Jeongin Kim | Searcharxiv

arXiv2026

Wave scattering around a submerged vertical permeable breakwater

An analytical solution for a wave velocity field scattered by a submerged permeable vertical plate-type breakwater under the linear monochromatic wave is obtained and the applications of the solution are presented. The water has an infinite depth, and the flow is assumed to be incompressible, inviscid, and irrotational, which leads to the two-dimensional potential wave theory. The permeable breakwater vertically occupies a finite interval beneath the water surface and the water flows through the breakwater. The resulting nonlinear boundary condition is resolved by the perturbation method with a small parameter representing the permeability. The solution was expanded up to the first order so that the leading-order term can represent the wave scattered by the impermeable breakwater and the first-order term can give the correction to the solution considering the wave scattered by the permeable breakwater. Each order of the wave velocity potential is determined by a reduction method and this leads to the homogeneous Riemann-Hilbert problem for the leading-order problem and the nonhomogeneous Riemann-Hilbert problem for the first-order problem. \rev{The effects} of wavelength, breakwater length, and breakwater permeability conditions on the reflection and transmission coefficients are discussed in detail as an illustrative example of the application of the solution. \rev{An exact energy identity is also derived; it verifies the first-order solution and yields a closed-form boundary $\varepsilon_{\max}(kb)$ of the validity range of the expansion.

physics.flu-dyn↗

arXiv2025

Diffusion-Driven Two-Stage Active Learning for Low-Budget Semantic Segmentation

Semantic segmentation demands dense pixel-level annotations, which can be prohibitively expensive - especially under extremely constrained labeling budgets. In this paper, we address the problem of low-budget active learning for semantic segmentation by proposing a novel two-stage selection pipeline. Our approach leverages a pre-trained diffusion model to extract rich multi-scale features that capture both global structure and fine details. In the first stage, we perform a hierarchical, representation-based candidate selection by first choosing a small subset of representative pixels per image using MaxHerding, and then refining these into a diverse global pool. In the second stage, we compute an entropy-augmented disagreement score (eDALD) over noisy multi-scale diffusion features to capture both epistemic uncertainty and prediction confidence, selecting the most informative pixels for annotation. This decoupling of diversity and uncertainty lets us achieve high segmentation accuracy with only a tiny fraction of labeled pixels. Extensive experiments on four benchmarks (CamVid, ADE-Bed, Cityscapes, and Pascal-Context) demonstrate that our method significantly outperforms existing baselines under extreme pixel-budget regimes. Our code is available at https://github.com/jn-kim/two-stage-edald.

cs.CV↗