Contributed Talks and Posters

Authors: Rodney Pino (Data Science Program, University of the Philippines Diliman)*; Renier Mendoza (Institute of Mathematics, University of the Philippines Diliman); Rachelle Sambayan (Institute of Mathematics, University of the Philippines Diliman)

Recent advances in natural language processing (NLP) and large language models (LLMs) have significantly enhanced optical character recognition (OCR) through automated text correction and refinement. However, most OCR–NLP pipelines focused on major scripts such as Latin while underrepresented writing systems like Baybayin, a precolonial Tagalog script, remain underexplored. This gap reflects both the script’s antiquity and the limited availability of digital resources. To support its cultural revival and digital preservation, this study enhances Baybayin OCR by integrating advanced NLP. Building on a previous framework that recognizes Baybayin characters using SVM, we address a key limitation: Baybayin words often map to multiple Latin equivalents. To resolve this, we incorporate GPT-5 to perform Filipino contextual analysis within the phrases. Results demonstrate improved phrase-level accuracy in Baybayin translation. Both the proposed algorithm and dataset are made publicly available

Authors: Zhonghao Sun (AMSS, CAS)*; Jizu Huang (AMSS, CAS); Chuanfu Xiao (Xiangtan University); Chao Yang (Peking University)

The Hadamard product of tensor train (TT) tensors is a key nonlinear operation in scientific computing and data analysis, but it often causes a rapid increase in TT ranks, leading to high computational and storage costs. In this work, we propose a Hadamard avoiding TT recompression (HaTT) algorithm that recompresses Hadamard products without explicitly constructing them. By exploiting the intrinsic structure of the Hadamard product in TT format, HaTT significantly reduces both computational complexity and memory requirements. Theoretical complexity analysis and numerical experiments confirm its efficiency over existing recompression methods. As an application, HaTT is used to solve the Allen–Cahn equation, achieving substantial acceleration without loss of accuracy.

Authors: Chun-Hsien Li (National Kaohsiung Normal University)*

The study investigates cluster synchronization in a Kuramoto model with frustration, a feature that enhances fidelity in replicating real-world network dynamics. While complete synchronization is widely researched, cluster synchronization mechanisms remain less explored. For a network with multiple identical-phase oscillator groups, we perform a rigorous stability analysis and derive quantitative conditions—incorporating coupling weights, cluster configurations, natural frequencies, and the frustration parameter—to guarantee the asymptotic stability of the cluster synchronization manifold. Numerical simulations are provided to validate the established theoretical results.

Authors: Jiyeon Kim (Ajou University)*; Dongwook Shin (Ajou University)

Operator learning is a promising paradigm for parametric partial differential equations (PDEs), yet network parameters grow rapidly with mesh resolution. We propose Sparse Neural Operator netWorks (SNOW), a framework that embeds the sparse structure of PDE discretizations into the network architecture. As a primary application, Sparse FEONet restricts each layer's connectivity to the local support of finite element basis functions, supported by a universal approximation theorem and stability analysis. Across various experiments, Sparse FEONet achieves up to a 98% parameter reduction while maintaining or improving accuracy. Furthermore, we extend SNOW to the Hybridizable Discontinuous Galerkin (HDG) method, the SNOW-HDG learns trace variables on the mesh skeleton. Building on our stability analysis, we further apply SNOW to Extreme Learning Machines (ELM), which enables a principled selection of stable standard deviation for the frozen weight matrix.

Authors: 杨 胡 (Hong Kong Baptist University)*

We study a curvature-regularized variational model for surface reconstruction from point clouds and develop an efficient operator-splitting solver. To avoid the expensive reinitialization required in level-set formulations, we adopt an indicator-function representation of the surface. By introducing an auxiliary variable, we decouple the nonlinear curvature term and reformulate the minimization problem as the steady-state limit of an associated evolution system. The resulting splitting scheme reduces each iteration to two tractable subproblems, including a thresholding step that can be solved efficiently. This provides a new link between threshold dynamics and curvature-regularized variational reconstruction. Numerical results in both two and three dimensions show that the proposed method preserves sharp and concave geometric features while achieving substantially lower computational cost than level-set-based methods.

Authors: Junwon You (KAIST)*

Vision-language models learn a shared embedding space by aligning image and text representations. In this talk, I discuss how topological data analysis can be used to analyze and align this shared embedding space. The main focus is on topological alignment between representations. Instead of considering only pairwise image-text similarity, we examine whether the two modalities have similar structural organization in the embedding space. Persistent homology is used to extract topological information from image and text embeddings, including connectivity and cycle-related structures. I will present two related studies on this topic: one on the topological alignment of shared vision-language embedding spaces, and another on topology-aware representation alignment for semi-supervised vision-language learning. Together, these studies suggest that topological information can provide an additional signal for aligning vision and language representations, especially when supervision is limited.

