相关论文: Accurate gradient computations for shape optimizat…
The optimization of the latents and parameters of diffusion models with respect to some differentiable metric defined on the output of the model is a challenging and complex problem. The sampling for diffusion models is done by solving…
This work focuses on numerically solving a shape identification problem related to advection-diffusion processes with space-dependent coefficients using shape optimization techniques. Two boundary-type cost functionals are considered, and…
In this article we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since…
Real-time estimations of temperature distributions and geometric configurations are important to energy efficient buildings and the development of smarter cities. In this paper we formulate a gradient-based estimation algorithm capable of…
Sensitivity analysis plays an important role in searching for constitutive parameters (e.g. permeability) subsurface flow simulations. The mathematics behind is to solve a dynamic constrained optimization problem. Traditional methods like…
The ability to differentiate through optimization problems has unlocked numerous applications, from optimization-based layers in machine learning models to complex design problems formulated as bilevel programs. It has been shown that…
Aerodynamic design optimization is an important problem in aircraft design that depends on the interplay between a numerical optimizer and a high-fidelity flow physics solver. Derivative-based, first and (quasi) second order, optimization…
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…
The conjugate gradient method is a widely used algorithm for the numerical solution of a system of linear equations. It is particularly attractive because it allows one to take advantage of sparse matrices and produces (in case of infinite…
For a given {\it misfit function}, a specified optimality measure of a model, its gradient describes the manner in which one may alter properties of the system to march towards a stationary point. The adjoint method, arising from…
Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics. Automatic differentiation offers an algorithmic way to efficiently evaluate these derivatives from computer programs that execute relevant…
This work proposes a novel shape optimization framework for geometric inverse problems governed by the advection--diffusion equation, based on the coupled complex boundary method (CCBM). Building on recent developments [Afr22, Rab23, Rab25,…
Two of the most important areas in computational finance: Greeks and, respectively, calibration, are based on efficient and accurate computation of a large number of sensitivities. This paper gives an overview of adjoint and automatic…
We introduce Adjoint Sampling, a highly scalable and efficient algorithm for learning diffusion processes that sample from unnormalized densities, or energy functions. It is the first on-policy approach that allows significantly more…
This study presents an efficient and accurate discrete adjoint gas-kinetic scheme (GKS) for sensitivity analysis and aerodynamic shape optimization in continuum flow regimes. Developed using the backward mode of algorithmic differentiation…
We propose a deterministic adjoint matching framework that formulates human preference alignment for flow-based generative models as an optimal control problem over velocity fields. One can directly regress the control toward a…
Stellarators are a promising route to steady-state fusion power. However, to achieve the required confinement, the magnetic geometry must be highly optimized. This optimization requires navigating high-dimensional spaces, often…
In this paper we study an abstract framework for computing shape derivatives of functionals subject to PDE constraints. We revisit the Lagrangian approach using the implicit function theorem in an abstract setting tailored for applications…
Gradient-based optimization of engineering designs is limited by non-differentiable components in the typical computer-aided engineering (CAE) workflow, which calculates performance metrics from design parameters. While gradient-based…
A variety of shooting methods for computing fully discrete time-periodic solutions of partial differential equations, including Newton-Krylov and optimization-based methods, are discussed and used to determine the periodic, compressible,…