Related papers: A Memory Efficient Adjoint Method to Enable Billio…
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 parallel simulation, convergence and parallelism are often seen as inherently conflicting objectives. Improved parallelism typically entails lighter local computation and weaker coupling, which unavoidably slow the global convergence.…
The present paper aims at providing a numerical strategy to deal with PDE-constrained optimization problems solved with the adjoint method. It is done through out a unified formulation of the constraint PDE and the adjoint model. The…
This paper presents a novel adjoint solver for differentiable fluid simulation based on bidirectional flow maps. Our key observation is that the forward fluid solver and its corresponding backward, adjoint solver share the same flow map as…
In gradient-based time domain topology optimization, design sensitivity analysis (DSA) of the dynamic response is essential, and requires high computational cost to directly differentiate, especially for high-order dynamic system. To…
Existing customization methods require access to multiple reference examples to align pre-trained diffusion probabilistic models (DPMs) with user-provided concepts. This paper aims to address the challenge of DPM customization when the only…
The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory computation of gradients…
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…
The self-join finds all objects in a dataset within a threshold of each other defined by a similarity metric. As such, the self-join is a building block for the field of databases and data mining, and is employed in Big Data applications.…
First-order optimization methods, such as stochastic gradient descent (SGD) and its variants, are widely used in machine learning applications due to their simplicity and low per-iteration costs. However, they often require larger numbers…
Adjoint methods enable the accurate calculation of the sensitivities of a quantity of interest. The sensitivity is obtained by solving the adjoint system, which can be derived by continuous or discrete adjoint strategies. In acoustic wave…
Due to critical environmental issues, the power systems have to accommodate a significant level of penetration of renewable generation which requires smart approaches to the power grid control. Associated optimal control problems are…
Adjoint methods have gained popularity in recent years for driving adaptation procedures which aim to reduce error in solution functionals. While adjoint methods have been proven effective for functional-based adaptation, the practical…
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…
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…
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…
We consider the task of solving generic inverse problems, where one wishes to determine the hidden parameters of a natural system that will give rise to a particular set of measurements. Recently many new approaches based upon deep learning…
Innovative machine learning techniques have facilitated the inverse design of photonic structures for numerous practical applications. Nevertheless, within these approaches, the quantity of data and the initial data distribution are…
We consider the unit commitment (UC) problem that employs the alternating current optimal power flow (ACOPF) constraints, which is formulated as a mixed-integer nonlinear programming problem and thus challenging to solve in practice. We…
The recently introduced Gradient Methods with Memory use a subset of the past oracle information to create an accurate model of the objective function that enables them to surpass the Gradient Method in practical performance. The model…