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Hojin Kim

Publications and source records attributed to Hojin Kim.

At least 19 recordsLinked to original sources
arXiv2026

Who Should Teach? Confidence-Aware Dual-Teacher Learning for Few-Shot Node Classification on Text-Attributed Graphs

Text-Attributed Graphs (TAGs) integrate graph structures and node-associated textual attributes, and recent studies have increasingly leveraged Large Language Models (LLMs) to improve TAG learning in few-shot settings. However, existing approaches typically utilize LLM-derived information uniformly across all nodes, despite substantial variations in its reliability, while also incurring considerable monetary costs. We argue that the most appropriate source of supervision may differ across nodes, as Graph Neural Networks (GNNs) and LLMs exhibit complementary strengths in exploiting structural and semantic information, respectively. To this end, we propose CoTeach, a Confidence-aware dual-teacher learning framework that dynamically selects the more reliable teacher for each node. Experimental results demonstrate that CoTeach consistently improves few-shot node classification performance while reducing unnecessary LLM utilization and associated monetary costs.

cs.LG↗
arXiv2026

Multiscale Hypersonic Boundary Layer Reconstruction via Spectral Binning and Subdomain-wise Conditional Diffusion

We propose a multiscale probabilistic reconstruction framework for hypersonic Couette flow, where near-wall states are inferred from limited top-wall observations using conditional diffusion model. The boundary layer is divided into overlapping wall-normal subdomains, and a single height- and Mach-conditioned Elucidating Diffusion Model (EDM) is trained jointly for M=6,7,8 to sample velocity, density, pressure, and temperature fields conditioned on a top-wall boundary slice. A soft overlap inpainting strategy assembles subdomain predictions into full-volume reconstructions while maintaining inter-subdomain continuity and small-scale variability. To improve the spectral fidelity of the generated fields, we introduce a novel bounded binned spectral power (BSP) loss that preserves high-wavenumber content while remaining numerically stable across the diffusion noise schedule. Validation against direct numerical simulation data shows that the model recovers instantaneous structures, spectra, statistical profiles, correlations, and wall quantities across all training Mach numbers, while providing spatially structured uncertainty estimates. The reconstructed Mach-conditioned profiles also collapse under the Trettel-Larsson transformation, indicating consistency with compressibility scaling. These results establish the domain decomposed conditional diffusion model with a bounded binned spectral loss as an effective probabilistic surrogate for near-wall reconstruction in hypersonic wall-bounded turbulence.

physics.flu-dyn↗
arXiv2026

The Role of Hydrogen Bridging Bonds in the Shear-Thickening and Jamming of Dense Suspensions

Strong shear thickening and jamming in dense suspensions are driven by friction as particles are sheared into contact. Control over these frictional interactions can be achieved via particle shape and roughness, and also via the particles' surface chemistry and interactions with the surrounding solvent. We report on experiments with cornstarch suspensions where friction is enhanced by molecular bridging when hydrogen atoms at the ends of solvent molecules bond with hydroxyl groups on the surfaces of adjacent particles. We systematically vary the hydrogen bonding propensity by increasing the size of the backbone of the solvent molecule, from water to diols with up to 4 carbon atoms. For a fixed particle weight fraction, we find a sudden transition from strong shear thickening (in water and ethylene glycol) to shear thinning (in propanediol and butanediol). Combining data from rheology, density functional theory simulations, and fixed-rate pull tests, our results show how changes in the solvent's molecular structure affect both particle-solvent and solvent-solvent interactions, and how this can be used to tailor the shear thickening and jamming behavior of suspensions.

cond-mat.soft↗
arXiv2026

The threshold for linear independence of multiple zeta values in positive characteristic

A fundamental conjecture formulated by Thakur in 2009, which has guided significant developments in function field arithmetic, asserts that multiple zeta values (MZV's) in positive characteristic of fixed weight are linearly independent over $\mathbb{F}_q$. In this paper we settle this conjecture by determining the precise threshold for this independence. We prove that linear independence holds for all weights up to 2q, while for weight 2q+1 we establish the existence of a unique and explicit $\mathbb{F}_q$-linear relation. This result provides the first counterexample to Thakur's conjecture. Our proof relies on a new connection between MZVs and Carlitz multiple polylogarithms over $\mathbb{F}_q$, generalizing a central result of [IKLNDP24]. We also introduce a modification of the algorithm from [ND21] that yields a weight-preserving operator acting on $\mathbb{F}_q$-linear relations, providing the algebraic framework for these results.

math.NT↗
arXiv2026

Interpretable Diagnostics and Adaptive Data Assimilation for Neural ODEs via Discrete Empirical Interpolation

