Related papers: A discrete adjoint method for deterministic and pr…
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 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…
We derive and implement a second-order adjoint method to compute exact gradients and Hessians for a prototypical quantum optimal control problem, that of solving for the minimal energy applied electric field that drives a molecule from a…
A deep learning approach to numerically approximate the solution to the Eikonal equation is introduced. The proposed method is built on the fast marching scheme which comprises of two components: a local numerical solver and an update…
Travel time tomography for the velocity structure of a medium is a highly non-linear and non-unique inverse problem. Monte Carlo methods are becoming increasingly common choices to provide probabilistic solutions to tomographic problems but…
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…
Gradient-based inverse design in photonics has already achieved remarkable results in designing small-footprint, high-performance optical devices. The adjoint variable method, which allows for the efficient computation of gradients, has…
The purpose of this study is to show some mathematical aspects of the adjoint method that is a numerical method for the Cauchy problem, an inverse boundary value problem. The adjoint method is an iterative method based on the variational…
A space-time interface-fitted approximation of an inverse source problem for the advection-diffusion equation with moving subdomains is investigated. The problem is reformulated as an optimization problem using Tikhonov regularization. A…
We introduce a `double-difference' method for the inversion for seismic wavespeed structure based on adjoint tomography. Differences between seismic observations and model predictions at individual stations may arise from factors other than…
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…
We present an iterative method to efficiently solve the optimal transportation problem for a class of strictly convex costs which includes quadratic and p-power costs. Given two probability measures supported on a discrete grid with n…
In recent years, high-order finite element methods on high-order meshes have attracted considerable attention. This work investigates the isoparametric upwind discontinuous Galerkin method for the radiation transport equation on a bounded…
Diffusion models have been widely studied as effective generative tools for solving inverse problems. The main ideas focus on performing the reverse sampling process conditioned on noisy measurements, using well-established numerical…
Boundary integral methods are attractive for solving homogeneous linear constant coefficient elliptic partial differential equations on complex geometries, since they can offer accurate solutions with a computational cost that is linear or…
We present a family of fast and accurate Dijkstra-like solvers for the eikonal equation and factored eikonal equation which compute solutions on a regular grid by solving local variational minimization problems. Our methods converge…
This paper introduces a statistical treatment of inverse problems constrained by models with stochastic terms. The solution of the forward problem is given by a distribution represented numerically by an ensemble of simulations. The goal is…
Marine controlled-source electromagnetic (CSEM) method has proved its potential in detecting highly resistive hydrocarbon bearing formations. A novel frequency domain CSEM inversion approach using fictitious wave domain time stepping…
The travel time tomography problem is a coefficient inverse problem for the eikonal equation. This problem has well known applications in seismic. The eikonal equation is considered here in the circular cylinder, where point sources run…
Federated learning heavily relies on distributed gradient descent techniques. In the situation where gradient information is not available, the gradients need to be estimated from zeroth-order information, which typically involves computing…