Related papers: Bayesian Calibration of Imperfect Computer Models …

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

Data-driven machine learning models often require extensive datasets, which can be costly or inaccessible, and their predictions may fail to comply with established physical laws. Current approaches for incorporating physical priors…

Physics-Informed Neural Networks (PINNs) have been widely used to obtain solutions to various physical phenomena modeled as Differential Equations. As PINNs are not naturally equipped with mechanisms for Uncertainty Quantification, some…

Industrial applications frequently pose a notorious challenge for state-of-the-art methods in the contexts of optimization, designing experiments and modeling unknown physical response. This problem is aggravated by limited availability of…

The mean field variational Bayes (VB) algorithm implemented in Stan is relatively fast and efficient, making it feasible to produce model-estimated official statistics on a rapid timeline. Yet, while consistent point estimates of parameters…

Machine learning (ML) has been increasingly used for topology optimization (TO). However, most existing ML-based approaches focus on simplified benchmark problems due to their high computational cost, spectral bias, and difficulty in…

We present a Bayesian tomography framework operating with prior-knowledge-based parametrization that is accelerated by surrogate models. Standard high-fidelity forward solvers solve wave equations with natural spatial parametrizations based…

Model-form uncertainties in complex mechanics systems are a major obstacle for predictive simulations. Reducing these uncertainties is critical for stake-holders to make risk-informed decisions based on numerical simulations. For example,…

High fidelity radio interferometric data calibration that minimises spurious spectral structure in the calibrated data is essential in astrophysical applications, such as 21 cm cosmology, which rely on knowledge of the relative spectral…

Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without…

Reliable models of the thermodynamic properties of materials are critical for industrially relevant applications that require a good understanding of equilibrium phase diagrams, thermal and chemical transport, and microstructure evolution.…

Simulation-based calibration (SBC) is a method for validating inference algorithms and model implementations through repeated inference on data simulated from a generative model. For a model to be generative, one must specify proper priors.…

Quality control in industrial processes is increasingly making use of prior scientific knowledge, often encoded in physical models that require numerical approximation. Statistical prediction, and subsequent optimization, is key to ensuring…

Model error estimation remains one of the key challenges in uncertainty quantification and predictive science. For computational models of complex physical systems, model error, also known as structural error or model inadequacy, is often…

This paper proposes a hierarchical, multi-resolution framework for the identification of model parameters and their spatially variability from noisy measurements of the response or output. Such parameters are frequently encountered in…

In this article, an overview of Bayesian methods for sequential simulation from posterior distributions of nonlinear and non-Gaussian dynamic systems is presented. The focus is mainly laid on sequential Monte Carlo methods, which are based…

In robotics, simulation has the potential to reduce design time and costs, and lead to a more robust engineered solution and a safer development process. However, the use of simulators is predicated on the availability of good models. This…

We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…

Identifying accurate dynamic models is required for the simulation and control of various technical systems. In many important real-world applications, however, the two main modeling approaches often fail to meet requirements: first…

Learning and predicting the dynamics of physical systems requires a profound understanding of the underlying physical laws. Recent works on learning physical laws involve generalizing the equation discovery frameworks to the discovery of…