Authors: Chin-Lung Li (National Tsing Hua University)*; Ren-Chuen Chen (National Kaohsiung Normal University); Xiaodong Liang (Technical University of Denmark); Jinn-Liang Liu (National Tsing Hua University)

This work introduces a generalized Debye-Hückel (GDH) theory proposed from a fourth-order molecular mean-field Poisson-Fermi model, which describes ionic activities in mixed-salt and mixed-solvent electrolyte solutions. The electric potential is analytically derived through the linearization of the fourth-order Poisson−Fermi model under rigorous boundary and interface conditions in a spherically symmetric domain. The GDH parameters, which vary with these conditions, are either obtained from physical principles or based on experiments, whereas most of these parameters are fixed in the classical Debye-Hückel theory. Some numerical examples are presented to demonstrate the novel capability of the GDH theory in capturing these physical properties and interactions.

Authors: Ryo Sagawa (Graduate School of Information Science and Technology, The University of Osaka)*; Daisuke Furihata (D3 Center, The University of Osaka); Yuto Miyatake (D3 Center, The University of Osaka)

Recently, optimization methods based on the RSAV (relaxed scalar auxiliary variable) approach have been proposed, which ensure a modified dissipation law. Existing studies, however, rely solely on gradient information and may converge slowly for ill-conditioned problems. In this work, we incorporate Hessian information into the linear operator arising in the RSAV scheme to accelerate convergence. Directly using the Hessian, however, presents two challenges: (i) increased computational cost at each iteration; and (ii) potential loss of the modified dissipation law when the Hessian is indefinite. To overcome these challenges, we propose using an approximate Hessian as the linear operator. It is efficiently constructed by using the Nyström method, a randomized low-rank approximation technique, and its positive semidefiniteness is enforced via eigenvalue decomposition. To further reduce the computational cost, we adaptively reuse the approximate Hessian based on the energy deviation.

Authors: Cheng-Pu Lin (National Yang Ming Chiao Tung University)*

In this talk, I will present how to establish local well-posedness for the one-dimensional interface problem associated with the Korteweg–de Vries equation. I will begin with a brief historical overview of the development of Korteweg--de Vries equation, and then introduce an effective approach now known as the Fokas method. This method can be adapted to the linear Korteweg--de Vries equation with piecewise constant coefficient. Finally, by applying the contraction mapping theorem, we obtain a local well-posedness result.

Authors: Rachelle Anne Guanga (University of the Philippines Diliman)*

Efficient routing of service personnel is critical in systems where timely service delivery and limited resources affect operational performance. In the Philippines, the Department of Agriculture–Philippine Carabao Center (DA–PCC) implements a nationwide artificial insemination (AI) program to improve the genetic quality and productivity of carabaos.

Authors: Sunyoung Bu (Kwangwoon University)*; Minuk Hyun (Kwangwoon University); Sungkyu Kim (Kwangwoon Univerisity)

Fractional differential equations have attracted considerable attention due to their ability to model memory effects in various scientific and engineering applications. In particular, the fractional Verhulst model provides an effective framework for describing population dynamics with memory effects. However, the nonlocal nature of fractional derivatives and the weak singularity near the initial time make numerical approximation challenging. In this study, we apply a higher-order Enhanced Predictor Corrector Method (EPCM) to the fractional Verhulst model. To improve numerical accuracy near the initial singularity, a graded mesh is employed instead of a uniform mesh. The accuracy and convergence behavior of the higher order graded-mesh EPCM are investigated for various fractional orders and grading parameters. Numerical results demonstrate that graded meshes can improve the performance of high-order predictor-corrector methods for fractional population models.

Authors: Shuping Lin (Nagoya University)*; Qiang Ma (Harbin Institute of Technology at Weihai); Zhenyu Wang (Harbin Institute of Technology at Weihai); Xiaohua Ding (Harbin Institute of Technology at Weihai); Shao-Liang Zhang (Nagoya University)

This report proposes a structure-preserving numerical method for a nonlinear wave equation driven by Stratonovich-type multiplicative noise under periodic boundary conditions. A Galerkin spectral element method is employed for spatial semi-discretization, followed by temporal discretization using the Crank–Nicolson method. In particular, a specially designed structure-preserving discretization of the nonlinear terms is introduced to ensure that the resulting fully discrete method preserves the underlying multi-symplectic structure and conserves momentum. Furthermore, convergence of the fully discrete method is analyzed, yielding an error bound. Numerical experiments are presented to validate the theoretical analysis and to demonstrate the effectiveness of the proposed method in maintaining physical invariants over long-time simulations.

