arXiv subjects

Zetao Lin

Publications and source records attributed to Zetao Lin.

11 recordsLinked to original sources

arXiv2026

HyperANFIS: Enhancing Rule Representation and Interpretability in Adaptive Neuro-Fuzzy Systems via Hyperbolic Geometry

The adaptive neuro-fuzzy inference system (ANFIS) is an interpretable reasoning framework capable of generating explicit IF-THEN fuzzy rules, making it suitable for tasks requiring transparent reasoning. However, existing ANFIS models generally construct rule antecedents and perform inference in Euclidean space, limiting their representational capacity and predictive performance. To address this issue, we propose Hyperbolic ANFIS (HyperANFIS), a hyperbolic extension of ANFIS. HyperANFIS preserves the fuzzy semantics and core architecture of conventional ANFIS while performing rule-prototype learning, rule activation, and consequent aggregation in hyperbolic space. It also retains the ability to generate interpretable IF-THEN rules. By exploiting the representational properties of hyperbolic geometry, HyperANFIS strengthens the fuzzy inference process, thereby improving predictive accuracy, inter-rule collaboration, and the credibility of its interpretable rules. Experimental results show that HyperANFIS consistently outperforms the standard ANFIS baseline and various ANFIS variants across all datasets, while also generating higher-quality fuzzy rules.

cs.AI↗

arXiv2026

Anisotropy and intermittency in drift-wave turbulence with zonal flows: a two-dimensional continuous wavelet analysis

We examine anisotropy and spatial intermittency at small scales in drift-wave turbulence with zonal flows. We use a two-dimensional directional continuous wavelet transform, which allows simultaneous localization in scale, position, and direction. This wavelet analysis is applied to vorticity fields obtained from numerical simulations of the modified Hasegawa--Wakatani model, a reduced model of resistive drift-wave turbulence in magnetized plasmas with zonal flows. Directional wavelet statistics characterize the anisotropy of the turbulence. The second-order moment is enhanced around directions perpendicular to the zonal flow. Spatial intermittency, characterized by scale-dependent flatness, is more pronounced around directions along the zonal flow.

physics.plasm-ph↗

arXiv2026

A Hybrid semi-Lagrangian Flow Mapping Approach for Vlasov Systems: Combining Iterative and Compositional Flow Maps

We propose a hybrid semi-Lagrangian scheme for the Vlasov--Poisson equation that combines the Numerical Flow Iteration (NuFI) method with the Characteristic Mapping Method (CMM). Both approaches exploit the semi-group property of the underlying diffeomorphic flow, enabling the reconstruction of solutions through flow maps that trace characteristics back to their initial positions. NuFI builds this flow map iteratively, preserving symplectic structure and conserving invariants, but its computational cost scales quadratically with time. Its advantage lies in a compact, low-dimensional representation depending only on the electric field. In contrast, CMM achieves low computational costs when remapping by composing the global flow map from explicitly stored submaps. The proposed hybrid method merges these strengths: NuFi is employed for accurate and conservative local time stepping, while CMM efficiently propagates the solution through submap composition. This approach reduces storage requirements, maintains accuracy, and improves structural properties. Numerical experiments demonstrate the effectiveness of the scheme and highlight the trade-offs between memory usage and computational cost. We benchmark against a semi-Lagrangian predictor-corrector scheme used in modern gyrokinetic codes, evaluating accuracy and conservation properties.

math.NA↗

arXiv2025

Auslander-Reiten theory via Nakayama duality in abelian categories

Using the Nakayama duality induced by a Nakayama functor, we provide a novel and concise account of the existence of Auslander-Reiten dualities and almost split sequences in abelian categories with enough projective objects or enough injective objects. As an example, we establish the existence of almost split sequences ending with finitely presented modules and those starting with finitely copresented modules in the category of all modules over a small endo-local Hom-reflexive category. Specializing to algebras given by (not necessarily finite) quivers with relations, we further investigate when the categories of finitely presented modules, finitely copresented modules and finite dimensional modules have almost split sequences on either or both sides.

math.RT↗

arXiv2025

Nondiffusive transport of inertial heavy impurities in drift-wave turbulence

We investigate the transport behavior of tungsten impurities with finite inertia in drift-wave turbulence using the Hasegawa-Wakatani model. Unlike previous tracer-based models, our simulations reveal a transition to non-diffusive dynamics for a range of charge states. This novel mechanism offers a turbulence-driven route to core impurity accumulation. This finding underscores the nontrivial role of particle inertia in impurity dynamics and has strong implications for impurity control in future fusion devices.

physics.plasm-ph↗

arXiv2025

Multiscale geometrical Lagrangian statistics of heavy impurities in drift-wave turbulence

We investigate the behavior of heavy impurities in edge plasma turbulence by analyzing their trajectories using the Hasegawa-Wakatani model. Through direct numerical simulations, we track ensembles of charged impurity particles over hundreds of eddy turnover times within statistically steady turbulent flows. Assuming that heavy impurities lag behind the flow, a novel derivation of relaxation time of heavy impurities is proposed. Our results reveal that heavy impurities can cluster within turbulence. We provide multiscale geometrical Lagrangian statistics of heavy impurities trajectories. To quantify directional changes, we analyze the scale-dependent curvature angle, along with the influence of the Stokes number on the mean curvature angles and the probability distribution function of curvature angles.

