Related papers: Adjoint-based optimization of two-dimensional Stef…
We present a strategy for the numerical solution of convection-coupled phase-transition problems, with focus on solidification and melting. We solve for the temperature and flow fields over time. The position of the phase-change interface…
A continuous system of moment equations is introduced that models the transverse dynamics of a beam of charged particles as it passes through an arbitrary lattice of quadrupoles and solenoids in the presence of self-fields. Then, figures of…
We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…
A brief review of the Stefan problem of solidification from a mixture, and its main numerical solution methods is given. Simulation of this problem in 2D or 3D is most practically done on a regular grid, where a sharp solid-liquid interface…
We develop a continuous adjoint formulation and implementation for controlling the deformation of clean, neutrally buoyant droplets in Stokes flow through farfield velocity boundary conditions. The focus is on dynamics where surface tension…
We present a numerical method for the solution of interfacial growth governed by the Stefan model coupled with incompressible fluid flow. An algorithm is presented which takes special care to enforce sharp interfacial conditions on the…
The paper is concerned with a node-based, gradient-driven, continuous adjoint two-phase flow procedure to optimize the shapes of free-floating vessels and discusses three topics. First, we aim to convey that elements of a Cahn-Hilliard…
Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…
We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to…
This paper applies a discrete adjoint gradient computation method for a multi-class traffic flow model on road networks. Vehicle classes are characterized by their specific velocity functions, which depend on the total traffic density,…
Bilevel optimization enjoys a wide range of applications in emerging machine learning and signal processing problems such as hyper-parameter optimization, image reconstruction, meta-learning, adversarial training, and reinforcement…
This work focuses on the numerical assessment of the accuracy of an adjoint-based gradient in the perspective of variational data assimilation and parameter identification in glaciology. Using noisy synthetic data, we quantify the ability…
Applications for kinetic equations such as optimal design and inverse problems often involve finding unknown parameters through gradient-based optimization algorithms. Based on the adjoint-state method, we derive two different frameworks…
Optimizing shapes and topology of physical devices is crucial for both scientific and technological advancements, given its wide-ranging implications across numerous industries and research areas. Innovations in shape and topology…
In this work, we investigate the use of data-driven equation discovery for dynamical systems to model and forecast continuous-time dynamics of unconstrained optimization problems. To avoid expensive evaluations of the objective function and…
This work deals with the one-dimensional Stefan problem with a general time-dependent boundary condition at the fixed boundary. Stochastic solutions are obtained using discrete random walks, and the results are compared with analytic…
A simulation framework based on the level-set and the immersed boundary methods (LS-IBM) has been developed for reactive transport problems in porous media involving a moving solid-fluid interface. The interface movement due to surface…
In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…
In this paper we present a topology optimization technique applicable to a broad range of flow design problems. We propose also a discrete adjoint formulation effective for a wide class of Lattice Boltzmann Methods (LBM). This adjoint…
In this paper we study a system of advection-diffusion equations in a bulk domain coupled to an advection-diffusion equation on an embedded surface. Such systems of coupled partial differential equations arise in, for example, the modeling…