Related papers: Adjoint DSMC for nonlinear Boltzmann equation cons…
This survey explores the development of adjoint Monte Carlo methods for solving optimization problems governed by kinetic equations, a common challenge in areas such as plasma control and device design. These optimization problems are…
This study demonstrates how the adjoint-based framework traditionally used to compute gradients in PDE optimization problems can be extended to handle general constraints on the state variables. This is accomplished by constructing a…
This manuscript derives adjoint equations for the numerical solution of the spatially inhomogeneous Boltzmann equation using Direct Simulation Monte Carlo (DSMC). The formulation accounts for spatial transport and a range of boundary…
High dimensional and/or nonconvex optimization remains a challenging and important problem across a wide range of fields, such as machine learning, data assimilation, and partial differential equation (PDE) constrained optimization. Here we…
We derive an adjoint method for the Direct Simulation Monte Carlo (DSMC) method for the spatially homogeneous Boltzmann equation with a general collision law. This generalizes our previous results in [Caflisch, R., Silantyev, D. and Yang,…
We establish that nonconvex definable parametric optimization problems with possibly nonsmooth objectives, inequality constraints, conic constraint systems, and non-unique primal and dual solutions admit an adjoint state formula under a…
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…
The adjoint method is an efficient way to numerically compute gradients in optimization problems with constraints, but is only formulated to differentiable cost and constraint functions on real variables. With the introduction of complex…
Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal…
In this paper, we consider a class of constrained multiobjective optimization problems, where each objective function can be expressed by adding a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous…
This paper proposes a provably convergent multiblock ADMM for nonconvex optimization with nonlinear dynamics constraints, overcoming the divergence issue in classical extensions. We consider a class of optimization problems that arise from…
Can Monte Carlo (MC) solvers be directly used in gradient-based methods for PDE-constrained optimization problems? In these problems, a gradient of the loss function is typically presented as a product of two PDE solutions, one for the…
A range of optimization cases of two-dimensional Stefan problems, solved using a tracking-type cost-functional, is presented. A level set method is used to capture the interface between the liquid and solid phases and an immersed boundary…
Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…
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…
The nonlinear conjugate gradient methods are known to be an effective approach for standard unconstrained optimization problems especially for large-scale problems. This paper proposes a proximal nonlinear conjugate gradient method, which…
Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…
To study the nonlinear properties of complex natural phenomena, the evolution of the quantity of interest can be often represented by systems of coupled nonlinear stochastic differential equations (SDEs). These SDEs typically contain…
We propose a first-order method for solving inequality constrained optimization problems. The method is derived from our previous work [12], a modified search direction method (MSDM) that applies the singular-value decomposition of…
Adjoint based shape optimization is a powerful technique in fluid-dynamics optimization, capable of identifying an optimal shape within only dozens of design iterations. However, when extended to rarefied gas flows, the computational cost…