We present a framework that leverages the Discrete Empirical Interpolation Method (DEIM) for interpretable deep learning and dynamical system analysis. Although DEIM efficiently approximates nonlinear terms in projection-based reduced-order models (POD-ROM), its fixed interpolation points are repurposed for identifying dynamically representative spatial structures in learned models. We apply DEIM as an interpretability tool to examine the learned dynamics of a pre-trained Neural Ordinary Differential Equation (NODE) for two-dimensional vortex-merging and backward-facing step flows. DEIM trajectories reveal physically meaningful structures in NODE predictions and expose failure modes when extrapolating to unseen flow configurations. Building on this diagnostic capability, we further introduce a DEIM-guided data assimilation strategy that injects sparse, dynamically representative corrections into the NODE rollout. By allocating a limited nudging budget to DEIM-identified sampling locations, the framework significantly improves long-term stability and predictive accuracy in out-of-distribution scenarios for the two-dimensional vortex-merging flow. Additional experiments for a flow over a backward-facing step reveal regime-dependent gains, with alternative sampling strategies performing competitively as well. These results demonstrate that DEIM can serve as an interpretable diagnostic and control framework for understanding and enhancing neural differential equation models.

cs.LG↗
arXiv2026

Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systems

High-fidelity numerical simulations of chaotic, high dimensional nonlinear dynamical systems are computationally expensive, necessitating the development of efficient surrogate models. Most surrogate models for such systems are deterministic, for example when neural operators are involved. However, deterministic models often fail to capture the intrinsic distributional uncertainty of chaotic systems. This work presents a surrogate modeling formulation that leverages generative machine learning, where a deep learning diffusion model is used to probabilistically forecast turbulent flows over long horizons. We introduce a multi-step autoregressive diffusion objective that significantly enhances long-rollout stability compared to standard single-step training. To handle complex, unstructured geometries, we utilize a multi-scale graph transformer architecture incorporating diffusion preconditioning and voxel-grid pooling. More importantly, our modeling framework provides a unified platform that also predicts spatiotemporally important locations for sensor placement, either via uncertainty estimates or through an error-estimation module. Finally, the observations of the ground truth state at these dynamically varying sensor locations are assimilated using diffusion posterior sampling requiring no retraining of the surrogate model. We present our methodology on two-dimensional homogeneous and isotropic turbulence and for a flow over a backwards-facing step, demonstrating its utility in forecasting, adaptive sensor placement, and data assimilation for high dimensional chaotic systems.

cs.LG↗
arXiv2026

Improving the Accuracy of Community Detection on Signed Networks via Community Refinement and Contrastive Learning

Community detection (CD) on signed networks is crucial for understanding how positive and negative relations jointly shape network structure. However, existing CD methods often yield inconsistent communities due to noisy or conflicting edge signs. In this paper, we propose ReCon, a model-agnostic post-processing framework that progressively refines community structures through four iterative steps: (1) structural refinement, (2) boundary refinement, (3) contrastive learning, and (4) clustering. Extensive experiments on eighteen synthetic and four real-world networks using four CD methods demonstrate that ReCon consistently enhances community detection accuracy, serving as an effective and easily integrable solution for reliable CD across diverse network properties.

cs.SI↗
arXiv2026

Reasoning or Fluency? Dissecting Probabilistic Confidence in Best-of-N Selection

Probabilistic confidence metrics are increasingly adopted as proxies for reasoning quality in Best-of-N selection, under the assumption that higher confidence reflects higher reasoning fidelity. In this work, we challenge this assumption by investigating whether these metrics truly capture inter-step causal dependencies necessary for valid reasoning. We introduce three classes of inter-step causality perturbations that systematically disrupt dependencies between reasoning steps while preserving local fluency. Surprisingly, across diverse model families and reasoning benchmarks, we find that selection accuracy degrades only marginally under these disruptions. Even severe interventions, such as applying hard attention masks that directly prevent the model from attending to prior reasoning steps, do not substantially reduce selection performance. These findings provide strong evidence that current probabilistic metrics are largely insensitive to logical structure, and primarily capture surface-level fluency or in-distribution priors instead. Motivated by this gap, we propose a contrastive causality metric that explicitly isolates inter-step causal dependencies, and demonstrate that it yields more faithful output selection than existing probability-based approaches.

cs.AI↗
arXiv2025

Generalizable data-driven turbulence closure modeling on unstructured grids with differentiable physics

