arXiv subjects

Liying Zhang

Publications and source records attributed to Liying Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Articulating then Matching: Zero-Shot Shape Matching for Uncurated Data

Finding dense correspondences between 3D shapes is a fundamental yet unresolved challenge, especially in real-world environments. These environments present severe challenges, including the lack of time and sufficient samples for training, the prevalence of uncurated extreme-high resolution data with topological distortions, and the need to handle diverse 3D representations. In this paper, we present ATM, a zero-shot framework that requires no correspondence-specific training and robustly addresses these issues at once through an articulate-then-match paradigm. Rather than relying on intrinsic geometric properties, we leverage powerful pretrained vision foundation models and parametric shape priors to estimate parametric shape models from multi-view renderings, and systematically ground these estimations via multi-view geometric consistency. By mapping diverse inputs into a shared canonical parametric space, we inherently establish robust coarse correspondences that bypass topological noise, which are then refined into precise dense mappings via spectral refinement. Operating purely on test-time optimized parametric reconstructions, ATM requires no correspondence training data, is naturally immune to connectivity artifacts, and seamlessly handles diverse 3D modalities, including meshes, point clouds, and 3D Gaussians. Extensive experiments demonstrate that our method achieves strong results on non-isometric benchmarks (average geodesic errors of 2.4-TOPKIDS, 3.8-SMAL), reducing errors by 73% and 37% respectively compared to the baseline URSSM. Furthermore, it exhibits unprecedented robustness on in-the-wild raw scans of up to 200k vertices per shape while maintaining near-constant computation time and consistent superior accuracy.

cs.CV↗

arXiv2026

MolWorld: Molecule World Models for Actionable Molecular Optimization

Molecular optimization in drug discovery aims to discover molecules with improved target properties, but practical lead optimization often requires more than high predicted scores. A useful candidate should also be actionable: it should be reachable from known molecules through valid local structural transformations, so that it can be interpreted as a plausible revision within an evolving chemical series. Existing de novo and single-molecule optimization methods do not explicitly model such reachability, especially when both the target molecules and the intermediate molecules connecting them to known compounds are unknown. In this work, we formulate actionable molecular optimization as sequential expansion of a molecule-transfer graph, where nodes are molecules and edges encode valid local transformations. We propose MolWorld, a molecule world model-guided framework that treats the current molecule-transfer graph as an evolving search state. At each iteration, MolWorld selects local anchor contexts, generates candidate molecules conditioned on these contexts, evaluates their properties, and uses a learned world model to update the evolving molecule world by retaining admissible candidates and inserting them into the molecule-transfer graph. The expanded molecule world then guides subsequent optimization. Experiments on property optimization and docking-based tasks show that MolWorld discovers high-property molecules while maintaining substantially stronger structural connectivity, supporting actionable and sequential molecular design.

cs.LG↗

arXiv2026

Universal 3D Shape Matching via Coarse-to-Fine Language Guidance

Establishing dense correspondences between shapes is a crucial task in computer vision and graphics, while prior approaches depend on near-isometric assumptions and homogeneous subject types (i.e., only operate for human shapes). However, building semantic correspondences for cross-category objects remains challenging and has received relatively little attention. To achieve this, we propose UniMatch, a semantic-aware, coarse-to-fine framework for constructing dense semantic correspondences between strongly non-isometric shapes without restricting object categories. The key insight is to lift "coarse" semantic cues into "fine" correspondence, which is achieved through two stages. In the "coarse" stage, we perform class-agnostic 3D segmentation to obtain non-overlapping semantic parts and prompt multimodal large language models (MLLMs) to identify part names. Then, we employ pretrained vision language models (VLMs) to extract text embeddings, enabling the construction of matched semantic parts. In the "fine" stage, we leverage these coarse correspondences to guide the learning of dense correspondences through a dedicated rank-based contrastive scheme. Thanks to class-agnostic segmentation, language guiding, and rank-based contrastive learning, our method is versatile for universal object categories and requires no predefined part proposals, enabling universal matching for inter-class and non-isometric shapes. Extensive experiments demonstrate UniMatch consistently outperforms competing methods in various challenging scenarios.

cs.CV↗

arXiv2026

Retrieval-Augmented Foundation Models for Matched Molecular Pair Transformations to Recapitulate Medicinal Chemistry Intuition

