Related papers: A discrete adjoint method for deterministic and pr…
We begin by addressing the time-domain full-waveform inversion using the adjoint method. Next, we derive the scaled boundary semi-weak form of the scalar wave equation in heterogeneous media through the Galerkin method. Unlike conventional…
In this work, a flexible higher-order space-time adaptive finite element approximation of convection-dominated transport with coupled fluid flow is developed and studied. Convection-dominated transport is a challenging subproblem in…
We consider the problem of inference in discrete probabilistic models, that is, distributions over subsets of a finite ground set. These encompass a range of well-known models in machine learning, such as determinantal point processes and…
We provide a method to compute the entropy-satisfying weak solution to the eikonal equation in an arbitrary-order polynomial space. The method uses an artificial viscosity approach and is demonstrated for the signed distance function, where…
In this paper, we develop an adaptive Generalized Multiscale Discontinuous Galerkin Method (GMs-DGM) for a class of high-contrast flow problems, and derive a-priori and a-posteriori error estimates for the method. Based on the a-posteriori…
Eikonal tomography has become a popular methodology for deriving phase velocity maps from surface wave phase delay measurements. Its high efficiency makes it popular for handling datasets deriving from large-N arrays, in particular in the…
This paper discusses the computation of derivatives for optimization problems governed by linear hyperbolic systems of partial differential equations (PDEs) that are discretized by the discontinuous Galerkin (dG) method. An efficient and…
Recent literature has effectively leveraged diffusion models trained on continuous variables as priors for solving inverse problems. Notably, discrete diffusion models with discrete latent codes have shown strong performance, particularly…
We investigate a numerical behaviour of robust deterministic optimal control problem subject to a convection diffusion equation containing uncertain inputs. Stochastic Galerkin approach, turning the original optimization problem containing…
Motivated by the need to develop a general framework for performing statistical inference for discretely observed random rough differential equations, our aim is to construct a geometric $p$-rough path ${\bf X}$ whose response $Y$, when…
A scaled conjugate gradient method that accelerates existing adaptive methods utilizing stochastic gradients is proposed for solving nonconvex optimization problems with deep neural networks. It is shown theoretically that, whether with…
This paper proposes and analyzes a gradient-type algorithm based on Burer-Monteiro factorization, called the Asymmetric Projected Gradient Descent (APGD), for reconstructing the point set configuration from partial Euclidean distance…
We study an inverse design problem for the linear multiple fragmentation equation arising in particle dynamics. Our objective is to reconstruct an unknown initial size distribution that evolves, under a prescribed fragmentation law, into a…
We present a novel acceleration technique for improving the convergence of source iteration for discrete ordinates transport calculations. Our approach uses the idea of the dynamic mode decomposition (DMD) to estimate the slowly decaying…
Many differential equations with physical backgrounds are described as gradient systems, which are evolution equations driven by the gradient of some functionals, and such problems have energy conservation or dissipation properties. For…
This paper introduces two variational inference approaches for infinite-dimensional inverse problems, developed through gradient descent with a constant learning rate. The proposed methods enable efficient approximate sampling from the…
We study posterior sampling for inverse problems in discrete state spaces using discrete diffusion models as generative priors. While continuous diffusion models have become widely used for inverse problems, their discrete counterparts…
Sensitivity analysis plays an important role in searching for constitutive parameters (e.g. permeability) subsurface flow simulations. The mathematics behind is to solve a dynamic constrained optimization problem. Traditional methods like…
We propose a new numerical method to solve the linearized problem of travel time tomography with incomplete data. Our method is based on the technique of the truncation of the Fourier series with respect to a special basis of L2. This way…
Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems, due to its excellent scalability with respect to data size. In this work, we analyze a new data-driven regularized stochastic gradient descent…