Differentiable physical simulators are proving to be valuable tools for developing data-driven models for computational fluid dynamics (CFD). In particular, these simulators enable end-to-end training of machine learning (ML) models embedded within CFD solvers. This paradigm enables novel algorithms which combine the generalization power and low cost of physics-based simulations with the flexibility and automation of deep learning methods. In this study, we introduce a framework for embedding deep learning models within a finite element solver for incompressible Navier-Stokes equations, specifically applying this approach to learn a subgrid-scale (SGS) closure with a graph neural network (GNN). We first demonstrate the feasibility of the approach on flow over a two-dimensional backward-facing step, using it as a proof of concept to show that solver-consistent training produces stable and physically meaningful closures. Then, we extend this to a turbulent flow over a three-dimensional backward-facing step. In this setting, the GNN-based closure not only attains low prediction errors, but also recovers key turbulence statistics and preserves multiscale turbulent structures. We further demonstrate that the closure can be identified in data-limited learning scenarios as well. Overall, the proposed end-to-end learning paradigm offers a viable pathway toward physically consistent and generalizable data-driven SGS modeling on complex and unstructured domains.

physics.flu-dyn↗
arXiv2025

Dense suspensions as trainable rheological metafluids

Memory-forming properties introduce a new paradigm to the design of adaptive materials. In dense suspensions, an adaptive response is enabled by non-Newtonian rheology; however, typical suspensions have little memory, which implies rapid cessation of any adapted behavior. Here we show how multiple adaptive responses can be achieved by designing suspensions where different stress levels trigger different memories. This is enabled by the interplay of interactions based on frictional contact and dynamic chemical bridging. These two interactions lead to novel rheology with several well-delineated shear thinning and thickening regimes, which enable stress-activated memories associated with opposite time-dependent trends. As a result, in response to different stress levels, the suspension can evolve by either softening or stiffening and is trainable, exhibiting targeted viscosity and energy dissipation with repeated low-velocity impact. Such behavior, usually associated with mechanical metamaterials, suggests that dense suspensions with multiple memories can be viewed as trainable rheological metafluids.

cond-mat.soft↗
arXiv2024

Interpretable A-posteriori Error Indication for Graph Neural Network Surrogate Models

Data-driven surrogate modeling has surged in capability in recent years with the emergence of graph neural networks (GNNs), which can operate directly on mesh-based representations of data. The goal of this work is to introduce an interpretability enhancement procedure for GNNs, with application to unstructured mesh-based fluid dynamics modeling. Given a black-box baseline GNN model, the end result is an interpretable GNN model that isolates regions in physical space, corresponding to sub-graphs, that are intrinsically linked to the forecasting task while retaining the predictive capability of the baseline. These structures identified by the interpretable GNNs are adaptively produced in the forward pass and serve as explainable links between the baseline model architecture, the optimization goal, and known problem-specific physics. Additionally, through a regularization procedure, the interpretable GNNs can also be used to identify, during inference, graph nodes that correspond to a majority of the anticipated forecasting error, adding a novel interpretable error-tagging capability to baseline models. Demonstrations are performed using unstructured flow field data sourced from flow over a backward-facing step at high Reynolds numbers, with geometry extrapolations demonstrated for ramp and wall-mounted cube configurations.

cs.LG↗
arXiv2024

Shear thickening inside elastic open-cell foams under dynamic compression

We measure the response of open-cell polyurethane foams filled with a dense suspension of fumed silica particles in polyethylene glycol at compression speeds spanning several orders of magnitude. The gradual compressive stress increase of the composite material indicates the existence of shear rate gradients in the interstitial suspension caused by wide distributions in pore sizes in the disordered foam network. The energy dissipated during compression scales with an effective internal shear rate, allowing for the collapse of three data sets for different pore-size foams. When scaled by this effective shear rate, the most pronounced energy increase coincides with the effective shear rate corresponding to the onset of shear thickening in our bulk suspension. Optical measurements of the radial deformation of the foam network and of the suspension flow under compression provide additional insight into the interaction between shear thickening fluid and foam. This optical data, combined with a simple model of a spring submerged in viscous flow, illustrates the dynamic interaction of viscous drag with foam elasticity as a function of compression rate, and identifies the foam pore size distribution as a critically important model parameter. Taken together, the stress measurements, dissipated energy, and relative motion of the fluid and the foam can be rationalized by knowing the pore size distribution and the average pore size of the foam.