Matched molecular pairs (MMPs) capture the local chemical edits that medicinal chemists routinely use to design analogs, but existing ML approaches either operate at the whole-molecule level with limited edit controllability or learn MMP-style edits from restricted settings and small models. We propose a variable-to-variable formulation of analog generation and train a foundation model on large-scale MMP transformations (MMPTs) to generate diverse variables conditioned on an input variable. To enable practical control, we develop prompting mechanisms that let the users specify preferred transformation patterns during generation. We further introduce MMPT-RAG, a retrieval-augmented framework that uses external reference analogs as contextual guidance to steer generation and generalize from project-specific series. Experiments on general chemical corpora and patent-specific datasets demonstrate improved diversity, novelty, and controllability, and show that our method recovers realistic analog structures in practical discovery scenarios.

cs.LG↗

arXiv2026

Transformer-Based Approach for Automated Functional Group Replacement in Chemical Compounds

Functional group replacement is a pivotal approach in cheminformatics to enable the design of novel chemical compounds with tailored properties. Traditional methods for functional group removal and replacement often rely on rule-based heuristics, which can be limited in their ability to generate diverse and novel chemical structures. Recently, transformer-based models have shown promise in improving the accuracy and efficiency of molecular transformations, but existing approaches typically focus on single-step modeling, lacking the guarantee of structural similarity. In this work, we seek to advance the state of the art by developing a novel two-stage transformer model for functional group removal and replacement. Unlike one-shot approaches that generate entire molecules in a single pass, our method generates the functional group to be removed and appended sequentially, ensuring strict substructure-level modifications. Using a matched molecular pairs (MMPs) dataset derived from ChEMBL, we trained an encoder-decoder transformer model with SMIRKS-based representations to capture transformation rules effectively. Extensive evaluations demonstrate our method's ability to generate chemically valid transformations, explore diverse chemical spaces, and maintain scalability across varying search sizes.

cs.LG↗

arXiv2025

Two operator splitting methods for three-dimensional stochastic Maxwell equations with multiplicative noise

In this paper, we develop two energy-preserving splitting methods for solving three-dimensional stochastic Maxwell equations driven by multiplicative noise. We use operator splitting methods to decouple stochastic Maxwell equations into simple one-dimensional subsystems and construct two stochastic splitting methods, Splitting Method I and Splitting Method II, through a combination of spatial compact difference methods and the midpoint rule in time discretization for the deterministic parts, and exact unitary analytical solutions for the stochastic parts. Theoretical proofs show that both methods strictly preserve the discrete energy conservation law. Finally, numerical experiments fully verify the energy conservation of the methods and demonstrate that the temporal convergence order of the two splitting methods is first-order.

math.NA↗

arXiv2025

Stochastic positivity-preserving symplectic splitting methods for stochastic Lotka--Volterra predator-prey model

In this paper, we present two stochastic positive-preserving symplectic methods for the stochastic Lotka-Volterra predator-prey model driven by a multiplicative noise. To inherit the intrinsic characteristic of the original system, the stochastic Lie--Trotter splitting method and the stochastic Strang splitting method are introduced, which are proved to preserve the positivity of the numerical solution and possess the discrete stochastic symplectic conservation law as well. By deriving the uniform boundedness of the $p$-th moment of the numerical solution, we prove that the strong convergence orders of these two methods are both one in the $L^2(Ω)$-norm. Finally, we validate the theoretical results through two and four dimensional numerical examples.

math.NA↗

arXiv2025

An Efficient Machine Learning Framework for Option Pricing via Fourier Transform

The increasing need for rapid recalibration of option pricing models in dynamic markets places stringent computational demands on data generation and valuation algorithms. In this work, we propose a hybrid algorithmic framework that integrates the smooth offset algorithm (SOA) with supervised machine learning models for the fast pricing of multiple path-independent options under exponential Lévy dynamics. Building upon the SOA-generated dataset, we train neural networks, random forests, and gradient boosted decision trees to construct surrogate pricing operators. Extensive numerical experiments demonstrate that, once trained, these surrogates achieve order-of-magnitude acceleration over direct SOA evaluation. Importantly, the proposed framework overcomes key numerical limitations inherent to fast Fourier transform-based methods, including the consistency of input data and the instability in deep out-of-the-money option pricing.