Authors: Shawnrick Andrei Pacura (University of the Philippines Diliman)*

This study presents a network-based modeling framework integrating exponential random graph models and a Markov Chain Monte Carlo-informed gradient ascent method. Dynamic networks are generated and an SEIL model is ran to simulate the tuberculosis spread, which remains a public health concern in populations where interactions facilitate TB transmission. Temporal centrality measures are then used to identify individuals whose targeted intervention may disrupt infection pathways. Simulation results show that targeted intervention can substantially reduce epidemic peak and size, with greater benefit in initially infectious populations. This temporal centrality-based targeted approach, overall, can yield benefits in structured networks, but its advantage is decreased in less organized settings. The framework provides a basis for evaluating targeted and data-driven public health interventions, particularly in resource-constrained settings where large-scale solutions may be impractical.

Authors: Chin-Chin Wu (National Chung Hsing University Department of Applied Mathematic)*; JONG-SHENQ GUO (Department of Applied Mathematics and Data Science, Tamkang University); YU ICHIDA (Department of Mathematical Sciences, School of Science, Kwansei Gakuin University); SHOJI YOTSUTANI (Ryukoku University)

This work is to study the structure of stationary solutions of a model arising in the polarized ionic conductor incorporating the fringing field effect. Our strategy is to transform the original quasilinear equation into a semilinear equation so that the classical method can be applied. Moreover, we are able to deal with both Dirichlet and Robin boundary cases simultaneously.

Authors: Chang-En Du (NYCU)*

The Total Variation (TV) model and adaptive variational models have been successfully applied to image enhancement problems. However, the quality of the reconstructed image strongly depends on the choice of model parameters, which are often selected empirically. In this talk, I will present the basic ideas of the TV model and adaptive variational models and show some results based on these models. We will discuss the role of model parameters and their impact on reconstruction quality. Finally, I will present our ongoing work on formulating parameter selection as a bilevel optimization problem, aiming to automatically determine optimal parameters.

Authors: Christian James Galotera (University of the Philippines)*; Renier Mendoza (University of the Philippines); Reinabelle Reyes (Philippine Space Agency)

Physics-Informed Neural Networks and Physics-Informed Kolmogorov–Arnold Networks are developed as data-driven discovery frameworks for reconstructing cosmological expansion and recovering cosmological parameters across three dark-energy models: the standard cosmological model, the Chevallier–Polarski–Linder parametrization, and quintessence cosmology. Cosmological datasets motivated by theoretical dark-energy scenarios were used to evaluate expansion-history reconstruction and parameter inference. Friedmann and Klein–Gordon physics constraints were embedded into the training process, while PRCC analysis with Latin Hypercube Sampling was performed to assess parameter sensitivities directly from the governing equations. Results demonstrate that both frameworks successfully reconstruct the expansion history and recover cosmological parameters, highlighting the potential of physics-informed deep learning for cosmological reconstruction, parameter inference, and data-driven discovery.

Authors: Kyoungjin Jung (Ajou University)*; Dongwook Shin (Ajou University)

We propose residual-based finite element convolutional operator networks for elliptic partial differential equations with a local propagation architecture. The architecture preserves finite-element locality without resolution reduction and reduces the number of parameters through shared local convolutional kernels. The method trains surrogate solvers directly from finite element residual losses and approximates solution operators without paired input-output data. Finite element analysis establishes a relation between residual loss decay and the H1-error under mesh refinement, which provides training criteria for optimal convergence rates. We further prove a layer-wise approximation result showing that the proposed local block can approximate any Sparse FEONet affine layer on fixed structured grids. Numerical experiments demonstrate comparable accuracy with reduced model size and lower computational cost.