physics.plasm-ph↗

arXiv2024

A Representation theoretic perspective of Koszul theory

We discover a new connection between Koszul theory and representation theory. Let $\La$ be a quadratic algebra defined by a locally finite quiver with relations. Firstly, we give a combinatorial description of the local Koszul complexes and the quadratic dual $\La^!$, which enables us to describe the linear projective resolutions and the colinear injective coresolutions of graded simple $\La$-modules in terms of $\La^!$. As applications, we obtain a new class of Koszul algebras and a stronger version of the Extension Conjecture for finite dimensional Koszul algebras with a noetherian Koszul dual. Then we construct two Koszul functors, which induce a $2$-real-parameter family of pairs of derived Koszul functors between categories derived from graded $\La$-modules and those derived from graded $\La^!$-modules. In case $\La$ is Koszul, each pair of derived Koszul functors are mutually quasi-inverse, one of the pairs is Beilinson, Ginzburg and Soergel's Koszul duality. If $\La$ and $\La^!$ are locally bounded on opposite sides, then the Koszul functors induce two equivalences of bounded derived categories: one for finitely piece-supported graded modules, and one for finite dimensional graded modules. And if $\La$ and $\La^!$ are both locally bounded, then the bounded derived category of finite dimensional graded $\La$-modules has almost split triangles with the Auslander-Reiten translations and the Serre functors given by composites of derived Koszul functors.

math.RT↗

arXiv2024

Representation theory of graded algebras given by locally finite quivers

This paper aims to study graded modules over a graded algebra $\La$ given by a locally finite quiver with homogeneous relations. By constructing a graded Nakayama functor, we discover a novel approach to establish Auslander-Reiten formulas, from which we derive almost split sequences in the category of all graded $\La$-modules. In case $\La$ is locally left (respectively, right) bounded, the category of finitely presented graded modules and that of finitely copresented graded modules both have almost split sequences on the left (respectively, right). We shall also obtain existence theorems for almost split triangles in various derived categories of graded $\La$-modules. In case $\La$ is locally bounded, an indecomposable complex in the bounded derived category of finite dimensional graded modules is the starting (respectively, ending) term of an almost split triangle if and only if it has a finite graded projective reso\-lution (respectively, injective coresolution); and consequently, this bounded derived category has almost split triangles on the right (respectively, left) if and only if every graded simple module is of finite graded projective (respectively, injective) dimension. Finally, we specialize to the existence of almost split sequences and almost split triangles for graded representations of any locally finite quiver.

math.RT↗

arXiv2024

Tessellation-based analysis of impurity clustering in the edge plasma of tokamaks

Confinement quality in fusion plasma is significantly influenced by the presence of heavy impurities, which can lead to radiative heat loss and reduced confinement. This study explores the clustering of heavy impurity, \textit{i.e.}, Tungsten in edge plasma, using high-resolution direct numerical simulations of the Hasegawa--Wakatani equations. We use Stokes number to quantify the inertia of impurity particles. It is found that particle inertia will cause spatial intermittency in particle distribution and the formation of large-scale structures, \textit{i.e.}, the clustering of particles. The degrees of clustering are influenced by Stokes number. To quantify these observations, we apply a modified Voronoi tessellation, which assigns specific volumes to impurity particles. By determining time changes of these volumes, we can calculate the impurity velocity divergence, which allows to assess the clustering dynamics. To quantify the clustering statistically, several approaches are applied, such as probability density function (PDF) of impurity velocity divergence and joint PDF of volume and divergence.

physics.plasm-ph↗

arXiv2024

Synthesizing impurity clustering in the edge plasma of tokamaks using neural networks

This work investigates the behavior of impurities in edge plasma of tokamaks using high-resolution numerical simulations based on Hasegawa--Wakatani equations. Specifically, it focuses on the behavior of inertial particles, which has not been extensively studied in the field of plasma physics. Our simulations utilize one-way coupling of a large number of inertial point particles, which model plasma impurities. We observe that with Stokes number ($St$) which characterizes the inertia of particles being much less than one, such light impurities closely track the fluid flow without pronounced clustering. For intermediate $St$ values, distinct clustering appears, with larger Stokes values, {\it i.e.} heavy impurities even generating more substantial clusters. When $St$ is significantly large, very heavy impurities tend to detach from the flow and maintain their trajectory, resulting in fewer observable clusters and corresponding to random motion. A core component of this work involves machine learning techniques. Applying three different neural networks - Autoencoder, U-Net, and Generative Adversarial Network (GAN) - to synthesize preferential concentration fields of impurities, we use vorticity as input and predict impurity number density fields. GAN outperforms the two others by aligning closely with direct numerical simulation data in terms of probability density functions of the particle distribution and energy spectra. This machine learning technique holds the potential to reduce computational costs by eliminating the need to track millions of particles modeling impurities in simulations.

physics.plasm-ph↗

arXiv2024

Breaking the Black-Box: Confidence-Guided Model Inversion Attack for Distribution Shift

Model inversion attacks (MIAs) seek to infer the private training data of a target classifier by generating synthetic images that reflect the characteristics of the target class through querying the model. However, prior studies have relied on full access to the target model, which is not practical in real-world scenarios. Additionally, existing black-box MIAs assume that the image prior and target model follow the same distribution. However, when confronted with diverse data distribution settings, these methods may result in suboptimal performance in conducting attacks. To address these limitations, this paper proposes a \textbf{C}onfidence-\textbf{G}uided \textbf{M}odel \textbf{I}nversion attack method called CG-MI, which utilizes the latent space of a pre-trained publicly available generative adversarial network (GAN) as prior information and gradient-free optimizer, enabling high-resolution MIAs across different data distributions in a black-box setting. Our experiments demonstrate that our method significantly \textbf{outperforms the SOTA black-box MIA by more than 49\% for Celeba and 58\% for Facescrub in different distribution settings}. Furthermore, our method exhibits the ability to generate high-quality images \textbf{comparable to those produced by white-box attacks}. Our method provides a practical and effective solution for black-box model inversion attacks.

cs.CV↗