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Shu Yan

Publications and source records attributed to Shu Yan.

9 recordsLinked to original sources
arXiv2026

Fourier-Latent Diffusion for Constrained Generation of Triply Periodic Minimal Surfaces

We propose a diffusion-based generative framework for controllable generation of triply periodic minimal surface (TPMS) structures with low residual mean curvature. Existing TPMS generation approaches are often restricted to a small set of canonical families or produce TPMS-like approximations that deviate from exact minimality. To enable this generative framework, we first construct a large-scale dataset of over 18K unique TPMS by enumerating admissible boundary loops on mirrorable fundamental bounding volumes and solving for diverse minimal-surface patches. Each surface is then projected onto a compact Fourier latent space that explicitly enforces periodicity and $D_{2h}$ symmetry. Next, a transformer-based diffusion model is trained in this latent space to support unconditional sampling, deterministic inversion, local editing, and conditional generation under user-specified constraints. Experiments demonstrate that the model generates diverse, low-curvature TPMS candidates that, under conditioning, satisfy sparse geometric constraints and match target homogenized linear elastic properties, providing a practical tool for TPMS inverse design.

cs.GR↗
arXiv2025

PC-NCLaws: Physics-Embedded Conditional Neural Constitutive Laws for Elastoplastic Materials

While data-driven methods offer significant promise for modeling complex materials, they often face challenges in generalizing across diverse physical scenarios and maintaining physical consistency. To address these limitations, we propose a generalizable framework called Physics-Embedded Conditional Neural Constitutive Laws for Elastoplastic Materials, which combines the partial differential equations with neural networks. Specifically, the model employs two separate neural networks to model elastic and plastic constitutive laws. Simultaneously, the model incorporates physical parameters as conditional inputs and is trained on comprehensive datasets encompassing multiple scenarios with varying physical parameters, thereby enabling generalization across different properties without requiring retraining for each individual case. Furthermore, the differentiable architecture of our model, combined with its explicit parameter inputs, enables the inverse estimation of physical parameters from observed motion sequences. This capability extends our framework to objects with unknown or unmeasured properties. Experimental results demonstrate state-of-the-art performance in motion reconstruction, robust long-term prediction, geometry generalization, and precise parameters estimation for elastoplastic materials, highlighting its versatility as a unified simulator and inverse analysis tool.

cs.GR↗
arXiv2025

A Survey on Large Language Models for Mathematical Reasoning

Mathematical reasoning has long represented one of the most fundamental and challenging frontiers in artificial intelligence research. In recent years, large language models (LLMs) have achieved significant advances in this area. This survey examines the development of mathematical reasoning abilities in LLMs through two high-level cognitive phases: comprehension, where models gain mathematical understanding via diverse pretraining strategies, and answer generation, which has progressed from direct prediction to step-by-step Chain-of-Thought (CoT) reasoning. We review methods for enhancing mathematical reasoning, ranging from training-free prompting to fine-tuning approaches such as supervised fine-tuning and reinforcement learning, and discuss recent work on extended CoT and "test-time scaling". Despite notable progress, fundamental challenges remain in terms of capacity, efficiency, and generalization. To address these issues, we highlight promising research directions, including advanced pretraining and knowledge augmentation techniques, formal reasoning frameworks, and meta-generalization through principled learning paradigms. This survey tries to provide some insights for researchers interested in enhancing reasoning capabilities of LLMs and for those seeking to apply these techniques to other domains.

cs.AI↗
arXiv2025

How Far Are We from Optimal Reasoning Efficiency?

Large Reasoning Models (LRMs) demonstrate remarkable problem-solving capabilities through extended Chain-of-Thought (CoT) reasoning but often produce excessively verbose and redundant reasoning traces. This inefficiency incurs high inference costs and limits practical deployment. While existing fine-tuning methods aim to improve reasoning efficiency, assessing their efficiency gains remains challenging due to inconsistent evaluations. In this work, we introduce the reasoning efficiency frontiers, empirical upper bounds derived from fine-tuning base LRMs across diverse approaches and training configurations. Based on these frontiers, we propose the Reasoning Efficiency Gap (REG), a unified metric quantifying deviations of any fine-tuned LRMs from these frontiers. Systematic evaluation on challenging mathematical benchmarks reveals significant gaps in current methods: they either sacrifice accuracy for short length or still remain inefficient under tight token budgets. To reduce the efficiency gap, we propose REO-RL, a class of Reinforcement Learning algorithms that minimizes REG by targeting a sparse set of token budgets. Leveraging numerical integration over strategically selected budgets, REO-RL approximates the full efficiency objective with low error using a small set of token budgets. Through systematic benchmarking, we demonstrate that our efficiency metric, REG, effectively captures the accuracy-length trade-off, with low-REG methods reducing length while maintaining accuracy. Our approach, REO-RL, consistently reduces REG by >=50 across all evaluated LRMs and matching Qwen3-4B/8B efficiency frontiers under a 16K token budget with minimal accuracy loss. Ablation studies confirm the effectiveness of our exponential token budget strategy. Finally, our findings highlight that fine-tuning LRMs to perfectly align with the efficiency frontiers remains an open challenge.