Authors: Resa Mae Sangco (North Eastern Mindanao State University)*

This study developed a Health Coverage Index (HCI) to assess subnational health coverage across provinces and highly urbanized cities using 2024 administrative data. The HCI integrates five dimensions—Promotion, Prevention, Treatment, Rehabilitation, and Palliation—and five health components: Reproductive, Maternal, Newborn and Child Health, Infectious Diseases, Non-Communicable Diseases, Health Services, and Financial Protection. Three weighting methods (AHP, EWM, and PCA) were evaluated through simulation analyses of bias, MSE, and CV. Results showed that EWM performed best, yielding the lowest bias, MSE, and CV. The national HCI was 0.3401, indicating low health coverage, with substantial disparities across areas. Highly urbanized cities generally outperformed rural provinces, while BARMM provinces exhibited the lowest coverage. The HCI provides a robust tool for identifying inequities and guiding targeted health interventions and resource allocation.

Authors: SANGEUN YOUN (Kyung Hee University)*; Hyoseon Yang (Kyung Hee University); Kyungrok Lee (Kyung Hee University)

We propose a new Runge–Kutta discontinuous Galerkin (RKDG) framework for one-dimensional hyperbolic conservation laws, designed to improve numerical accuracy and convergence order. The method incorporates a cell-dependent parameter into an exponential approximation space, allowing the local basis functions to adapt dynamically to solution features within each cell. This adaptive approximation enhances the convergence order without increasing the number of degrees of freedom. To reduce numerical dissipation near singularities, we further incorporate a modified WENO-type limiter guided by a newly developed singularity detector. The detector identifies troubled cells based on local smoothness information, enabling selective application of the limiter while preserving high-order accuracy in smooth regions. The proposed method is evaluated on a range of benchmark problems, including one-dimensional scalar equations and systems of hyperbolic conservation laws.

Authors: Hiroki Takeda (The University of Osaka)*; Yuto Miyatake (The University of Osaka); Daisuke Furihata (The University of Osaka)

Analyzing high-dimensional streaming data is vital for real-time applications. Tensor Train (TT) decomposition compresses data efficiently, but batch methods are too slow for streaming. Existing online methods often suffer from numerical instability or slow convergence. We propose an efficient online algorithm for TT decomposition of streaming tensors. Our strictly online, single-sweep method leverages temporal continuity and continuously enforces orthogonality constraints on TT cores. This sequential orthogonalization avoids inverting ill-conditioned matrices, ensuring numerical stability and enabling deterministic, low-latency updates suitable for resource-constrained environments. We also establish several theoretical results. For example, we prove the monotonic decrease of the objective function and derive a local error bound. Experiments on video and high-dimensional synthetic streams demonstrate our method's superior scalability, tracking quality, and long-term stability.

Authors: Boyu Wu (Osaka University)*; Daisuke Furihata (Osaka University); Yuto Miyatake (Osaka University); Shinya Maeyama (National Institute for Fusion Science)

Kinetic shear Alfvén waves develop nonlinear perturbations in turbulent regimes, where phase mixing and field-particle energy exchange shape the electron distribution and electromagnetic response, causing Alfvénic instabilities. Existing dynamical low rank (DLR) methods solve the electromagnetic closure with the generalized minimal residual method (GMRES), which can fail to converge when turbulent dynamics generate strongly coupled field and distribution structures. The present work introduces a tensor tree representation for kinetic shear Alfvén dynamics. The electron distribution, electromagnetic closure, and force operators are encoded and evolved in the same tensor tree coordinates. Numerical simulations confirm that the tensor tree method reproduces the electron distribution, electromagnetic field response, and system invariants in close agreement with DLR, while using less memory and compute, remaining stable in turbulent regimes where GMRES is hard to converge.

Authors: Jianlu Yan (Nanjing University of Aeronautics and Astronautics)*

We investigate a Keller-Segel system with flux limitation under no-flux boundary conditions in a ball. We prove that the system possesses a unique classical solution that can be extended in time up to a maximal T_{max}. Moreover, it is shown that the above solution is global and bounded under some suitable conditions. In particular, our result is corresponding to the result in [Bellomo-Winkler, Commun. Partial Differ. Equ. 42, 436-473 (2017)]. This is a joint work with Yuxiang Li (SEU).

Authors: Minjong Kim (Konkuk University)*; Donggu Lee (Konkuk University); Yangjin Kim (Konkuk University)

Glioblastoma (GBM) features an immunosuppressive microenvironment that limits standard therapies. To address this, the STING pathway is targeted to stimulate local immune responses. This study presents a Finite Element Method (FEM) framework modeling the therapeutic impact of the STING agonist ADU-S100 on glioma growth. Utilizing a realistic brain mesh, we implemented a coupled reaction-diffusion system reflecting tissue heterogeneity in gray and white matter. The simulation tracks ADU-S100 diffusion, subsequent intracellular signaling, and Type I interferon (IFN-β) production leading to tumor cell death. Results show ADU-S100 treatment drives significant tumor suppression compared to rapid expansion in the control group. Validated by experimental data from the Sean Lawler group (Brown University), this computational model provides a robust, predictive tool for optimizing STING-targeted immunotherapy in GBM.

