Related papers: Sensitivity Calculations for the Poisson's Equatio…
Adjoint methods have been the pillar of gradient-based optimization for decades. They enable the accurate computation of a gradient (sensitivity) of a quantity of interest with respect to all system's parameters in one calculation. When the…
The auxiliary field method is a technique to obtain approximate closed formulae for the solutions of both nonrelativistic and semirelativistic eigenequations in quantum mechanics. For a many-body Hamiltonian describing identical particles,…
This paper presents a novel computational scheme for sensitivity analysis of the velocity field in the level set method using the discrete adjoint method. The velocity field is represented in B-spline space, and the adjoint equations are…
In recent years, it has been convincingly shown that weather forecasting models can be run in single-precision arithmetic. Several models or components thereof have been tested with even lower precision than this. This previous work has…
Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is the…
We present twelve numerical methods for evaluation of objects and concepts from Poisson geometry. We describe how each method works with examples, and explain how it is executed in code. These include methods that evaluate Hamiltonian and…
An adjoint-based shape optimization method for solid bodies subjected to both rarefied and continuum gas flows is proposed. The gas-kinetic BGK equation with the diffuse-reflection boundary condition is used to describe the multiscale gas…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
Using oblique projections and angles between subspaces we write condition number estimates for abstract nonsymmetric domain decomposition methods. In particular, we consider a restricted additive method for the Poisson equation and write a…
We present an adjoint sensitivity method for hybrid discrete -- continuous systems, extending previously published forward sensitivity methods. We treat ordinary differential equations and differential-algebraic equations of index up to two…
Every conformal field theory has the symmetry of taking each field to its adjoint. We consider here the quotient (orbifold) conformal field theory obtained by twisting with respect to this symmetry. A general method for computing such…
In the present research, a variational technique to modifying the Poisson equation is presented, expanding its modelling capabilities to include a wider range of physical processes and resonant structures. The study examines the…
This paper proposes the utilization of a periodic Parareal with a periodic coarse problem to efficiently perform adjoint sensitivity analysis for the steady state of time-periodic nonlinear circuits. In order to implement this method, a…
We present two analytical formulae for estimating the sensitivity -- namely, the gradient or Jacobian -- at given realizations of an arbitrary-dimensional random vector with respect to its distributional parameters. The first formula…
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…
An information-theoretic development is given for the problem of compound Poisson approximation, which parallels earlier treatments for Gaussian and Poisson approximation. Let $P_{S_n}$ be the distribution of a sum $S_n=\Sumn Y_i$ of…
This paper develops methodology for local sensitivity analysis based on directional derivatives associated with spatial processes. Formal gradient analysis for spatial processes was elaborated in previous papers, focusing on distribution…
The shooting method is used to solve a boundary value problem with separated and explicit constraints. To obtain approximations of an unknown initial values there are considered arguments based on the adjoint differential system attached to…
In this paper we present a methodology that allows the efficient computation of the topological derivative for semilinear elliptic problems within the averaged adjoint Lagrangian framework. The generality of our approach should also allow…
Complex computer codes are widely used in science to model physical systems. Sensitivity analysis aims to measure the contributions of the inputs on the code output variability. An efficient tool to perform such analysis are the…