Related papers: Fireshape: a shape optimization toolbox for Firedr…
Shape formation has been recently studied in distributed systems of programmable particles. In this paper we consider the shape recovery problem of restoring the shape when $f$ of the $n$ particles have crashed. We focus on the basic line…
We consider the shape optimization of flow fields for electrochemical cells. Our goal is to improve the cell by modifying the shape of its flow field. To do so, we introduce simulation models of the flow field with and without the porous…
We have developed a simulation technique that uses non-linear finite element analysis and elastic fracture mechanics to compute physically plausible motion for three-dimensional, solid objects as they break, crack, or tear. When these…
Manipulating the shape of a liquid droplet is essential for a wide range of applications in medicine and industry. However, existing methods are typically limited to generating simple shapes, such as ellipses, or rely on predefined…
This paper presents a piecewise convexification method to approximate the whole approximate optimal solution set of non-convex optimization problems with box constraints. In the process of box division, we first classify the sub-boxes and…
The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated reassemblage of finite element matrices for nonlinear PDEs is…
We propose a new method to design adaptation algorithms that guarantee a certain prescribed level of performance and are applicable to systems with nonconvex parameterization. The main idea behind the method is, given the desired…
The fireworks algorithm is an optimization algorithm for simulating the explosion phenomenon of fireworks. Because of its fast convergence and high precision, it is widely used in pattern recognition, optimal scheduling, and other fields.…
We present a novel variational quantum framework for linear partial differential equation (PDE) constrained optimization problems. Such problems arise in many scientific and engineering domains. For instance, in aerodynamics, the PDE…
In atomistic simulations, pseudo-dynamics relaxation schemes often exhibit better performance and accuracy in finding local minima than line-search-based descent algorithms like steepest descent or conjugate gradient. Here, an improved…
The design of interplanetary trajectories often involves a preliminary search for options later refined/assembled into one final trajectory. It is this broad search that, often being intractable, inspires the international event called…
ParticLS (\emph{Partic}le \emph{L}evel \emph{S}ets) is a software library that implements the discrete element method (DEM) and meshfree methods. ParticLS tracks the interaction between individual particles whose geometries are defined by…
Interconnection and damping assignment passivity-based control scheme has been used to stabilize many physical systems such as underactuated mechanical systems through total energy shaping. In this method, some partial differential…
A robust and fast solver for the fractional differential equation (FDEs) involving the Riesz fractional derivative is developed using an adaptive finite element method on non-uniform meshes. It is based on the utilization of hierarchical…
This work introduces ParAMS -- a versatile Python package that aims to make parameterization workflows in computational chemistry and physics more accessible, transparent and reproducible. We demonstrate how ParAMS facilitates the parameter…
Shapley values are widely used to explain black-box models, but they are costly to calculate because they require many model evaluations. We introduce FastSHAP, a method for estimating Shapley values in a single forward pass using a learned…
We propose a general framework for differentiating shapes represented in binary images with respect to their parameters. This framework functions as an automatic differentiation tool for shape parameters, generating both binary density maps…
Partial differential equations can be solved on general polygonal and polyhedral meshes, through Polytopal Element Methods (PEMs). Unfortunately, the relation between geometry and analysis is still unknown and subject to ongoing research in…
FIRE is a program which performs integration-by-parts (IBP) reduction of Feynman integrals. Originally, the C++ version of FIRE relies on the computer algebra system Fermat by Robert Lewis to simplify rational functions. We present an…
This work studies a variational formulation and numerical solution of a regularized morphoelasticity problem of shape evolution. The foundation of our analysis is based on the governing equations of linear elasticity, extended to account…