Authors: Congzhuo Fang (Northwestern Polytechnical University); Zihao Yang (Northwestern Polytechnical University)*

We propose a phase-field-smoothed PINN (PFS-PINN) for finite-deformation hyperelastic interface problems. Internal material interfaces cause discontinuous elasticity tensors and globally H1 displacement fields, making standard strong-form PINNs difficult to train. PFS-PINN combines phase-field smoothing with a displacement-stress mixed formulation. The phase-field network replaces the sharp interface with a continuous order parameter and builds a smooth material tensor, converting the original nonlinear interface problem into a smooth-coefficient hyperelastic equilibrium problem. The mixed PINN treats the first Piola-Kirchhoff stress as an independent output, so the residual involves first-order stress divergence rather than second-order displacement derivatives. For the smoothed problem, energy convergence and an H1 displacement error bound are established. Tests on regular, high-curvature, and multiple-interface cases show improved accuracy, efficiency, and robustness.

Authors: Yanfu Chen (Northwestern Polytechnical University); Zihao Yang (Northwestern Polytechnical University)*

We propose a machine learning-enhanced high-order stochastic multiscale (HOSM) method for multiscale diffusion equations in stationary and non-stationary random materials. It preserves local oscillations while avoiding the extensive sampling and fine meshes required by direct numerical simulations. Multiscale asymptotic expansion formulas are derived for both problems. The homogenized equation is solved using a two-stage stochastic homogenization method induced by the normalizing field flow and multimodes Monte Carlo strategy. A limited number of cell problems are solved using the finite element method, and a neural network is developed to establish the mapping between macroscopic and microscopic coordinates and the expected values of the cell functions. The HOSM solutions are constructed by integrating the two-stage stochastic homogenization solutions with the neural-network-predicted cell functions. Numerical examples demonstrate the accuracy and efficiency of the method.

Authors: Christophe Heneffe (UCLouvain)*

In the last two decades, a variety of algorithms have been developed for solving Laplacian systems in nearly linear time, that is, in O(n log n) time, independently of the system's condition number. These methods construct effective preconditioners by generating carefully chosen subgraphs of the graph underlying the Laplacian matrix. We focus on Laplacian systems arising from structured graphs such as grids and meshes. Such systems occur naturally in the discretization of elliptic partial differential equations, for example, Poisson equations arising in incompressible flow simulations. We show how subgraph preconditioning techniques originally developed for general graph Laplacians can be adapted to structured PDE discretizations. By exploiting the special structure of these graphs, we obtain a robust and practical solver. This talk provides an overview of the underlying algorithms and presents numerical results demonstrating their effectiveness.

Authors: Xiangwen Zhao (The University of Osaka)*; Yuto Miyatake (The University of Osaka); Furihata Daisuke (The University of Osaka)

Large-scale shifted skew-symmetric (SSS) linear systems of the form (αI + S)x = b arise in a variety of scientific and engineering applications. When the shift parameter α is relatively small, the system becomes highly ill-conditioned, leading to the slow convergence of standard Krylov subspace methods. To address this challenge, we propose a randomized deflation preconditioner tailored specifically for SSS systems. By leveraging the property that the matrix α^2I − S^2 is symmetric positive definite, we apply a randomized Nyström approximation to efficiently approximate its dominant spectral components. Theoretical analysis establishes that the expected condition number of the preconditioned system is strictly bounded. Extensive numerical experiments demonstrate that, when integrated with GMRES, the proposed method achieves significant spectral clustering and convergence acceleration for large-scale SSS matrices exhibiting effectively low-rank structures.

Authors: Janith Wijesinghe (National Chung Hsing University)*

Point set matching seeks meaningful matches between point clouds, which can be viewed as discrete probability measures and compared using optimal transport. In this work, we reformulate optimal transport as a sequence of Newton-based matrix balancing problems along the central path of an interior-point method with a negative entropy barrier. To address the high-dimensional transport plan, dense constraints, and ill-conditioned Hessian systems, we derive a reduced Schur complement formulation from the block-structured Hessian system, avoiding large dense matrix formation and enabling a more efficient implementation. To improve scalability, we incorporate sparse support constraints into the matrix balancing procedure and solve the resulting Schur complement system using a preconditioned conjugate gradient method. The preconditioner captures dominant spectral information and reduces the number of matrix-vector products, leading to accurate and robust computations in numerical experiments.