cs.CL↗
arXiv2015

Identification of highly susceptible individuals in complex networks

Identifying highly susceptible individuals in spreading processes is of great significance in controlling outbreaks. In this paper, we explore the susceptibility of people in susceptible-infectious-recovered (SIR) and rumor spreading dynamics. We first study the impact of community structure on people's susceptibility. Despite that the community structure can reduce the infected population given same infection rates, it will not deterministically affect nodes' susceptibility. We find the susceptibility of individuals is sensitive to the choice of spreading dynamics. For SIR spreading, since the susceptibility is highly correlated to nodes' influence, the topological indicator k-shell can better identify highly susceptible individuals, outperforming degree, betweenness centrality and PageRank. In contrast, in rumor spreading model, where nodes' susceptibility and influence have no clear correlation, degree performs the best among considered topological measures. Our finding highlights the significance of both topological features and spreading mechanisms in identifying highly susceptible population.

physics.soc-ph↗
arXiv2015

Phase diagram and optimal switching induced by spin Hall effect in a perpendicular magnetic layer

In a ferromagnet/heavy-metal bilayer device with strong spin Hall effect an in-plane current excites magnetic dynamics through spin torque. We analyze bilayers with perpendicular magnetization and calculate three-dimensional phase diagrams describing switching by external magnetic field at a fixed current. We then concentrate on the case of a field applied in the plane formed by the film normal and the current direction. Here we analytically study the evolution of both the conventional "up"/"down" magnetic equilibria and the additional equilibria created by the spin torque. Expressions for the stability regions of all equilibria are derived, and the nature of switching at each critical boundary is discussed. The qualitative picture obtained this way predicts complex hysteresis patterns that should occur in bilayers. By analyzing the phase portraits of the system we show that when the spin torque induced equilibrium exists, switching between "up" and "down" states proceeds through it as an intermediate state. Using numeric simulations we analyze the switching time and compare it to that of a conventional spin torque device with collinear magnetizations of the polarizer and the free layer.

cond-mat.mes-hall↗
arXiv2014

Dynamical Immunization Strategy for Seasonal Epidemics

The topic of finding effective strategy to halt virus in complex network is of current interest. We propose an immunization strategy for seasonal epidemics that occur periodically. Based on the local information of the infection status from the previous epidemic season, the selection of vaccinated nodes is optimized gradually. The evolution of vaccinated nodes during iterations demonstrates that the immunization tends to locate in both global hubs and local hubs. We analyze the epidemic prevalence by a heterogeneous mean-field method and present numerical simulations of our model. This immunization performs superiorly to some other previously known strategies. Our work points out a new direction in immunization of seasonal epidemics.

stat.AP↗
arXiv2013

How to enhance the dynamic range of excitatory-inhibitory excitable networks

We investigate the collective dynamics of excitatory-inhibitory excitable networks in response to external stimuli. How to enhance dynamic range, which represents the ability of networks to encode external stimuli, is crucial to many applications. We regard the system as a two-layer network (E-Layer and I-Layer) and explore the criticality and dynamic range on diverse networks. Interestingly, we find that phase transition occurs when the dominant eigenvalue of E-layer's weighted adjacency matrix is exactly one, which is only determined by the topology of E-Layer. Meanwhile, it is shown that dynamic range is maximized at critical state. Based on theoretical analysis, we propose an inhibitory factor for each excitatory node. We suggest that if nodes with high inhibitory factors are cut out from I-Layer, dynamic range could be further enhanced. However, because of the sparseness of networks and passive function of inhibitory nodes, the improvement is relatively small compared tooriginal dynamic range. Even so, this provides a strategy to enhance dynamic range.

q-bio.NC↗