Related papers: Error control for statistical solutions
We study a recent timestep adaptation technique for hyperbolic conservation laws. The key tool is a space-time splitting of adjoint error representations for target functionals due to S\"uli and Hartmann. It provides an efficient choice of…
Inverse problems in physical or biological sciences often involve recovering an unknown parameter that is random. The sought-after quantity is a probability distribution of the unknown parameter, that produces data that aligns with…
Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…
This work introduces a general framework for establishing the long time accuracy for approximations of Markovian dynamical systems on separable Banach spaces. Our results illuminate the role that a certain uniformity in Wasserstein…
We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error…
This paper is focused on the study of entropic regularization in optimal transport as a smoothing method for Wasserstein estimators, through the prism of the classical tradeoff between approximation and estimation errors in statistics.…
This paper deals with the estimation of a probability measure on the real line from data observed with an additive noise. We are interested in rates of convergence for the Wasserstein metric of order $p\geq 1$. The distribution of the…
The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…
We consider systems of ordinary differential equations with multiple scales in time. In general, we are interested in the long time horizon of a slow variable that is coupled to solution components that act on a fast scale. Although the…
We study numerical methods for dissipative particle dynamics (DPD), which is a system of stochastic differential equations and a popular stochastic momentum-conserving thermostat for simulating complex hydrodynamic behavior at mesoscales.…
Statistical models often include thousands of parameters. However, large models decrease the investigator's ability to interpret and communicate the estimated parameters. Reducing the dimensionality of the parameter space in the estimation…
The nested distance builds on the Wasserstein distance to quantify the difference of stochastic processes, including also the information modelled by filtrations. The Sinkhorn divergence is a relaxation of the Wasserstein distance, which…
We consider a general online stochastic optimization problem with multiple budget constraints over a horizon of finite time periods. In each time period, a reward function and multiple cost functions are revealed, and the decision maker…
Gaussian mixture models find their place as a powerful tool, mostly in the clustering problem, but with proper preparation also in feature extraction, pattern recognition, image segmentation and in general machine learning. When faced with…
This article provides a brief introduction to the a posteriori error analysis of parabolic partial differential equations, with an emphasis on challenges distinct from those of steady-state problems. Using the heat equation as a model…
Wasserstein distributionally robust control (WDRC) is an effective method for addressing inaccurate distribution information about disturbances in stochastic systems. It provides various salient features, such as an out-of-sample…
The statistical finite element method (StatFEM) is an emerging probabilistic method that allows observations of a physical system to be synthesised with the numerical solution of a PDE intended to describe it in a coherent statistical…
Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the…
This paper is concerned by statistical inference problems from a data set whose elements may be modeled as random probability measures such as multiple histograms or point clouds. We propose to review recent contributions in statistics on…
We consider multiperiod stochastic control problems with non-parametric uncertainty on the underlying probabilistic model. We derive a new metric on the space of probability measures, called the adapted $(p, \infty)$--Wasserstein distance…