Related papers: Sensitivity Calculations for the Poisson's Equatio…

In high-temperature plasma physics, a strong magnetic field is usually used to confine charged particles. Therefore, for studying the classical mathematical models of the physical problems it needs to consider the effect of external…

We consider the reconstruction of a heterogeneous coefficient field in a Robin boundary condition on an inaccessible part of the boundary in a Poisson problem with an uncertain (or unknown) inhomogeneous conductivity field in the interior…

The possible mismatch between the theoretical and experimental absorption of the edge peaks in semiconductors in a magnetic field background may arise due to the approximation scheme used to analytically calculate the absorption…

Bayesian methods estimate a measure of uncertainty by using the posterior distribution. One source of difficulty in these methods is the computation of the normalizing constant. Calculating exact posterior is generally intractable and we…

First-order optimization algorithms, often preferred for large problems, require the gradient of the differentiable terms in the objective function. These gradients often involve linear operators and their adjoints, which must be applied…

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,…

Mean-field variational methods are widely used for approximate posterior inference in many probabilistic models. In a typical application, mean-field methods approximately compute the posterior with a coordinate-ascent optimization…

Beginning with a relativistic action principle for the irrotational flow of collisionless matter, we compute higher order corrections to the Zel'dovich approximation by deriving a nonlinear Hamilton-Jacobi equation for the velocity…

Removing geometrical details from a complex domain is a classical operation in computer aided design. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. However, depending on the…

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…

A method is presented to include irregular domain boundaries in a geometric multigrid solver. Dirichlet boundary conditions can be imposed on an irregular boundary defined by a level set function. Our implementation employs quadtree/octree…

Typically, objects with the same semantics are not always prominent in images containing different backgrounds. Motivated by this observation that accurately salient object detection is related to both foreground and background, we proposed…

The adjoint method allows efficient calculation of the gradient with respect to the design variables of a topology optimization problem. This method is almost exclusively used in combination with traditional Finite-Element-Analysis, whereas…

This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity guarantees and practical performance. The method contains elements of two existing methods: the…

We consider a scalar function depending on a numerical solution of an initial value problem, and its second-derivative (Hessian) matrix for the initial value. The need to extract the information of the Hessian or to solve a linear system…

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…

One of the fundamental challenges in drawing causal inferences from observational studies is that the assumption of no unmeasured confounding is not testable from observed data. Therefore, assessing sensitivity to this assumption's…

Less than 10 meters deep, shallow landslides are rapidly moving and strongly dangerous slides. In the present work, the probabilistic distribution of the landslide detachment points within a valley is modelled as a spatial Poisson point…

Perturbation and operator adjoint method are used to give the right adjoint form rigourously. From the derivation, we can have following results: 1) The loss gradient is not an ODE, it is an integral and we shows the reason; 2) The…

This paper proposes a new approach for the calibration of material parameters in local elastoplastic constitutive models. The calibration is posed as a constrained optimization problem, where the constitutive model evolution equations for a…