arXiv subjects

Yun Su

Publications and source records attributed to Yun Su.

5 recordsLinked to original sources

arXiv2025

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems

Leveraging a stochastic extension of Zubov's equation, we develop a physics-informed neural network (PINN) approach for learning a neural Lyapunov function that captures the largest probabilistic region of attraction (ROA) for stochastic systems. We then provide sufficient conditions for the learned neural Lyapunov functions that can be readily verified by satisfiability modulo theories (SMT) solvers, enabling formal verification of both local stability analysis and probabilistic ROA estimates. By solving Zubov's equation for the maximal Lyapunov function, our method provides more accurate and larger probabilistic ROA estimates than traditional sum-of-squares (SOS) methods. Numerical experiments on nonlinear stochastic systems validate the effectiveness of our approach in training and verifying neural Lyapunov functions for probabilistic stability analysis and ROA estimates.

math.OC↗

arXiv2023

Message-passing selection: Towards interpretable GNNs for graph classification

In this paper, we strive to develop an interpretable GNNs' inference paradigm, termed MSInterpreter, which can serve as a plug-and-play scheme readily applicable to various GNNs' baselines. Unlike the most existing explanation methods, MSInterpreter provides a Message-passing Selection scheme(MSScheme) to select the critical paths for GNNs' message aggregations, which aims at reaching the self-explaination instead of post-hoc explanations. In detail, the elaborate MSScheme is designed to calculate weight factors of message aggregation paths by considering the vanilla structure and node embedding components, where the structure base aims at weight factors among node-induced substructures; on the other hand, the node embedding base focuses on weight factors via node embeddings obtained by one-layer GNN.Finally, we demonstrate the effectiveness of our approach on graph classification benchmarks.

cs.LG↗

arXiv2023

Robust 3.7 V-Na$_{2/3}$[Cu$_{1/3}$Mn$_{2/3}$]O$_2$ Cathode for Na-ion Batteries

Na-ion batteries (NIBs), which are recognized as a next-generation alternative technology for energy storage, still suffer from commercialization constraints due to the lack of low-cost, high-performance cathode materials. Since our first discovery of Cu$^{3+}$/Cu$^{2+}$ electrochemistry in 2014, numerous Cu-substituted/doped materials have been designed for NIBs. However for almost ten years, the potential of Cu$^{3+}$/Cu$^{2+}$ electrochemistry has been grossly underappreciated and normally regarded as a semielectrochemically active redox. Here, we re-synthesized P2-Na$_{2/3}$[Cu$_{1/3}$Mn$_{2/3}$]O$_2$ and reinterpreted it as a high-voltage, cost-efficient, air-stable, long-life, and high-rate cathode material for NIBs, which demonstrates a high operating voltage of 3.7 V and a completely active Cu$^{3+}$/Cu$^{2+}$ redox reaction. The 2.3 Ah cylindrical cells exhibit excellent cycling (93.1% capacity after 2000 cycles), high rate (97.2% capacity at 10C rate), good low-temperature performance (86.6% capacity at -30$^\circ$C), and high safety, based on which, a 56 V-11.5 Ah battery pack for E-bikes is successfully constructed, exhibiting stable cycling (96.5% capacity at the 800th cycle) and a long driving distance (36 km, tester weight 65 kg). This work offers a commercially feasible cathode material for low-cost, high-voltage NIBs, paving the way for advanced NIBs in power and stationary energy storage applications.

cond-mat.mtrl-sci↗

arXiv2015

On Betti Numbers of Milnor Fiber of Hyperplane Arrangements

Let $\mathcal{A}$ be a central hyperplane arrangement in $\mathbb{C}^{n+1}$ and $H_i,i=1,2,...,d$ be the defining equations of the hyperplanes of $\mathcal{A}$. Let $f=\prod_i H_i$. There is a global Milnor fibration $F\hookrightarrow \mathbb{C}^{n+1} \setminus \mathcal{A} \xrightarrow{f} \mathbb{C}^*,$ where $F$ is called the Milnor fiber and can be identified as the affine hypersurface $f=1$ in $\mathbb{C}^{n+1}$. Many open questions have been raised subject to $F$. In particular, it has been conjectured that the integral homology, or the characteristic polynomial, hence the Betti numbers, of $F$ are also determined by the intersection lattice $L(\mathcal{A})$. In this paper, we find a combinatorial upper bound for the first the characteristic polynomial of the Milnor fiber for central hyperplane arrangements, which improves existing results in the study. As a corollary, we obtain a combinatorial obstruction for trivial algebraic monodromy of the first homology of Milnor fiber. Calculations and comparisons to known examples computed using Fox calculus will be provided.

math.GT↗

arXiv2015

Higher-order Alexander Invariants of Hypersurface Complements

We define the higher-order Alexander modules $A_{n,i}(\mathcal{U})$ and higher-order degrees $δ_{n,i}(\mathcal{U})$ which are invariants of a complex hypersurface complement $\mathcal{U}$. These invariants come from the module structure of the homology of certain solvable covers of the hypersurface complement. Such invariants were originally developed by T. Cochran in [1] and S. Harvey in [8], and were used to study knots and 3-manifolds. In this paper, I generalize the result proved by C. Leidy and L. Maxim [22] from the plane curve complements to higher-dimensional hypersurface complements. Zariski observed that the position of singularities on a singular complex plane curve affects the topology of the curve. My results on higher-order degrees of hypersurface complements also show that global topology is controlled by the local topologies. In particular, the higher-order degrees of the hypersurface complement are bounded by a linear combination of the higher-order degrees of the local link pairs.

math.GT↗