehensive evaluation of its thermodynamic implications. Results indicate that Wood's model alters the definition of the two-phase mixture entropy in the Euler equations, introducing an isentropic path characterized by a "density lag" effect and non-physical entropy decrease. Comparative analysis of the FeRP under typical scramjet fuel injection conditions reveals that, although Wood's model captures the general trend of the Riemann solution curve, it significantly underestimates intermediate pressure, velocity, and the extent of vaporization relative to the complete equilibrium model.

physics.flu-dyn↗

arXiv2025

Machine Learning Techniques for Multifactor Analysis of National Carbon Dioxide Emissions

This paper presents a comprehensive study leveraging Support Vector Machine (SVM) regression and Principal Component Regression (PCR) to analyze carbon dioxide emissions in a global dataset of 62 countries and their dependence on idiosyncratic, country-specific parameters. The objective is to understand the factors contributing to carbon dioxide emissions and identify the most predictive elements. The analysis provides country-specific emission estimates, highlighting diverse national trajectories and pinpointing areas for targeted interventions in climate change mitigation, sustainable development, and the growing carbon credit markets and green finance sector. The study aims to support policymaking with accurate representations of carbon dioxide emissions, offering nuanced information for formulating effective strategies to address climate change while informing initiatives related to carbon trading and environmentally sustainable investments.

cs.LG↗

arXiv2025

Dynamic Investment Strategies Through Market Classification and Volatility: A Machine Learning Approach

This study introduces a dynamic investment framework to enhance portfolio management in volatile markets, offering clear advantages over traditional static strategies. Evaluates four conventional approaches : equal weighted, minimum variance, maximum diversification, and equal risk contribution under dynamic conditions. Using K means clustering, the market is segmented into ten volatility-based states, with transitions forecasted by a Bayesian Markov switching model employing Dirichlet priors and Gibbs sampling. This enables real-time asset allocation adjustments. Tested across two asset sets, the dynamic portfolio consistently achieves significantly higher risk-adjusted returns and substantially higher total returns, outperforming most static methods. By integrating classical optimization with machine learning and Bayesian techniques, this research provides a robust strategy for optimizing investment outcomes in unpredictable market environments.

q-fin.PM↗

arXiv2024

Scaling New Frontiers: Insights into Large Recommendation Models

Recommendation systems are essential for filtering data and retrieving relevant information across various applications. Recent advancements have seen these systems incorporate increasingly large embedding tables, scaling up to tens of terabytes for industrial use. However, the expansion of network parameters in traditional recommendation models has plateaued at tens of millions, limiting further benefits from increased embedding parameters. Inspired by the success of large language models (LLMs), a new approach has emerged that scales network parameters using innovative structures, enabling continued performance improvements. A significant development in this area is Meta's generative recommendation model HSTU, which illustrates the scaling laws of recommendation systems by expanding parameters to thousands of billions. This new paradigm has achieved substantial performance gains in online experiments. In this paper, we aim to enhance the understanding of scaling laws by conducting comprehensive evaluations of large recommendation models. Firstly, we investigate the scaling laws across different backbone architectures of the large recommendation models. Secondly, we conduct comprehensive ablation studies to explore the origins of these scaling laws. We then further assess the performance of HSTU, as the representative of large recommendation models, on complex user behavior modeling tasks to evaluate its applicability. Notably, we also analyze its effectiveness in ranking tasks for the first time. Finally, we offer insights into future directions for large recommendation models. Supplementary materials for our research are available on GitHub at https://github.com/USTC-StarTeam/Large-Recommendation-Models.

cs.IR↗

arXiv2024

Breaking Determinism: Fuzzy Modeling of Sequential Recommendation Using Discrete State Space Diffusion Model

Sequential recommendation (SR) aims to predict items that users may be interested in based on their historical behavior sequences. We revisit SR from a novel information-theoretic perspective and find that conventional sequential modeling methods fail to adequately capture the randomness and unpredictability of user behavior. Inspired by fuzzy information processing theory, this paper introduces the DDSR model, which uses fuzzy sets of interaction sequences to overcome the limitations and better capture the evolution of users' real interests. Formally based on diffusion transition processes in discrete state spaces, which is unlike common diffusion models such as DDPM that operate in continuous domains. It is better suited for discrete data, using structured transitions instead of arbitrary noise introduction to avoid information loss. Additionally, to address the inefficiency of matrix transformations due to the vast discrete space, we use semantic labels derived from quantization or RQ-VAE to replace item IDs, enhancing efficiency and improving cold start issues. Testing on three public benchmark datasets shows that DDSR outperforms existing state-of-the-art methods in various settings, demonstrating its potential and effectiveness in handling SR tasks.

