arXiv subjects

Chang Hou

Publications and source records attributed to Chang Hou.

6 recordsLinked to original sources

arXiv2026

Local convergence analysis of a linearized Alikhanov scheme for the time fractional sine-Gordon equation

This paper investigates the time fractional sine-Gordon equation whose solution exhibits a weak singularity of type t^{\alpha}. By means of the Alikhanov formula we derive a fully discrete, linearized scheme. Using the more general regularity assumption, we derive a sharp truncation-error bound for the fractional derivative. Furthermore, we prove a key inequality and a less restrictive stability result that is valid on general graded temporal meshes. Consequently, the temporal local convergence order is shown to be min{2, r} in H^1-seminorm, where r is the degree of grading; numerical experiments confirm that the optimal rate is already attained as soon as r = 2.

math.NA↗

arXiv2026

Pointwise-in-time convergence analysis of an Alikhanov scheme for a 2D nonlinear subdiffusion equation

In this paper, we discretize the Caputo time derivative of order \alpha \in (0,1) using the Alikhanov scheme on a quasi-graded temporal mesh, and employ the Newton linearization method to approximate the nonlinear term. This yields a linearized fully discrete scheme for the two-dimensional nonlinear time fractional subdiffusion equation with weakly singular solutions. For the purpose of conducting a pointwise convergence analysis using the comparison principle, we develop a new stability result. The global L^2-norm convergence order is min{\alpha r, 2}, and the local L^2-norm convergence order is min{r, 2} under appropriate conditions and assumptions. Ultimately, the rates of convergence demonstrated by the numerical experiments serve to validate the analytical outcomes.

math.NA↗

arXiv2025

Sensor optimization for urban wind estimation with cluster-based probabilistic framework

We propose a physics-informed machine-learned framework for sensor-based flow estimation for drone trajectories in complex urban terrain. The input is a rich set of flow simulations at many wind conditions. The outputs are velocity and uncertainty estimates for a target domain and subsequent sensor optimization for minimal uncertainty. The framework has three innovations compared to traditional flow estimators. First, the algorithm scales proportionally to the domain complexity, making it suitable for flows that are too complex for any monolithic reduced-order representation. Second, the framework extrapolates beyond the training data, e.g., smaller and larger wind velocities. Last, and perhaps most importantly, the sensor location is a free input, significantly extending the vast majority of the literature. The key enablers are (1) a Reynolds number-based scaling of the flow variables, (2) a physics-based domain decomposition, (3) a cluster-based flow representation for each subdomain, (4) an information entropy correlating the subdomains, and (5) a multi-variate probability function relating sensor input and targeted velocity estimates. This framework is demonstrated using drone flight paths through a three-building cluster as a simple example. We anticipate adaptations and applications for estimating complete cities and incorporating weather input.

cs.LG↗

arXiv2024

Machine-learned flow estimation with sparse data -- exemplified for the rooftop of a UAV vertiport

We propose a physics-informed data-driven framework for urban wind estimation. This framework validates and incorporates the Reynolds number independence for flows under various working conditions, thus allowing the extrapolation for wind conditions far beyond the training data. Another key enabler is a machine-learned non-dimensionalized manifold from snapshot data. The velocity field is modeled using a double encoder-decoder approach. The first encoder normalizes data using the oncoming wind speed, while the second encoder projects this normalized data onto the isometric feature mapping manifold. The decoders reverse this process, with $k$-nearest neighbor performing the first decoding and the second undoing the normalization. The manifold is coarse-grained by clustering to reduce the computational load for de- and encoding. The sensor-based flow estimation is based on the estimate of the oncoming wind speed and a mapping from sensor signal to the manifold latent variables. The proposed machine-learned flow estimation framework is exemplified for the flow above an Unmanned Aerial Vehicle vertiport. The wind estimation is shown to generalize well for rare wind conditions, not included in the original database.

physics.flu-dyn↗

arXiv2023

Dynamics-augmented cluster-based network model

In this study, we propose a novel data-driven reduced-order model for complex dynamics, including nonlinear, multi-attractor, multi-frequency, and multiscale behaviours. The starting point is a fully automatable cluster-based network model (CNM) (Li et al. J. Fluid Mech. vol.906, 2021, A21) which kinematically coarse-grains the state with clusters and dynamically predicts the transitions in a network model. In the proposed dynamics-augmented CNM (dCNM), the prediction error is reduced with trajectory-based clustering using the same number of centroids. The dCNM is first exemplified for the Lorenz system and then implemented for the three-dimensional sphere wake featuring periodic, quasi-periodic and chaotic flow regimes. For both plants, the dCNM significantly outperforms the CNM in resolving the multi-frequency and multiscale dynamics. This increased prediction accuracy is obtained by stratification of the state space aligned with the direction of the trajectories. Thus, the dCNM has numerous potential applications to a large spectrum of shear flows, even for complex dynamics.

physics.flu-dyn↗

arXiv2022

Trajectory-optimized cluster-based network model for the sphere wake

We propose a novel trajectory-optimized Cluster-based Network Model (tCNM) for nonlinear model order reduction from time-resolved data following Li et al. ["Cluster-based network model, " J. Fluid Mech. 906, A21 (2021)] and improving the accuracy for a given number of centroids. The starting point is k-means++ clustering which minimizes the representation error of the snapshots by their closest centroids. The dynamics is presented by 'flights' between the centroids. The proposed trajectory-optimized clustering aims to reduce the kinematic representation error further by shifting the centroids closer to the snapshot trajectory and refining state propagation with trajectory support points. Thus, curved trajectories are better resolved. The resulting tCNM is demonstrated for the sphere wake for three flow regimes, including the periodic, quasi-periodic, and chaotic dynamics. The representation error of tCNM is 5 times smaller as compared to the approximation by the closest centroid. Thus, the error at the same level as Proper Orthogonal Decomposition (POD) of same order. Yet, tCNM has distinct advantages over POD modeling: it is human interpretable by representing dynamics by a handful of coherent structures and their transitions; it shows robust dynamics by design, i.e., stable long-time behavior; and its development is fully automatable, i.e., it does not require tuneable auxiliary closure and other models.

physics.flu-dyn↗