arXiv subjects

Shengqi Zhang

Publications and source records attributed to Shengqi Zhang.

8 recordsLinked to original sources

arXiv2026

Mode-realigned pointwise interpolation (MRPWI) for efficient POD-Galerkin parametric reduced-order models

As a cornerstone of reduced-order modeling, the POD-Galerkin framework has garnered widespread attention and remains one of the most widely adopted approaches. Constructing POD-Galerkin PROMs involves integrating this framework with advanced interpolation techniques to obtain POD modes at target (unseen) parameters. While Grassmann manifold interpolation (GMI) serves as an accurate baseline, mode-realigned pointwise interpolation (MRPWI) is proposed to develop highly efficient PROMs that maintain comparable accuracy. Notably, the MRPWI employs a two-step mode realignment procedure, consisting of sign alignment and rotation alignment, to effectively synchronize the POD modes. Demonstration and evaluation of the constructed POD-Galerkin PROMs are conducted by examining flow over a cylinder. These models exhibit high fidelity in comparison to direct numerical simulation and standard POD-Galerkin ROMs. PROMs constructed via MRPWI achieve accuracy comparable to those using GMI, while providing significantly higher computational efficiency.

math.NA↗

arXiv2026

LawMind: A Law-Driven Paradigm for Discovering Analytical Solutions to Partial Differential Equations

Partial differential equations (PDEs) encode fundamental physical laws, yet closed-form analytical solutions for many important equations remain unknown and typically require substantial human insight to derive. Existing numerical, physics-informed, and data-driven approaches approximate solutions from data rather than systematically deriving symbolic expressions directly from governing equations. Here we introduce LawMind, a law-driven symbolic discovery framework that autonomously constructs closed-form solutions from PDEs and their associated conditions without relying on data or supervision. By integrating structured symbolic exploration with physics-constrained evaluation, LawMind progressively assembles valid solution components guided solely by governing laws. Evaluated on 100 benchmark PDEs drawn from two authoritative handbooks, LawMind successfully recovers closed-form analytical solutions for all cases. Beyond known solutions, LawMind further discovers previously unreported closed-form solutions to both linear and nonlinear PDEs. These findings establish a computational paradigm in which governing equations alone drive autonomous symbolic discovery, enabling the systematic derivation of analytical PDE solutions.

cs.SC↗

arXiv2025

SegEarth-OV3: Exploring SAM 3 for Open-Vocabulary Semantic Segmentation in Remote Sensing Images

Most existing methods for training-free open-vocabulary semantic segmentation are based on CLIP. While these approaches have made progress, they often face challenges in precise localization or require complex pipelines to combine separate modules, especially in remote sensing scenarios where numerous dense and small targets are present. Recently, Segment Anything Model 3 (SAM 3) was proposed, unifying segmentation and recognition in a promptable framework. In this paper, we present a comprehensive exploration of applying SAM 3 to the remote sensing open-vocabulary tasks (i.e., 2D semantic segmentation, change detection, and 3D semantic segmentation) without any training. First, we implement a mask fusion strategy that combines the outputs from SAM 3's semantic segmentation head and the Transformer decoder (instance head). This allows us to leverage the strengths of both heads for better land coverage. Second, we utilize the presence score from the presence head to filter out categories that do not exist in the scene, reducing false positives caused by the vast vocabulary sizes and patch-level processing in geospatial scenes. Furthermore, we extend our method to open-vocabulary change detection by a joint instance- and pixel-level verification strategy built directly upon our fused logits. We evaluate our method on extensive remote sensing datasets and tasks, including 20 segmentation datasets, 3 change detection datasets, and a 3D segmentation dataset. Experiments show that our method achieves promising performance, demonstrating the potential of SAM 3 for remote sensing open-vocabulary tasks. Our code is released at https://github.com/earth-insights/SegEarth-OV-3.

cs.CV↗

arXiv2025

Isotropic extension of first-order wave equations

The anisotropy of many one-dimensional and first-order-in-time (T$^1$) scalar wave equations (e.g., Korteweg-de Vries and Camassa-Holm) limits their physical completeness and applicability to bidirectional/high-dimensional systems. We define the T$^n\Lambda^m$ isotropic extension consisting of temporal order elevation and spatial tensorization, which is the only possible approach to eliminate anisotropy while preserving original solutions. Our analysis finds that the Burgers equation exhibits T$^{\mathbb{N}_+}\Lambda^{2\mathbb{N}+1}$ extensibility and the Korteweg-de Vries (KdV) equation exhibits the T$^{2\mathbb{N}_+}\Lambda^{2\mathbb{N}}$ extensibility. The T$^2\Lambda^0$ extension of the KdV equation leads to the corresponding isotropic T$^2$ equation (KdV$^2$) for shallow water dynamics, which is physically more complete and suitable for 2D generalization. In addition to inheriting all KdV solutions and conservation laws, the KdV$^2$ equation also provides linearly stable corrections to the Boussinesq equation. In contrast, the KdV-Burgers equation is inherently anisotropic as it fails to exhibit any T$^n\Lambda^m$ extensibility.

nlin.PS↗

arXiv2025

Flow reorganization and transport enhancement in two-dimensional horizontal convection near a density extremum

