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We develop a rigorous asymptotic derivation for two mathematical models of water waves that capture the full nonlinearity of the Euler equations up to quadratic and cubic interactions, respectively. Specifically, letting epsilon denote an…
This study investigates the effects of geometric model reduction on blood flow simulations in the patient-specific descending aorta, followed by speed-accuracy trade-off analysis using 3D simulations. We demonstrate how wall shear stresses…
We propose Dirichlet Winding Reconstruction (DiWR), a robust method for reconstructing watertight surfaces from unoriented point clouds with non-uniform sampling, noise, and outliers. Our method uses the generalized winding number (GWN)…
Meshless methods are commonly used to determine numerical solutions to partial differential equations (PDEs) for problems involving free surfaces and/or complex geometries, approximating spatial derivatives at collocation points via local…
We propose a geometry constrained network, termed GC-Net, for weakly supervised object localization (WSOL). GC-Net consists of three modules: a detector, a generator and a classifier. The detector predicts the object location defined by a…
In this paper, a new algorithm based on differential geometry viewpoint to solve the 3D rotating Navier-Stokes equations with complex Boundary is proposed, which is called Bi-parallel algorithm. For xample, it can be applied to passage flow…
The idea that symmetries simplify or reduce the complexity of a system has been remarkably fruitful in physics, and especially in quantum mechanics. On a mathematical level, symmetry groups single out a certain structure in the Hilbert…
Single-Hessian Gaussian wavepacket dynamics (GWD) significantly reduces the computational burden of Heller's local harmonic GWD, while maintaining comparable accuracy in approximating vibronic spectra. Here, we provide a new, symplectic…
A unidirectional reduction of the deep-water surface gravity wave problem is derived in physical space using real variables. By employing a near-identity canonical transformation, cubic interactions are eliminated from the Hamiltonian, with…
In many modern data sets, High dimension low sample size (HDLSS) data is prevalent in many fields of studies. There has been an increased focus recently on using machine learning and statistical methods to mine valuable information out of…
Computational scientists have investigated swimming performance across a multitude of different systems for decades. Most models depend on numerous model parameters and performance is sensitive to those parameters. In this paper, parameter…
The probabilistic velocity obstacle (PVO) extends the concept of velocity obstacle (VO) to work in uncertain dynamic environments. In this paper, we show how a robust model predictive control (MPC) with PVO constraints under non-parametric…
In recent years, applications such as real-time simulations, autonomous systems, and video games increasingly demand the processing of complex geometric models under stringent time constraints. Traditional geometric algorithms, including…
Establishing a precise connection between imaged intensity and the incident wavefront is essential for emerging applications in adaptive optics, holography, computational microscopy, and non-line-of-sight imaging. While prior work has shown…
This contribution describes the implementation of a data--driven shape optimization pipeline in a naval architecture application. We adopt reduced order models (ROMs) in order to improve the efficiency of the overall optimization, keeping a…
Optimization problems constrained by high-dimensional, time-dependent partial differential equations require repeated forward and sensitivity solves, making high-fidelity optimization computationally prohibitive in many-query design and…
In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the…
In this paper we present a shape optimization scheme which utilizes the alternating direction method of multipliers (ADMM) to approximate a direction of steepest descent in $W^{1,\infty}$. The followed strategy is a combination of the…
This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…
The availability of low cost sensors has led to an unprecedented growth in the volume of spatial data. However, the time required to evaluate even simple spatial queries over large data sets greatly hampers our ability to interactively…