Related papers: On a recent development in stochastic inversion wi…
We survey different perspectives on the stochastic localization process of Eldan, a powerful construction that has had many exciting recent applications in high-dimensional probability and algorithm design. Unlike prior surveys on this…
The near-surface environment is often too complex to enable inference of hydrological and environmental variables using one geophysical data type alone. Joint inversion and coupled inverse modeling involving numerical flow- and transport…
Atmospheric trace-gas inversion refers to any technique used to predict spatial and temporal fluxes using mole-fraction measurements and atmospheric simulations obtained from computer models. Studies to date are most often of a…
We present a method for incorporating a stochastic point of view into physics exercises of mathematics education. The core of our method is the randomization of some inputs, the system model used does not differ from what we would use in…
We review some recent developments which make use of the concept of `superstatistics', an effective description for nonequilibrium systems with a varying intensive parameter such as the inverse temperature. We describe how the asymptotic…
Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…
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…
Atmospheric models used for weather and climate prediction are traditionally formulated in a deterministic manner. In other words, given a particular state of the resolved scale variables, the most likely forcing from the sub-grid scale…
A new approach of obtaining stratified random samples from statistically dependent random variables is described. The proposed method can be used to obtain samples from the input space of a computer forward model in estimating expectations…
Effective structural assessment of urban infrastructure is essential for sustainable land use and resilience to climate change and natural hazards. Seismic wave methods are widely applied in these areas for subsurface characterization and…
In object detection, determining which anchors to assign as positive or negative samples, known as anchor assignment, has been revealed as a core procedure that can significantly affect a model's performance. In this paper we propose a…
In this paper, a new earthquake location method based on the waveform inversion is proposed. As is known to all, the waveform misfit function is very sensitive to the phase shift between the synthetic waveform signal and the real waveform…
Variational inequalities have gained significant attention in machine learning and optimization research. While stochastic methods for solving these problems typically assume independent data sampling, we investigate an alternative approach…
Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a…
Spatial confounding between the spatial random effects and fixed effects covariates has been recently discovered and showed that it may bring misleading interpretation to the model results. Solutions to alleviate this problem are based on…
In this paper, we describe a representation for spatial information, called the stochastic map, and associated procedures for building it, reading information from it, and revising it incrementally as new information is obtained. The map…
This paper studies some asymptotic properties of adaptive algorithms widely used in optimization and machine learning, and among them Adagrad and Rmsprop, which are involved in most of the blackbox deep learning algorithms. Our setup is the…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…
We consider the question of estimating a solution to a system of equations that involve convex nonlinearities, a problem that is common in machine learning and signal processing. Because of these nonlinearities, conventional estimators…