q-fin.CP↗

arXiv2025

Dynamic Risk Assessment of Wildland-Urban Interface Fires

Wildland-Urban Interface (WUI) fires represent a compound disaster resulting from the interactions between natural ecosystems and human settlements, characterized by significantly dynamic evolving risks. However, most current risk assessment studies are based on static frameworks, which struggle to effectively capture the dynamic changes in risk over time. To address this issue, this paper proposes an innovative method that integrates a dynamic evaluation matrix, grey incidence analysis, and an optimization model for the dynamic risk assessment of WUI fires. This method incorporates time-series data by constructing a dynamic evaluation matrix, subsequently calculates the weighted standardized matrix for each evaluated area and its local volume matrices relative to the positive and negative ideal matrices. The dynamic differences between the evaluated areas and the ideal state are quantified by calculating the grey incidence degree, and an optimization model is established to solve for the superiority degree used for risk ranking. Research demonstrates that this method not only simplifies the computational process but also effectively captures the dynamic evolution patterns of fire risk across different areas, enabling refined risk classification. Compared to existing static methods, this framework overcomes their limitation in adequately representing risk dynamics, providing a more scientific basis for decision-making in the dynamic management and proactive prevention and control of WUI fires.

q-fin.RM↗

arXiv2025

Wiener chaos expansion for stochastic Maxwell equations driven by Wiener process

A novel and efficient algorithm based on the Wiener chaos expansion is proposed for the stochastic Maxwell equations driven by Wiener process. The proposed algorithm can reduce the original stochastic system to the deterministic case and separate the randomness in the computation. Therefore, it can yield a significant improvement of efficiency and lead to less computational errors compared to the Monte Carlo method, since the statistics of the solution can be solved directly without repeating over many realizations. In particular, the proposed algorithm could inherit the multi-symplecticity. Numerical experiments are dedicated to performing the efficiency and accuracy of the Wiener chaos expansion algorithm.

math.NA↗

arXiv2025

Optimal Estimation and Uncertainty Quantification for Stochastic Inverse Problems via Variational Bayesian Methods

The Bayesian inversion method demonstrates significant potential for solving inverse problems, enabling both point estimation and uncertainty quantification (UQ). However, Bayesian maximum a posteriori (MAP) estimation may become unstable when handling data from diverse distributions (e.g., solutions of stochastic partial differential equations (SPDEs)). Additionally, Monte Carlo sampling methods are computationally expensive. To address these challenges, we propose a novel two-stage optimization method based on optimal control theory and variational Bayesian methods. This method not only yields stable solutions for stochastic inverse problems but also efficiently quantifies the uncertainty of solutions. In the first stage, we introduce a new weighting formulation to ensure the stability of the Bayesian MAP estimation. In the second stage, we derive the necessary condition for efficiently quantifying the uncertainty of the solutions by combining the new weighting formula with variational inference. Furthermore, we establish an error estimation theorem that relates the exact solution to the optimally estimated solution under different amounts of observed data. Finally, the efficiency of the proposed method is demonstrated through numerical examples.

math.NA↗

arXiv2025

Temporal Attention Evolutional Graph Convolutional Network for Multivariate Time Series Forecasting

Multivariate time series forecasting enables the prediction of future states by leveraging historical data, thereby facilitating decision-making processes. Each data node in a multivariate time series encompasses a sequence of multiple dimensions. These nodes exhibit interdependent relationships, forming a graph structure. While existing prediction methods often assume a fixed graph structure, many real-world scenarios involve dynamic graph structures. Moreover, interactions among time series observed at different time scales vary significantly. To enhance prediction accuracy by capturing precise temporal and spatial features, this paper introduces the Temporal Attention Evolutional Graph Convolutional Network (TAEGCN). This novel method not only integrates causal temporal convolution and a multi-head self-attention mechanism to learn temporal features of nodes, but also construct the dynamic graph structure based on these temporal features to keep the consistency of the changing in spatial feature with temporal series. TAEGCN adeptly captures temporal causal relationships and hidden spatial dependencies within the data. Furthermore, TAEGCN incorporates a unified neural network that seamlessly integrates these components to generate final predictions. Experimental results conducted on two public transportation network datasets, METR-LA and PEMS-BAY, demonstrate the superior performance of the proposed model.

cs.LG↗

arXiv2025

Parareal Algorithms for Stochastic Maxwell Equations Driven by Multiplicative Noise

This paper investigates the parareal algorithms for solving the stochastic Maxwell equations driven by multiplicative noise, focusing on their convergence, computational efficiency and numerical performance. The algorithms use the stochastic exponential integrator as the coarse propagator, while both the exact integrator and the stochastic exponential integrator are used as fine propagators. Theoretical analysis shows that the mean square convergence rates of the two algorithms selected above are proportional to $k/2$, depending on the iteration number of the algorithms. Numerical experiments validate these theoretical findings, demonstrating that larger iteration numbers $k$ improve convergence rates, while larger damping coefficients $σ$ accelerate the convergence of the algorithms. Furthermore, the algorithms maintain high accuracy and computational efficiency, highlighting their significant advantages over traditional exponential methods in long-term simulations.

