相关论文: Active Contour with A Tangential Component

Although gradient descent (GD) almost always escapes saddle points asymptotically [Lee et al., 2016], this paper shows that even with fairly natural random initialization schemes and non-pathological functions, GD can be significantly…

In this paper we study the dynamics of a fast-slow Fokker-Planck partial differential equation (PDE) viewed as the evolution equation for the density of a multiscale planar stochastic differential equation (SDE). Our key focus is on the…

Recent theoretical research proposes that computational complexity can be seen as an ultimate constraint that allows for open-ended biological evolution on finite static fitness landscapes. Whereas on easy fitness landscapes, evolution will…

Coordinating the design of sampling and sparse-dense matrix multiplication (SpMM) is crucial for accelerating graph neural networks (GNNs). However, due to irrational sampling strategies, existing methods face a trade-off between accuracy…

In this paper, an important discovery has been found for nonconforming immersed finite element (IFE) methods using the integral values on edges as degrees of freedom for solving elliptic interface problems. We show that those IFE methods…

This paper presents the design and analysis of the extremum seeking for static maps with input passed through a partial differential equation (PDE) of the diffusion type defined on a time-varying spatial domain whose boundary position is…

Parabolic mean curvature flow-driven active contour models (PMCF-ACMs) are widely used for image segmentation, yet they suffer severe degradation under high-intensity noise because gradient-descent evolutions exhibit the well-known zig-zag…

We analyze two fully time-discrete numerical schemes for the incompressible Navier-Stokes equations posed on evolving surfaces in $\mathbb{R}^3$ with prescribed normal velocity using the evolving surface finite element method (ESFEM). We…

In this work, Entropy-Stable (ES) schemes are formulated for the multicomponent compressible Euler equations. Entropy-conservative (EC) and ES fluxes are derived. Particular attention is paid to the limit case of zero partial densities…

Current state-of-the-art methods of image classification using convolutional neural networks are often constrained by both latency and power consumption. This places a limit on the devices, particularly low-power edge devices, that can…

Sparse deep neural networks have proven to be efficient for predictive model building in large-scale studies. Although several works have studied theoretical and numerical properties of sparse neural architectures, they have primarily…

For the simulation of rectilinearly moving conductors across a magnetic field, the Galer-kin finite element method (GFEM) is generally employed. The inherent instability of GFEM is very often addressed by employing Streamline…

Edge detection is a fundamental image analysis task that underpins numerous high-level vision applications. Recent advances in Transformer architectures have significantly improved edge quality by capturing long-range dependencies, but this…

A theoretical performance analysis of the $(\mu/\mu_I,\lambda)$-$\sigma$-Self-Adaptation Evolution Strategy ($\sigma$SA-ES) is presented considering a conically constrained problem. Infeasible offspring are repaired using projection onto…

We analyze the variance of stochastic gradients along negative curvature directions in certain non-convex machine learning models and show that stochastic gradients exhibit a strong component along these directions. Furthermore, we show…

We address surface gradient flows which allow for energy dissipation by evolving the surface and a scalar quantity on it, simultaneously. A proper choice of the time derivative and the gauge of surface independence guarantees energy…

In this paper, we prove convergence rates for time discretisation schemes for semi-linear stochastic evolution equations with additive or multiplicative Gaussian noise, where the leading operator $A$ is the generator of a strongly…

Primal-dual gradient dynamics that find saddle points of a Lagrangian have been widely employed for handling constrained optimization problems. Building on existing methods, we extend the augmented primal-dual gradient dynamics (Aug-PDGD)…

In the early-stage design of advanced electronic packages, designers face a critical trade-off between simulation fidelity and computational turnaround time. Conventional early-stage methodologies typically achieve speed by relying on…

This is the second part to our companion paper. The novel method to quantify artificial dissipation proposed in Part 1 is further applied in turbulent channel flow at $\mathrm{Re_\tau}=180$ using various subgrid-scale models, with an…