cond-mat.soft↗
arXiv2024

Zagier-Hoffman's conjectures in positive characteristic

Multiples zeta values and alternating multiple zeta values in positive characteristic were introduced by Thakur and Harada as analogues of classical multiple zeta values of Euler and Euler sums. In this paper we determine all linear relations among alternating multiple zeta values and settle the main goals of these theories. As a consequence we completely establish Zagier-Hoffman's conjectures in positive characteristic formulated by Todd and Thakur which predict the dimension and an explicit basis of the span of multiple zeta values of Thakur of fixed weight.

math.NT↗
arXiv2024

Shear thickening in suspensions of particles with dynamic brush layers

Control of frictional interactions among liquid-suspended particles has led to tunable, strikingly non-Newtonian rheology via the formation of strong flow constraints as particles come into close proximity under shear. Typically, these frictional interactions have been in the form of physical contact, controllable via particle shape and surface roughness. We investigate a different route, where molecular bridging between nearby particle surfaces generates a controllable "sticky" friction. This is achieved with surface-functionalized colloidal particles capable of forming dynamic covalent bonds with telechelic polymers that comprise the suspending fluid. At low shear stress this results in particles coated with a uniform polymer brush layer. Beyond an onset stress the telechelic polymers become capable of bridging and generate shear thickening. Over the size range investigated, we find that the dynamic brush layer leads to dependence of the onset stress on particle diameter that closely follows a power law with exponent -1.76. In the shear thickening regime, we observe an enhanced dilation in measurements of the first normal stress difference and reduction in the extrapolated volume fraction required for jamming, both consistent with an effective particle friction that increases with decreasing particle diameter. These results are discussed in light of predictions for suspensions of hard spheres and of polymer-grafted particles.

cond-mat.soft↗
arXiv2024

Data-Driven Physics-Informed Neural Networks: A Digital Twin Perspective

This study explores the potential of physics-informed neural networks (PINNs) for the realization of digital twins (DT) from various perspectives. First, various adaptive sampling approaches for collocation points are investigated to verify their effectiveness in the mesh-free framework of PINNs, which allows automated construction of virtual representation without manual mesh generation. Then, the overall performance of the data-driven PINNs (DD-PINNs) framework is examined, which can utilize the acquired datasets in DT scenarios. Its scalability to more general physics is validated within parametric Navier-Stokes equations, where PINNs do not need to be retrained as the Reynolds number varies. In addition, since datasets can be often collected from different fidelity/sparsity in practice, multi-fidelity DD-PINNs are also proposed and evaluated. They show remarkable prediction performance even in the extrapolation tasks, with $42\sim62\%$ improvement over the single-fidelity approach. Finally, the uncertainty quantification performance of multi-fidelity DD-PINNs is investigated by the ensemble method to verify their potential in DT, where an accurate measure of predictive uncertainty is critical. The DD-PINN frameworks explored in this study are found to be more suitable for DT scenarios than traditional PINNs from the above perspectives, bringing engineers one step closer to seamless DT realization.

physics.flu-dyn↗
arXiv2024

Zagier-Hoffman's conjectures in positive characteristic II

Zagier-Hoffman's conjectures predict the dimension and a basis for the $\mathbb Q$-vector spaces spanned by $N$th cyclotomic multiple zeta values (MZV's) of fixed weight where $N$ is a natural number. For $N=1$ (MZV's case), half of these conjectures have been solved by the work of Terasoma, Deligne-Goncharov and Brown with the help of Zagier's identity. The other half are completely open. For $N=2$ (alternating MZV's case) and $N=3,4,8$, Deligne-Goncharov and Deligne solved the same half of these conjectures for $N$th-cyclotomic MZV's. For other values of $N$, no sharp upper bound on the dimension is known. In this paper we completely establish, for all $N$, Zagier-Hoffman's conjectures for $N$th cyclotomic multiple zeta values in positive characteristic. By working with the tower of all cyclotomic extensions, we present a proof that is uniform on $N$ and give an effective algorithm to express any cyclotomic multiple zeta value in the chosen basis. This generalizes all previous work on these conjectures for MZV's and alternating MZV's in positive characteristic.

math.NT↗
arXiv2023

Hopf algebras and alternating multiple zeta values in positive characteristic

In \cite{IKLNDP23} we presented a systematic study of algebra structures of multiple zeta values in positive characteristic introduced by Thakur as analogues of classical multiple zeta values of Euler. In this paper we construct algebra and Hopf algebra structures of alternating multiple zeta values introduced by Harada, extending our previous work. Our results could be considered as an analogue of those of Hoffman \cite{Hof00} and Racinet \cite{Rac02} in the classical setting. The proof is based on two new ingredients: the first one is a direct and explicit construction of the shuffle Hopf algebra structure, and the second one is the notion of horizontal maps.

math.NT↗