Related papers: Computing Geodesic Paths Encoding a Curvature Prio…
We show how to speed up the computation of isomorphisms of hyperelliptic curves by using covariants. We also obtain new theoretical and practical results concerning models of these curves over their field of moduli.
For fourth-order geometric evolution equations for planar curves with the dissipation of the bending energy, including the Willmore and the Helfrich flows, we consider a numerical approach. In this study, we construct a structure-preserving…
The paper presents a new method for shape and topology optimization based on an efficient and scalable boundary integral formulation for elasticity. To optimize topology, our approach uses iterative extraction of isosurfaces of a…
We propose novel connections between several neural network architectures and viscosity solutions of some Hamilton--Jacobi (HJ) partial differential equations (PDEs) whose Hamiltonian is convex and only depends on the spatial gradient of…
Popular methods for identifying transition paths between energy minima, such as the nudged elastic band and string methods, typically do not incorporate potential energy curvature information, leading to slow relaxation to the minimum…
Stochastic optimal principle leads to the resolution of a partial differential equation (PDE), namely the Hamilton-Jacobi-Bellman (HJB) equation. In general, this equation cannot be solved analytically, thus numerical algorithms are the…
In recent algorithms that use deformation in order to compute the number of points on varieties over a finite field, certain differential equations of matrices over p-adic fields emerge. We present a novel strategy to solve this kind of…
A unified method for extracting geometric shape features from binary image data using a steady state partial differential equation (PDE) system as a boundary value problem is presented in this paper. The PDE and functions are formulated to…
We propose notions of minimax and viscosity solutions for a class of fully nonlinear path-dependent PDEs with nonlinear, monotone, and coercive operators on Hilbert space. Our main result is well-posedness (existence, uniqueness, and…
We address in this paper the study of a geometric evolution, corresponding to a curvature which is non-local and singular at the origin. The curvature represents the first variation of the energy recently proposed as a variant of the…
We propose an energy-optimized invariant energy quadratization method to solve the gradient flow models in this paper, which requires only one linear energy-optimized step to correct the auxiliary variables on each time step. In addition to…
In this article, a notion of viscosity solutions is introduced for first order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent evolution equations in Hilbert space. We…
In this work, an adaptive edge element method is developed for an H(curl)-elliptic constrained optimal control problem. We use the lowest-order Nedelec's edge elements of first family and the piecewise (element-wise) constant functions to…
In this paper, we propose an efficient continuation method for locating multiple power flow solutions. We adopt the holomorphic embedding technique to represent solution curves as holomorphic functions in the complex plane. The…
A finite element based computational scheme is developed and employed to assess a duality based variational approach to the solution of the linear heat and transport PDE in one space dimension and time, and the nonlinear system of ODEs of…
Topological features capture global geometric structure in imaging data, but practical adoption in deep learning requires both computational efficiency and differentiability. We present optimized GPU kernels for the Euler Characteristic…
The purpose of this paper is to describe the numerical solution of the Hamilton-Jacobi-Bellman (HJB) for an optimal control problem for quantum spin systems. This HJB equation is a first order nonlinear partial differential equation defined…
The same type of objects in different images may vary in their shapes because of rigid and non-rigid shape deformations, occluding foreground as well as cluttered background. The problem concerned in this work is the shape extraction in…
Computing shortest paths for curvature-constrained Dubins vehicles on the unit sphere is fundamental to many engineering applications, including long-range flight planning, persistent surveillance patterns, and global routing problems where…
Based on a local approximation of the Riemannian distance on a manifold by a computationally cheap dissimilarity measure, a time discrete geodesic calculus is developed, and applications to shape space are explored. The dissimilarity…