Authors: Haruka NAKAMURA (The University of Tokyo)*

This study proposes a numerical scheme for Hamilton--Jacobi--Bellman (HJB) equations in a setting where the Hamiltonian is prescribed directly, rather than derived from a Lagrangian. This formulation commonly appears in mean field game systems, where HJB equations are coupled with Fokker--Planck equations. Semi-Lagrangian schemes are well-known numerical methods for HJB equations. However, since they are designed for Lagrangian-based formulations, they require repeated minimization and may be less efficient in the present setting. Accordingly, we construct a monotone scheme using numerical Hamiltonians, inspired by the monotone scheme of Crandall and Lions. In particular, despite the presence of diffusion terms, the CFL restriction for the proposed explicit scheme remains comparable to that for first-order PDEs. Under suitable smoothness assumptions on the solution, we further derive error estimates. Finally, numerical experiments are presented to verify the theoretical results.

Authors: Dohyun Kim (Kyung Hee University)*; Hyoseon Yang (Kyung Hee University); Andrew Christlieb (Michigan State University)

This study aims to improve the accuracy of high-order finite volume methods (FVMs) for solving multi-dimensional nonlinear conservation laws. The conventional Weighted Essentially Non-Oscillatory (WENO) scheme achieves high-order convergence in smooth regions, but its accuracy deteriorates in multi-dimensional settings due to the dimension-by-dimension reconstruction, which introduces directional bias and averaging errors. To address these issues, we propose a numerical framework combining the Taylor-series-based correction of Buchmüller and Helzel with Radial Basis Function (RBF) reconstruction. The method converts cell averages into point values to correct leading-order averaging errors, and employs RBF reconstruction to reduce directional bias in multi-dimensional settings. Numerical experiments on one- and two-dimensional problems demonstrate improved accuracy over the classical WENO scheme and the potential to reduce grid-induced errors in high-resolution simulations.

Authors: Yu Yu Weng (National Yang Ming Chiao Tung University)*

In this paper, we propose and analyze a fully discrete Data Assimilation Reduced Order Model that incorporates Difference Quotients into the POD snapshot matrix (DQ-DA-ROM). We establish uniform-in-time error estimates for the proposed DQ-DA-ROM using both Backward Euler time discretizations. A major theoretical contribution of this work is the derivation of optimal error bounds for the Ritz projection within the DQ-POD space. By leveraging the continuous POD framework for multiple data streams, we decouple the spatial gradient and state errors from the ROM stiffness matrix, proving that the errors are exclusively bounded by the discarded DQ-POD eigenvalues. Furthermore, we apply a discrete Gronwall argument to demonstrate that the data assimilation nudging term effectively dampens the initial errors and removes the time-step accumulation, leading to bounds that are completely independent of the final simulation time.

Authors: Changhyeon Na (Kyunghee University)*; Hyoseon Yang (Kyung Hee University)

Electron backscatter diffraction (EBSD) maps often contain missing orientations that compromise downstream simulations. Because orientations lie on SO(3), Euclidean losses yield non-physical reconstructions, while hybrid state-of-the-art methods rely on O(N^2)patch search with limited scalability. We propose the Misori-Guided U-Net, a single-pass framework embedding crystallographic geometry via a differentiable cosine loss with bounded gradients, periodicity-aware reconstruction. On synthetic benchmarks the method achieves an angular mean disorientation of 0.470rad—within 1.3% of the state of the art—while executing 19 times faster with 53.5% lower error than MSE-only training. Accuracy degrades gracefully under severe noise across diverse damage patterns, enabling real-time, crystallographically faithful EBSD restoration without iterative patch matching.

Authors: Emmanuel David (University of the Philippines)*

Delay differential equations (DDEs) involve values and/or derivatives at present and past states. Building on \cite{jamilla, mezo} utilizing the $r$-Lambert $W$ function in solving first-order DDEs, this paper extends that framework to second-order DDEs of the form $$ay''(t)+by'(t)+cy(t)+a_dy''(t-h)+b_dy'(t-h)+c_dy(t-h)=0,$$ where $a,b,c,a_d,b_d,c_d,h\in\mathbb{R}$ with $a\ne0,h>0$. Given a history $y(t)=\varphi(t) \in \mathcal{C}^2[t_0-h,t_0]$, we show that the solution can be approximated by $$\tilde{y}(t) = \sum_{k=-N}^N \gamma_k e^{\lambda_k t}, \quad N\in\mathbb{N}.$$ Each $\lambda_k$ is obtained via the inverse of $w \to (w^2+q)e^w+rw^2+sw$ for $w\in\mathbb{C}, q,r,s\in\mathbb{R}$, while the coefficients $\{\gamma_k\}$ minimize $\|\tilde{y} - \varphi\|^2$. We test our method on an example with known solution and further compare the results with solution obtained using a built-in solver. Lastly, we pose an application in pendulum-mass-spring-damper model found in \cite{kyrychko}.

