Related papers: Novel and flexible parameter estimation methods fo…
A recently developed measure-theoretic framework solves a stochastic inverse problem (SIP) for models where uncertainties in model output data are predominantly due to aleatoric (i.e., irreducible) uncertainties in model inputs (i.e.,…
Model selection in machine learning (ML) is a crucial part of the Bayesian learning procedure. Model choice may impose strong biases on the resulting predictions, which can hinder the performance of methods such as Bayesian neural networks…
Invariant prediction [Peters et al., 2016] analyzes feature/outcome data from multiple environments to identify invariant features - those with a stable predictive relationship to the outcome. Such features support generalization to new…
In a Bayesian approach for solving linear inverse problems one needs to specify the prior laws for calculation of the posterior law. A cost function can also be defined in order to have a common tool for various Bayesian estimators which…
Inverse problems are paramount in Science and Engineering. In this paper, we consider the setup of Statistical Inverse Problem (SIP) and demonstrate how Stochastic Gradient Descent (SGD) algorithms can be used in the linear SIP setting. We…
The Bayesian approach has proved to be a coherent approach to handle ill posed Inverse problems. However, the Bayesian calculations need either an optimization or an integral calculation. The maximum a posteriori (MAP) estimation requires…
Mechanistic simulation models are inverted against observations in order to gain inference on modeled processes. However, with the increasing ability to collect high resolution observations, these observations represent more patterns of…
Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…
Seismic inverse modeling is a common method in reservoir prediction and it plays a vital role in the exploration and development of oil and gas. Conventional seismic inversion method is difficult to combine with complicated and abstract…
The Bayesian inversion method demonstrates significant potential for solving inverse problems, enabling both point estimation and uncertainty quantification (UQ). However, Bayesian maximum a posteriori (MAP) estimation may become unstable…
High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and…
The main contribution of this paper is to develop a hierarchical Bayesian formulation of PINNs for linear inverse problems, which is called BPINN-IP. The proposed methodology extends PINN to account for prior knowledge on the nature of the…
Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is…
We consider state and parameter estimation for compartmental models having both time-varying and time-invariant parameters. Though the described Bayesian computational framework is general, we look at a specific application to the…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
This paper develops a novel sequential Monte Carlo (SMC) approach for joint state and parameter estimation that can deal efficiently with abruptly changing parameters which is a common case when tracking maneuvering targets. The approach…
Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in…
Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells. These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not…
To quantify how well theoretical predictions of structural ensembles agree with experimental measurements, we depend on the accuracy of forward models. These models are computational frameworks that generate observable quantities from…
Self-organizing systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organization central to understanding natural complexity. A fundamental challenge…