cs.LG↗

arXiv2024

Bridging User Dynamics: Transforming Sequential Recommendations with Schrödinger Bridge and Diffusion Models

Sequential recommendation has attracted increasing attention due to its ability to accurately capture the dynamic changes in user interests. We have noticed that generative models, especially diffusion models, which have achieved significant results in fields like image and audio, hold considerable promise in the field of sequential recommendation. However, existing sequential recommendation methods based on diffusion models are constrained by a prior distribution limited to Gaussian distribution, hindering the possibility of introducing user-specific information for each recommendation and leading to information loss. To address these issues, we introduce the Schrödinger Bridge into diffusion-based sequential recommendation models, creating the SdifRec model. This allows us to replace the Gaussian prior of the diffusion model with the user's current state, directly modeling the process from a user's current state to the target recommendation. Additionally, to better utilize collaborative information in recommendations, we propose an extended version of SdifRec called con-SdifRec, which utilizes user clustering information as a guiding condition to further enhance the posterior distribution. Finally, extensive experiments on multiple public benchmark datasets have demonstrated the effectiveness of SdifRec and con-SdifRec through comparison with several state-of-the-art methods. Further in-depth analysis has validated their efficiency and robustness.

cs.IR↗

arXiv2024

Enabling Collaborative Clinical Diagnosis of Infectious Keratitis by Integrating Expert Knowledge and Interpretable Data-driven Intelligence

Although data-driven artificial intelligence (AI) in medical image diagnosis has shown impressive performance in silico, the lack of interpretability makes it difficult to incorporate the "black box" into clinicians' workflows. To make the diagnostic patterns learned from data understandable by clinicians, we develop an interpretable model, knowledge-guided diagnosis model (KGDM), that provides a visualized reasoning process containing AI-based biomarkers and retrieved cases that with the same diagnostic patterns. It embraces clinicians' prompts into the interpreted reasoning through human-AI interaction, leading to potentially enhanced safety and more accurate predictions. This study investigates the performance, interpretability, and clinical utility of KGDM in the diagnosis of infectious keratitis (IK), which is the leading cause of corneal blindness. The classification performance of KGDM is evaluated on a prospective validation dataset, an external testing dataset, and an publicly available testing dataset. The diagnostic odds ratios (DOR) of the interpreted AI-based biomarkers are effective, ranging from 3.011 to 35.233 and exhibit consistent diagnostic patterns with clinic experience. Moreover, a human-AI collaborative diagnosis test is conducted and the participants with collaboration achieved a performance exceeding that of both humans and AI. By synergistically integrating interpretability and interaction, this study facilitates the convergence of clinicians' expertise and data-driven intelligence. The promotion of inexperienced ophthalmologists with the aid of AI-based biomarkers, as well as increased AI prediction by intervention from experienced ones, demonstrate a promising diagnostic paradigm for infectious keratitis using KGDM, which holds the potential for extension to other diseases where experienced medical practitioners are limited and the safety of AI is concerned.

cs.AI↗

arXiv2023

MSAT: Matrix stability analysis tool for shock-capturing schemes

The simulation of supersonic or hypersonic flows often suffers from numerical shock instabilities if the flow field contains strong shocks, limiting the further application of shock-capturing schemes. In this paper, we develop the unified matrix stability analysis method for schemes with three-point stencils and present MSAT, an open-source tool to quantitatively analyze the shock instability problem. Based on the finite-volume approach on the structured grid, MSAT can be employed to investigate the mechanism of the shock instability problem, evaluate the robustness of numerical schemes, and then help to develop robust schemes. Also, MSAT has the ability to analyze the practical simulation of supersonic or hypersonic flows, evaluate whether it will suffer from shock instabilities, and then assist in selecting appropriate numerical schemes accordingly. As a result, MSAT is a helpful tool that can investigate the shock instability problem and help to cure it.

math.NA↗

arXiv2023

Numerical stability analysis of shock-capturing methods for strong shocks II: high-order finite-volume schemes