Authors: YUCHEN ZHANG (Yonsei University)*; Jung-Il Choi (Yonsei University)

The level-set method is widely used for interface transport due to its ability to handle complex deformations and topological changes. However, most existing level-set solvers rely on explicit time integration, resulting in restrictive CFL conditions. We develop a direct implicit high-order level-set method that combines frozen-weight WENO5 reconstruction, a fourth-order singly diagonally implicit Runge–Kutta (SDIRK4) scheme, and a Block-TDMA solver. An adaptive local reinitialization strategy is incorporated to maintain the signed-distance property of the level-set function. Benchmark tests, including rotating-circle and Zalesak slotted-disk problems, are used to assess interface accuracy and robustness at large CFL numbers. The proposed method aims to significantly relax the time-step restriction of conventional explicit level-set solvers while maintaining accurate interface representation for large-scale multiphysics simulations.

Authors: Shu-Min Tan (National Tsing Hua University)*

We study unsupervised decomposition of sentence-level hidden states from Llama 2 7B on MMLU-Pro (~31k sentences) into semantically meaningful features, a prerequisite for capability-level analysis of LLM pruning. We report two findings. First, comparing a TopK Sparse Autoencoder against Non-negative Matrix Factorization, we find a reconstruction–interpretability tradeoff: the SAE reconstructs near-perfectly (cosine 0.9988) but is largely uninterpretable (2.27/5), while NMF reconstructs less precisely (0.9520) yet yields far more readable features (3.43/5). We attribute this to a regime mismatch with the data-abundant setting where SAE monosemanticity was established. Second, input representation matters more than dictionary size: using the raw last-layer hidden state rather than its unit-normalized projection improves subject-alignment macro-F1 from 0.240 to 0.444, while scaling the dictionary fourfold does not. Last-layer magnitude carries subject signal that normalization discards.

Authors: Ryo Yoshikawa (The University of Fukuchiyama)*; Sennosuke Watanabe (The University of Fukuchiyama)

The SIR model is one of the most well-known mathematical models for infectious diseases. It has been widely used to analyze the temporal evolution of populations that are susceptible, infected, or recovered. A cellular automaton (CA) is a dynamical system in which each cell takes a certain state that evolves based on the states of neighboring cells. Two-dimensional CAs (2D CAs) defined on an 2D integer lattice have been used to simulate various phenomena. Fuzzification extends the discrete states of a CA to continuous values. Assigning a state vector to each cell yields a vector fuzzy CA. In this study, we construct an infection model based on a 2D vector fuzzy CA and investigate its applications. The proposed model can track the temporal evolution of populations and the locations of individuals. Based on the proposed model, we examine the effects of population distribution on the spread of infection.

Authors: Seunghoon Jeong (POSTECH)*

Over the past two decades, gradient flows in the optimal transport framework have received significant attention due to their wide-ranging applications. However, a general theory for non-convex energy functionals remains largely open. In my poster, I will discuss the theory of asymptotic convergence of the McKean-Vlasov equation \begin{align*} \partial_t \mu_t = \operatorname{div} \left( \nabla \mu_t + \mu_t \nabla \left[ V + W \ast \mu_t \right] \right) \end{align*} for non-convex functionals associated with $V, W$ on $\mathcal{P}_2(\mathbb{T}^n)$, by applying Łojasiewicz-Simon theory in its tangent space. As a fundamental application, I will present the asymptotic behaviour of parabolic--elliptic Keller--Segel system \begin{align*} \begin{cases} \partial_t \rho = \nabla\!\cdot\!\big(\nabla \rho - \chi\, \rho\, \nabla c\big) + \nabla\!\cdot\!\big(\rho\,\nabla V\big),\\ (-\Delta + \alpha)\,c \;=\; \rho - \overline{\rho}, \qquad \alpha\ge 0. \end{cases} \end{align*}

Authors: Tsubota Ryosuke (Musashino University)*; Higashi Kohei (Musashino Unversity)

