# Embedded Model Error Representation for Bayesian Model Calibration

arXiv: https://arxiv.org/abs/1801.06768 · HTML: https://mlsanity.com/paper/1801.06768/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2018.

## Built on by (most cited first, 7 of 7)

- [Learning About Structural Errors in Models of Complex Dynamical Systems](https://mlsanity.com/paper/2401.00035/) (2023)
- [Physics-informed Information Field Theory for Modeling Physical Systems with Uncertainty Quantification](https://mlsanity.com/paper/2301.07609/) (2023)
- [Bayesian Nonlocal Operator Regression (BNOR): A Data-Driven Learning Framework of Nonlocal Models with Uncertainty Quantification](https://mlsanity.com/paper/2211.01330/) (2022)
- [Deep learning for model correction of dynamical systems with data scarcity](https://mlsanity.com/paper/2410.17913/) (2024)
- [Simulation-based Bayesian inference with ameliorative learned summary statistics -- Part I](https://mlsanity.com/paper/2601.22441/) (2026)
- [Simulation-based parameter estimation via a combination of embedded normalizing flows and implied empirical probabilities under moment restrictions](https://mlsanity.com/paper/2607.25026/) (2026)
- [Embedded Nonlocal Operator Regression (ENOR): Quantifying model error in learning nonlocal operators](https://mlsanity.com/paper/2410.20331/) (2024)

## Abstract (arXiv)

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 the largest contributor to the overall predictive uncertainty. This work builds on a recently developed framework of embedded, internal model correction, in order to represent and quantify structural errors, together with model parameters, within a Bayesian inference context. We focus specifically on a Polynomial Chaos representation with additive modification of existing model parameters, enabling a non-intrusive procedure for efficient approximate likelihood construction, model error estimation, and disambiguation of model and data errors' contributions to predictive uncertainty. The framework is demonstrated on several synthetic examples, as well as on a chemical ignition problem.