EnsembleKalmanProcesses.jl: Derivative-free ensemble-based model calibration

Abstract

EnsembleKalmanProcesses.jl is a Julia-based toolbox that can be used for a broad class of black-box gradient-free optimization problems. Specifically, the tools enable the optimization, or calibration, of parameters within a computer model in order to best match user-defined outputs of the model with available observed data (Kennedy & O'Hagan, 2001). Some of the tools can also approximately quantify parametric uncertainty . Though the package is written in Julia (Bezanson et al., 2017), a read-write TOML-file interface is provided so that the tools can be applied to computer models implemented in any language. Furthermore, the calibration tools are non-intrusive, relying only on the ability of users to compute an output of their model given a parameter value.

Explainable Offline‐Online Training of Neural Networks for Parameterizations: A 1D Gravity Wave‐QBO Testbed in the Small‐Data Regime

“…Various optimization methods can be used to minimize $${\mathcal{L}}_{\mathit{online}}$$. As highlighted earlier, we employ EKI, which has been increasingly used for parameter estimation in recent climate studies (Cleary et al., 2021; Dunbar et al., 2022; Lopez‐Gomez et al., 2022). Briefly, as an iterative method to solve inverse problems, EKI starts with an ensemble of model parameters θ drawn from a prior distribution.…”

“…We use version 1.0.0 of open source software EnsembleKalmanProcesses.jl (Dunbar et al., 2022) for EKI analysis, accessible at Dunbar et al. (2023).…”

“…We use version 1.0.0 of open source software EnsembleKalmanProcesses.jl (Dunbar et al, 2022) for EKI analysis, accessible at Dunbar et al (2023). The code for the 1D-QBO model and the specifically modified EKI software used in this study can be accessed at Pahlavan (2023b).…”

CalibrateEmulateSample.jl: Accelerated Parametric Uncertainty Quantification

“…Kalman methods such as EKI (Iglesias et al, 2013) and its variants (Huang et al, 2022); and CES provides explicit utilities from the codebase EnsembleKalmanProcesses.jl (Dunbar, Lopez-Gomez, et al, 2022). • Emulation tools: CES integrates any statistical emulator, currently implemented are Gaussian Processes (GP) (Williams & Rasmussen, 2006), explicitly provided through packages SciKitLearn.jl (Pedregosa et al, 2011) and GaussianProcesses.jl (Fairbrother et al, 2022), and Random Features (Liu et al, 2022;Rahimi et al, 2007;Rahimi & Recht, 2008), explicitly provided through RandomFeatures.jl that can provide additional flexibility and scalability, particularly in higher dimensions.…”

“…In Julia there are a few tools for performing non-accelerated uncertainty quantification, from classical sensitivity analysis approaches, for example, UncertaintyQuantification.jl, GlobalSensitivity.jl (Dixit & Rackauckas, 2022), and MCMC, for example, Mamba.jl or Turing.jl. For computational efficiency, ensemble methods also provide approximate sampling, (Dunbar, Lopez-Gomez, et al, 2022;e.g., the Ensemble Kalman Sampler Garbuno-Inigo et al, 2020), though these only provide Gaussian approximations of the posterior.…”