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1. Calibration and Uncertainty Quantification of Convective Parameters in an Idealized GCM

   https://doi.org/10.1029/2020MS002454  

   Dunbar, Oliver R. A.; Garbuno‐Inigo, Alfredo; Schneider, Tapio; Stuart, Andrew M. (September 2021, Journal of Advances in Modeling Earth Systems)

   Abstract Parameters in climate models are usually calibrated manually, exploiting only small subsets of the available data. This precludes both optimal calibration and quantification of uncertainties. Traditional Bayesian calibration methods that allow uncertainty quantification are too expensive for climate models; they are also not robust in the presence of internal climate variability. For example, Markov chain Monte Carlo (MCMC) methods typically requiremodel runs and are sensitive to internal variability noise, rendering them infeasible for climate models. Here we demonstrate an approach to model calibration and uncertainty quantification that requires onlymodel runs and can accommodate internal climate variability. The approach consists of three stages: (a) a calibration stage uses variants of ensemble Kalman inversion to calibrate a model by minimizing mismatches between model and data statistics; (b) an emulation stage emulates the parameter‐to‐data map with Gaussian processes (GP), using the model runs in the calibration stage for training; (c) a sampling stage approximates the Bayesian posterior distributions by sampling the GP emulator with MCMC. We demonstrate the feasibility and computational efficiency of this calibrate‐emulate‐sample (CES) approach in a perfect‐model setting. Using an idealized general circulation model, we estimate parameters in a simple convection scheme from synthetic data generated with the model. The CES approach generates probability distributions of the parameters that are good approximations of the Bayesian posteriors, at a fraction of the computational cost usually required to obtain them. Sampling from this approximate posterior allows the generation of climate predictions with quantified parametric uncertainties. 

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2. A mathematical model of glomerular fibrosis in diabetic kidney disease to predict therapeutic efficacy

   https://doi.org/10.3389/fphar.2024.1481768  

   Thomas, Haryana Y; Ford_Versypt, Ashlee N (October 2024, Frontiers in Pharmacology)

   BackgroundGlomerular fibrosis is a tissue damage that occurs within the kidneys of chronic and diabetic kidney disease patients. Effective treatments are lacking, and the mechanism of glomerular damage reversal is poorly understood. MethodsA mathematical model suitable for hypothesis-driven systems pharmacology of glomerular fibrosis in diabetes was developed from a previous model of interstitial fibrosis. The adapted model consists of a system of ordinary differential equations that models the complex disease etiology and progression of glomerular fibrosis in diabetes. ResultsWithin the scope of the mechanism incorporated, advanced glycation end products (AGE)—matrix proteins that are modified due to high blood glucose—were identified as major contributors to the delay in the recovery from glomerular fibrosis after glucose control. The model predicted that inhibition of AGE production is not an effective approach for accelerating the recovery from glomerular fibrosis. Further, the model predicted that treatment breaking down accumulated AGE is the most productive at reversing glomerular fibrosis. The use of the model led to the identification that glucose control and aminoguanidine are ineffective treatments for reversing advanced glomerular fibrosis because they do not remove accumulated AGE. Additionally, using the model, a potential explanation was generated for the lack of efficacy of alagebrium in treating advanced glomerular fibrosis, which is due to the inability of alagebrium to reduce TGF- $\mathrm{\beta }$. ImpactUsing the mathematical model, a mechanistic understanding of disease etiology and complexity of glomerular fibrosis in diabetes was illuminated, and then hypothesis-driven explanations for the lack of efficacy of different pharmacological agents for treating glomerular fibrosis were provided. This understanding can enable the development of more efficacious therapeutics for treating kidney damage in diabetes. 

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3. Bayesian Optimization with High-Dimensional Outputs

   https://doi.org/10.48550/arXiv.2106.12997  

   Maddox, W. J.; Balandat, M.; Wilson, A. G.; Bakshy, E (January 2021, Advances in neural information processing systems)

   Bayesian optimization is a sample-efficient black-box optimization procedure that is typically applied to a small number of independent objectives. However, in practice we often wish to optimize objectives defined over many correlated outcomes (or “tasks”). For example, scientists may want to optimize the coverage of a cell tower network across a dense grid of locations. Similarly, engineers may seek to balance the performance of a robot across dozens of different environments via constrained or robust optimization. However, the Gaussian Process (GP) models typically used as probabilistic surrogates for multi-task Bayesian optimization scale poorly with the number of outcomes, greatly limiting applicability. We devise an efficient technique for exact multi-task GP sampling that combines exploiting Kronecker structure in the covariance matrices with Matheron’s identity, allowing us to perform Bayesian optimization using exact multi-task GP models with tens of thousands of correlated outputs. In doing so, we achieve substantial improvements in sample efficiency compared to existing approaches that model solely the outcome metrics. We demonstrate how this unlocks a new class of applications for Bayesian optimization across a range of tasks in science and engineering, including optimizing interference patterns of an optical interferometer with 65,000 outputs. 

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4. A Bayesian calibration framework for EDGES

   https://doi.org/10.1093/mnras/stac2600  

   Murray, Steven G.; Bowman, Judd D.; Sims, Peter H.; Mahesh, Nivedita; Rogers, Alan E. E.; Monsalve, Raul A.; Samson, Titu; Vydula, Akshatha Konakondula (September 2022, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT We develop a Bayesian model that jointly constrains receiver calibration, foregrounds, and cosmic 21 cm signal for the EDGES global 21 cm experiment. This model simultaneously describes calibration data taken in the lab along with sky-data taken with the EDGES low-band antenna. We apply our model to the same data (both sky and calibration) used to report evidence for the first star formation in 2018. We find that receiver calibration does not contribute a significant uncertainty to the inferred cosmic signal ($$\lt 1{{\ \rm per\ cent}}$$), though our joint model is able to more robustly estimate the cosmic signal for foreground models that are otherwise too inflexible to describe the sky data. We identify the presence of a significant systematic in the calibration data, which is largely avoided in our analysis, but must be examined more closely in future work. Our likelihood provides a foundation for future analyses in which other instrumental systematics, such as beam corrections and reflection parameters, may be added in a modular manner. 

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5. Simultaneous Bayesian Calibration and Engineering Design With an Application to a Vibration Isolation System

   https://doi.org/10.1115/1.4050075  

   Ehrett, Carl; Brown, D. Andrew; Kitchens, Christopher; Xu, Xinyue; Platz, Roland; Atamturktur, Sez (March 2021, Journal of Verification, Validation and Uncertainty Quantification)

   null (Ed.)

   Abstract Calibration of computer models and the use of those design models are two activities traditionally carried out separately. This paper generalizes existing Bayesian inverse analysis approaches for computer model calibration to present a methodology combining calibration and design in a unified Bayesian framework. This provides a computationally efficient means to undertake both tasks while quantifying all relevant sources of uncertainty. Specifically, compared with the traditional approach of design using parameter estimates from previously completed model calibration, this generalized framework inherently includes uncertainty from the calibration process in the design procedure. We demonstrate our approach to the design of a vibration isolation system. We also demonstrate how, when adaptive sampling of the phenomenon of interest is possible, the proposed framework may select new sampling locations using both available real observations and the computer model. This is especially useful when a misspecified model fails to reflect that the calibration parameter is functionally dependent upon the design inputs to be optimized. 

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