math.NA↗

arXiv2025

Structure-Preserving Implicit Runge-Kutta Methods for Stochastic Poisson Systems with Multiple Noises

In this paper, we propose the diagonal implicit Runge-Kutta methods and transformed Runge-Kutta methods for stochastic Poisson systems with multiple noises. We prove that the first methods can preserve the Poisson structure, Casimir functions, and quadratic Hamiltonian functions in the case of constant structure matrix. Darboux-Lie theorem combined with coordinate transformation is used to construct the transformed Runge-Kutta methods for the case of non-constant structure matrix that preserve both the Poisson structure and the Casimir functions. Finally, through numerical experiments on stochastic rigid body systems and linear stochastic Poisson systems, the structure-preserving properties of the proposed two kinds of numerical methods are effectively verified.

math.NA↗

arXiv2024

Parareal algorithms for stochastic Maxwell equations with the damping term driven by additive noise

In this paper, we investigate the strong convergence analysis of parareal algorithms for stochastic Maxwell equations with the damping term driven by additive noise. The proposed parareal algorithms proceed as two-level temporal parallelizable integrators with the stochastic exponential integrator as the coarse propagator and both the exact solution integrator and the stochastic exponential integrator as the fine propagator. It is proved that the convergence order of the proposed algorithms linearly depends on the iteration number. Numerical experiments are performed to illustrate the convergence of the parareal algorithms for different choices of the iteration number and the damping coefficient.

math.NA↗

arXiv2021

Surface Van Hove Singularity Enabled Efficient Catalysis: The Cases of CO Oxidation and Hydrogen Evolution Reactions

Surface Van Hove singularity (SVHS), defined as the surface states near the Fermi level (EF) in low-dimensional systems, triggers exciting physical phenomena distinct from bulk. We herein explore theoretically the potential role of SVHS in catalysis taking CO oxidation reaction as prototype over graphene/Ca2N (Gra/Ca2N) heterojunction and Pt2HgSe3 (001) surface. It is demonstrated that both systems with SVHS could serve as an electron bath to promote O2 adsorption and subsequent CO oxidation with low energy barriers of 0.2 ~ 0.6 eV for Gra/Ca2N and Pt2HgSe3 (001) surface. Importantly, the catalytically active sites associated with SVHS are well-defined and uniformly distributed over the whole surface plane, which is superior to the commonly adopted defect or doping strategy, and further the chemical reactivity of SVHS also can be tuned easily via adjusting its position with respect to EF. Our study demonstrates the enabling power of SVHS, and provides novel physical insights into the promising potential role of VHS in designing high-efficiency catalysts.

cond-mat.mtrl-sci↗

arXiv2021

Hydrogen-assisted layer-by-layer growth and robust nontrivial topology of stanene films on Bi(111)

Ever since the first successful synthesis of stanene via epitaxial growth, numerous efforts have been devoted to improving its overall quality and exploring its topological and other exotic properties under different growth conditions. Here, using first-principles approaches, we reveal the atomistic growth mechanisms and robust topological properties of few-layer stanene on Bi(111). We first show that monolayer stanene grown on Bi(111) follows a highly desirable nucleation-and-growth mechanism, characterized by attractive interaction of the Sn adatoms. More importantly, we reveal that surface passivation by the residual hydrogen is essential in achieving layer-by-layer growth of high-quality few-layer stanene, with the hydrogen functioning as a surfactant in stabilizing the growing films. Furthermore, we investigate systematically the dependence of the topological properties of stanene on the film thickness, hydrogen passivation, and substrate, and obtain robust quantum spin Hall effects under diverse physical conditions. The robustness of the nontrivial topology is attributable to the strong spin-orbit coupling of the Bi substrate. The atomistic growth mechanisms and nontrivial topology of stanene as presented here are also discussed in connection with recent experimental findings.

cond-mat.mtrl-sci↗

arXiv2020

Measurement of the neutron beam profile of the Back-n white neutron facility at CSNS with a Micromegas detector

The Back-n white neutron beam line, which uses back-streaming white neutrons from the spallation target of the China Spallation Neutron Source, is used for nuclear data measurements. A Micromegas-based neutron detector with two variants was specially developed to measure the beam spot distribution for this beam line. In this article, the design, fabrication, and characterization of the detector are described. The results of the detector performance tests are presented, which include the relative electron transparency, the gain and the gain uniformity, and the neutron beam profile reconstruction capability. The result of the first measurement of the Back-n neutron beam spot distribution is also presented.

physics.ins-det↗