Horizontal convection serves as a canonical model for geophysical and industrial flows. While the Oberbeck-Boussinesq approximation is well established, the impact of a nonlinear equation of state, specifically the density extremum of water near $4^\circ\mathrm{C}$, remains underexplored. Here we investigate this effect using two-dimensional direct numerical simulations over the Rayleigh number range $10^6 \le Ra \le 5\times 10^{10}$. We examine four configurations, contrasting extremum (EXT) and monotonic (MON) buoyancy boundary conditions against linear (LENT) and nonlinear (NELT) equations of state. Our results reveal that the EXT-NELT case undergoes a pronounced reorganization of the large-scale flow, evolving from a bicellular structure to a single-roll circulation driven by central `mixing plumes'. This reorganization manifests as transitional anomalies in the $Re$ scaling, while the emergence of full-depth plumes alters the heat transport mechanism. Consequently, distinct from the Rossby scaling ($Nu \sim Ra^{1/5}$) observed in the reference cases, the EXT-NELT case exhibits an enhanced heat transport scaling ranging from $Nu \sim Ra^{1/4}$ to $Nu \sim Ra^{1/3}$. To interpret this behaviour, we examine the total energy budget and identify an additional potential-energy transfer term, $\Phi_{i2}$, arising from the nonlinear equation of state. The scaling argument suggests that the magnitude of this contribution is controlled by the characteristic plume height ($\hat{z}$). Specifically, when plumes penetrate the entire cavity depth ($\hat{z} \sim H$), as observed in the EXT-NELT case, the global kinetic energy dissipation is no longer described by the standard OB HC energy closure alone. The resulting model captures the main trends of the numerical data and provides a possible energy budget interpretation of the enhanced transport observed in this two-dimensional configuration.

physics.flu-dyn↗

arXiv2022

Study of a droplet breakup process in decaying homogeneous isotropic turbulence based on the phase-field DUGKS approach

The breakup of a spherical droplet in a decaying homogeneous isotropic turbulence is studied by solving the Cahn-Hilliard-Navier-Stokes equations, using the discrete unified gas kinetic scheme combined with the free-energy-based phase-field model. We focus on the combined effects of turbulence and surface tension on the breakup process by assuming that the two fluid phases have the same density and same viscosity. The key physical parameters of the system include the volume fraction (6.54%), the initial Weber number (21.7), and the initial Taylor microscale Reynolds number (58). Three distinct stages of droplet evolution are identified, namely, the deformation stage when the initially spherical droplet evolves into an irregular geometric shape with complex structures, the breakup stage when many daughter droplets are formed, and the restoration stage when the droplets relax towards spherical shape. These three stages are analyzed systematically from several perspectives: (1) a geometric perspective concerning the maximum equivalent diameter, the total number of droplets, total interface area, and probability distribution of droplet diameters, (2) a dynamic perspective concerning the evolution of local velocity and vorticity at the fluid-fluid interface, (3) a global perspective concerning the evolution of average kinetic energy / dissipation rate and their Fourier spectra, (4) spherical harmonics based energetics concerning simultaneous transfer of kinetic energy across different length scales and different radii relative to initial droplet center, and (5) the time evolution of global kinetic energy and free energy of the system.

physics.flu-dyn↗

arXiv2022

Enhancing large-scale motions and turbulent transport in rotating plane Poiseuille flow

Based on the properties of large-scale plume currents, an injection/suction control strategy is introduced to enhance the strength of plume currents and the turbulent transport of passive scalar in rotating plane Poiseuille flow. The control keeps the classical non-penetrative condition on the stable side, and prescribes spanwise varying wall-normal velocity on the unstable side. Direct numerical simulations show that at medium rotation numbers, very weak injection/suction (the root-mean-square velocity on the controlled side is below $1\%$ of the bulk mean velocity) with properly distributed slots could significantly enhance the large-scale plume currents which have the same spatial distribution as the injection slots. In addition, if the distance between plume currents are increased, the turbulent transport efficiency can be promoted. Therefore, taking the strength and transport efficiency into account, the distance between injection slots should be slightly larger than the intrinsic distance between plume currents to achieve maximum enhancement of turbulent transport. For comparison, the control with non-penetrative condition on the unstable side and injection/suction on the stable side is also examined with simulations. It is found that the injection/suction on the stable side has much weaker influence compared with that on the unstable side. This is because that plumes are generated on the unstable side, and that controlling the origin of plumes is more effective.

physics.flu-dyn↗

arXiv2020

Perturbation analysis of baroclinic torque in low-Mach-number flows

In this paper, we propse a series expansion of the baroclinic torque in low-Mach-number flows, so that the accuracy and universality of any buoyancy term could be examined analytically, and new types of buoyancy terms could be constructed and validated. We first demonstrate that the purpose of introducing a buoyancy term is to approximate the baroclinic torque, and straightforwardly the accuracy of any buoyancy term could be measured by the deviation of its curl from the baroclinic torque. Then a regular perturbation method is introduced for the elliptic equation of the hydrodynamic pressure in low-Mach-number flows, resulting in a sequence of Poisson equations, whose solutions lead to the series representation of the baroclinic torque and the new types of buoyancy terms. With the error definition of buoyancy terms and the series representation of the baroclinic torque, the classical gravitational and centrifugal buoyancy term, as well as some other previously proposed buoyancy terms are revisited. Finally, numerical simulations confirm that, with a decreasing density variation or an increasing order of our newly proposed buoyancy term, the simplified equations with one of the new types of buoyancy terms can converge to the original low-Mach-number equations.

physics.flu-dyn↗