Related papers: Efficient inversion strategies for estimating opti…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
Radiative transfer describes the propagation of electromagnetic radiation through an interacting medium. This process is often simulated by the use of the Monte Carlo method, which involves the probabilistic determination and tracking of…
A challenge in high-dimensional inverse problems is developing iterative solvers to find the accurate solution of regularized optimization problems with low computational cost. An important example is computed tomography (CT) where both…
One native source of quality deterioration in medical imaging, and especially in our case optical coherence tomography (OCT), is the turbid biological media in which photon does not take a predictable path and many scattering events would…
Can Monte Carlo (MC) solvers be directly used in gradient-based methods for PDE-constrained optimization problems? In these problems, a gradient of the loss function is typically presented as a product of two PDE solutions, one for the…
Computer simulations of photon transport through an absorbing and/or scattering medium form an important research tool in astrophysics. Nearly all software codes performing such simulations for three-dimensional geometries employ the Monte…
When a Monte Carlo algorithm is used to evaluate a physical observable A, it is possible to slightly modify the algorithm so that it evaluates simultaneously A and the derivatives $\partial$ $\varsigma$ A of A with respect to each…
Monte Carlo approaches to radiation transport have several attractive properties such as simplicity of implementation, high accuracy, and good parallel scaling. Moreover, Monte Carlo methods can handle complicated geometries and are…
This paper is a broad and accessible survey of the methods we have at our disposal for Monte Carlo gradient estimation in machine learning and across the statistical sciences: the problem of computing the gradient of an expectation of a…
We present a new algorithm for radiative transfer-based on a statistical Monte Carlo approach-that does not suffer from teleportation effects, on the one hand, and yields smooth results, on the other hand. Implicit Monte Carlo (IMC)…
The following electromagnetism (EM) inverse problem is addressed. It consists in estimating local radioelectric properties of materials recovering an object from global EM scattering measurements, at various incidences and wave frequencies.…
We present Generative Monte Carlo (GMC), a novel paradigm for particle transport simulation that integrates generative artificial intelligence directly into the stochastic solution of the linear Boltzmann equation. By reformulating the…
Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…
In this paper, we consider the implementation of multi-level Monte Carlo method to a stochastic optimal control problem with log-normal coefficients and its surrogate model problem. From the perspective of two optimization problems, i.e.,…
We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…
This paper introduces a new Monte Carlo algorithm to invert large matrices. It is based on simultaneous coupled draws from two random vectors whose covariance is the required inverse. It can be considered a generalization of a previously…
This paper addresses the problem of Monte Carlo approximation of posterior probability distributions. In particular, we have considered a recently proposed technique known as population Monte Carlo (PMC), which is based on an iterative…
Multilevel sampling methods, such as multilevel and multifidelity Monte Carlo, multilevel stochastic collocation, or delayed acceptance Markov chain Monte Carlo, have become standard uncertainty quantification (UQ) tools for a wide class of…
Current differentiable renderers provide light transport gradients with respect to arbitrary scene parameters. However, the mere existence of these gradients does not guarantee useful update steps in an optimization. Instead, inverse…
Many inverse problems in nuclear fusion and high-energy astrophysics research, such as the optimization of tokamak reactor geometries or the inference of black hole parameters from interferometric images, necessitate high-dimensional…