The shock instability problem commonly arises in flow simulations involving strong shocks, particularly when employing high-order schemes, limiting their applications in hypersonic flow simulations. This study focuses on exploring the numerical characteristics and underlying mechanisms of shock instabilities in fifth-order finite-volume WENO schemes. To this end, for the first time, we have established the matrix stability analysis method for the fifth-order scheme. By predicting the evolution of perturbation errors in the exponential growth stage, this method provides quantitative insights into the behavior of shock-capturing and helps elucidate the mechanisms that cause shock instabilities. Results reveal that even dissipative solvers also suffer from shock instabilities when the spatial accuracy is increased to fifth-order. Further investigation indicates that this is due to the excessively high spatial accuracy of the WENO scheme near the numerical shock structure. Moreover, the shock instability problem of fifth-order schemes is demonstrated to be a multidimensional coupling problem. To stably capture strong shocks, it is crucial to have sufficient dissipation on transverse faces and ensure at least two points within the numerical shock structure in the direction perpendicular to the shock. The source location of instability is also clarified by the matrix stability analysis method, revealing that the instability arises from the numerical shock structure. Additionally, stability analysis demonstrates that local characteristic decomposition helps mitigate shock instabilities in high-order schemes, although the instability still persists. These conclusions pave the way for a better understanding of the shock instability in fifth-order schemes and provide guidance for the development of more reliable high-order shock-capturing methods for compressible flows with high Mach numbers.

math.NA↗

arXiv2023

Numerical stability analysis of shock-capturing methods for strong shocks I: second-order MUSCL schemes

Modern shock-capturing schemes often suffer from numerical shock anomalies if the flow field contains strong shocks, which may limit their further application in hypersonic flow computations. In the current study, we devote our efforts to exploring the primary numerical characteristics and the underlying mechanism of shock instability for second-order finite-volume schemes. To this end, we, for the first time, develop the matrix stability analysis method for the finite-volume MUSCL approach. Such a linearized analysis method allows to investigate the shock instability problem of the finite-volume shock-capturing schemes in a quantitative and efficient manner. Results of the stability analysis demonstrate that the shock stability of second-order scheme is strongly related to the Riemann solver, Mach number, limiter function, numerical shock structure, and computational grid. Unique stability characteristics associated with these factors for second-order methods are revealed quantitatively with the established method. Source location of instability is also clarified by the matrix stability analysis method. Results show that the shock instability originates from the numerical shock structure. Such conclusions pave the way to better understand the shock instability problem and may shed new light on developing more reliable shock-capturing methods for compressible flows with high Mach number.

math.NA↗

arXiv2021

A unified construction of all-speed HLL-type schemes for hypersonic heating computations

In this paper, a unified framework to develop all-speed HLL-type schemes for hypersonic heating computations is constructed. Such a unified construction method combines two effective improving techniques: a shock robustness improvement and a low-Mach number fix. It is implemented by properly modifying the approximate solutions of the local Riemann problem in the HLL framework, resulting in two all-speed HLL-type schemes, namely ASHLLC and ASHLLEM solvers. Results from both numerical analysis and experiments demonstrate that the newly proposed schemes not only preserve desirable properties of their original versions, but are also able to provide accurate and robust solutions for complex flows ranging from low-Mach number incompressible to hypersonic compressible regimes. Thus, both the ASHLLC and ASHLLEM schemes can be used as reliable methods for hypersonic heating computations.

cs.CE↗

arXiv2021

Further studies on numerical instabilities of Godunov-type schemes for strong shocks

In this paper, continuous research is undertaken to explore the underlying mechanism of numerical shock instabilities of Godunov-type schemes for strong shocks. By conducting dissipation analysis of Godunov-type schemes and a sequence of numerical experiments, we are able to clarify that the instability may be attributed to insufficient entropy production inside the numerical shock structure. As a result, a general entropy-control technique for improving the robustness of various Godunov-type schemes at strong shocks is developed. It plays a part in guaranteeing that enough entropy is produced inside the numerical shock structure. Furthermore, such a modified approach does not introduce any additional numerical dissipation on linear degenerate waves to suppress the shock instability. Numerical results that are obtained for various test cases indicate that the proposed methods have a good performance in terms of accuracy and robustness.

physics.comp-ph↗

arXiv2020

Deep Sequential Feature Learning in Clinical Image Classification of Infectious Keratitis

Infectious keratitis is the most common entities of corneal diseases, in which pathogen grows in the cornea leading to inflammation and destruction of the corneal tissues. Infectious keratitis is a medical emergency, for which a rapid and accurate diagnosis is needed for speedy initiation of prompt and precise treatment to halt the disease progress and to limit the extent of corneal damage; otherwise it may develop sight-threatening and even eye-globe-threatening condition. In this paper, we propose a sequential-level deep learning model to effectively discriminate the distinction and subtlety of infectious corneal disease via the classification of clinical images. In this approach, we devise an appropriate mechanism to preserve the spatial structures of clinical images and disentangle the informative features for clinical image classification of infectious keratitis. In competition with 421 ophthalmologists, the performance of the proposed sequential-level deep model achieved 80.00% diagnostic accuracy, far better than the 49.27% diagnostic accuracy achieved by ophthalmologists over 120 test images.

eess.IV↗