We study sharp lifespan estimates for a one-dimensional discrete semilinear wave equation based on a discrete model introduced by Matsuya in 2013. For compactly supported small initial data u_n^0=\varepsilon f_n, u_n^1=u_n^0+\varepsilon\delta g_n, we define the discrete lifespan T_\varepsilon as the maximal existence time before the nonlinear denominator degenerates. Our main result gives matching upper and lower bounds C_1\varepsilon^{-(p-1)/2}\le T_\varepsilon\le C_2\varepsilon^{-(p-1)/2} for sufficiently small \varepsilon>0, under suitable positivity assumptions. The proof combines the finite propagation property, discrete support estimates, convexity estimates for the nonlinear term, a discrete Kato-type iteration for the upper bound, and a contraction mapping argument based on a discrete Duhamel formula for the lower bound.

Authors: Min-Yoo Kim (KAIST)*; Yong-Jung Kim (KAIST)

Non-equilibrium steady states (NESS) are typically associated with systems driven by material exchange or external forces. In this work, we show that NESS can arise even in a closed system with Neumann boundary conditions, purely from heterogeneous anisotropic random-walk and diffusion dynamics. We consider a random walk with heterogeneous anisotropic jump probabilities $r_1(x,y)$ and $r_2(x,y)$ in the $x$- and $y$-directions. We identify a detailed-balance criterion for the associated Markov process; in particular, non-separability of $r_1/r_2$ yields a stationary state with broken detailed balance, namely, a NESS. In the diffusive limit, more general direction-discretized walks lead to diffusion equations of the form \[u_t=(k_1(m_1u)_x)_x+(k_2(m_2u)_y)_y,\] with the above case corresponding to $m_i=r_i$ and constant $k_i$. An analogous equilibrium criterion appears at the macroscopic level; non-separability of $m_1/m_2$ produces a steady state with nonzero internal flux.

Authors: Audrey Chen (Waseda University)*; Chenjian Xu (Waseda University); Kazuaki Tanaka (Waseda University)

This study focuses on approaches that directly learn solutions to differential equations using neural networks, such as PINNs and Neural Operators, and proposes the Adaptive Growth Learning Method (AGLM) as a grow-and-prune framework. AGLM progressively adds trainable correction components, enabling fast and efficient learning of solutions to differential equations. Furthermore, we simultaneously learn not only the desired true solution but also sub- and super-solutions, and by guaranteeing that the true solution lies between them, we perform rigorous error certification.

Authors: Yeva Fadhilah Ashari (Universitas Diponegoro)*; Ray Novita Yasa (Politeknik Siber dan Sandi Negara)

Graph labeling is an area of discrete mathematics that studies how labels can be assigned to graph elements while satisfying prescribed constraints. A simple graph G admits an H-covering if every edge in E(G) belongs to a subgraph of G isomorphic to a given graph H. In this case, a bijection $f:V(G) \cup E(G) \rightarrow \{1,2,\dots, |V(G)|+ |E(G)|\}$ is called an $(a, d)$-$H$-antimagic labeling if the sequence of subgraph-weight $w_f(H') = \sum_{v\in V(H')} f(v) + \sum_{e\in E(H')} f(e)$, for all subgraph H' of G that is isomorphic to H, constitutes an arithmetic progression with first term a>0 and common difference $d\geq 0$. Moreover, f is called a super (a,d)-antimagic if $f(V(G)) = \{1,2, \dots, |V(G)|\}$. In this talk, I present the structural properties concerning the existence of a super (a, d)-C3-antimagic labeling of a bipartite graph join with K1, and provide explicit constructions for various values of d. These results also hold for trees joined with K1.

Authors: Peitian Wang (The University of Osaka )*

We study the method of fundamental solutions for the Laplace Dirichlet problem in a \(d\)-dimensional ball, \(d\geq 3\). The source points are placed on a concentric sphere outside the domain and are paired radially with the boundary collocation points. By restricting the fundamental solutions to the boundary, the MFS approximation is formulated as a kernel interpolation problem on the unit sphere. Using the spherical harmonic expansion of the resulting zonal kernel, we compute its coefficients explicitly and describe the associated native space. Under the assumption that the boundary data belong to this native space, we derive an \(L^\infty\) error estimate in terms of the fill distance of the boundary nodes. The estimate gives exponential-type decay with respect to the inverse fill distance. Numerical experiments are included to illustrate the convergence behavior in several dimensions and to examine the influence of the source radius on accuracy and conditioning.