Seminar for machine learning and UQ in scientific computing

The focus of this seminar is application of Machine Learning (ML)  and Uncertainty Quantification in scientific computing. Topics of interest include, among others: 

• combination of data-driven models and (multi scale) simulations
• new ML architectures suited for scientific computing or UQ,   
• incorporation of (physical) constraints into data-driven models,   
• efficient (online) learning strategies,   
• using ML for dimension reduction / creating surrogates,   
• inverse problems using ML surrogates, 

and any other topic in which some form of ML and/or UQ is used to enhance (existing) scientific computing methodologies. All applications are welcome, be it financial, physical, biological or otherwise.

For more information, or if you'd like to attend one of the talks, please contact Wouter Edeling of the SC group.

Schedule upcoming talks:

25 Feb. 2021, 15h00: Maximilien de Zordo-Banliat (Safran Tech, Dynfluid Laboratory): Space-dependent Bayesian model averaging of turbulence models for compressor cascade flows.

Abstract

Predictions of systems described by multiple alternative models is of importance for many applications in science and engineering, namely when it is not possible to identify a model that significantly outperforms every other model for each criterion. Two mathematical approaches tackling this is-sue are Bayesian Model Averaging (BMA) [1, 2], which builds an average of the concurrent models weighted by their marginal posteriors probabilities, and Stacking [3, 4], where the unknown prediction is projected on a basis of alternative models, with weights to be learned from data. In both approaches, the weights are generally constant throughout the domain. More recently, Yu et al. [5] have proposed the Clustered Bayesian Averaging (CBA) algorithm, which leverages an ensemble of Regression Trees (RT) to infer weights as space-dependent functions. Similarly, we propose a Space-Dependent Stacking (SDS) algorithm which modifies the stacking formalism to include space-dependent weights, based on a spatial decomposition method.

In this work, the above-mentioned methods are investigated in a Computational Fluid Dynamics(CFD) context. Specifically, CFD of engineering systems often relies on Reynolds-Averaged Navier-Stokes (RANS) models to describe the effect of (unresolved) turbulent motions onto the mean (re-solved) field. Since all turbulent motions are modelled, RANS turbulence models tend to be uncertain and case-dependent. Quantifying and reducing such uncertainties is then of the utmost importance for aerodynamics design in general, and specifically for the analysis and optimization of complex turbo machinery flows. In previous work [6], the present authors used Bayesian model averages of RANS models for providing improved predictions of a compressor cascade configuration, alongside with a quantification of confidence intervals associated with modelling uncertainties. Constant weights throughout the field were used. It is however expected, based on theoretical considerations and ex-pert judgment, that different RANS models tend to perform better in some flow regions and less in other regions, and consequently they should be assigned space-varying weights. For this reason, we implement and assess space-dependent averages of RANS models for compressor flow predictions. More precisely the focus is put on two alternative algorithms: (i) a version of CBA adapted to flow variable fields, and (ii) a Space-Dependent Stacking (SDS) method based on Karhunen-Loeve decomposition of the mixture weights. Flow regions are described using selected features, formulated as functions of the mean flow quantities. Given a set of concurrent RANS models and a database of reference flow data corresponding to various operating conditions, the two algorithms are first trained against data, and subsequently applied to the prediction of an unobserved flow, i.e. another operating condition of the compressor cascade. The algorithms assign a probability to each model in each region of the feature space, based on their ability to accurately predict selected Quantities of Interest (QoI) in this region. The space-dependent weighted-average of the RANS models applied to the prediction scenario is used to reconstruct the expected solution and the associated confidence intervals. Preliminary results show that both of the methods generally yield more accurate solutions than the constant-weight BMA method, and provide a valuable estimate of the uncertainty intervals.

 References

[1] David Madigan, Adrian E Raftery, C Volinsky, and J Hoeting. Bayesian model averaging. In Proceedings of the AAAI Workshop on Integrating Multiple Learned Models, Portland, OR, pages 77–83,1996.

[2] Jennifer A. Hoeting, David Madigan, Adrian E. Raftery, and Chris T. Volinsky. Correction to: “bayesian model averaging: a tutorial” [statist. sci. 14 (1999), no. 4, 382–417; mr 2001a:62033]. Statist. Sci., 15(3):193–195, 08 2000.

[3] David H Wolpert. Stacked generalization. Neural networks, 5(2):241–259, 1992.

[4] Leo Breiman. Stacked regressions. Machine learning, 24(1):49–64, 1996.

[5] Qingzhao Yu, Steven N. MacEachern, and Mario Peruggia. Clustered bayesian model averaging. Bayesian Anal., 8(4):883–908, 12 2013.

[6] M de Zordo-Banliat, X Merle, G Dergham, and P Cinnella. Bayesian model-scenario averaged predictions of compressor cascade flows under uncertain turbulence models. Computers & Fluids, 201:104473, 2020.

11 Mar. 2021: Benjamin Sanderse (CWI)

25 Mar. 2021: Jurriaan Buist (CWI)

8 Apr. 2021: Nikolaj Mücke (CWI)

22 Apr. 2021: Luis Souto (CWI)

6 May 2021: John Harlim (Penn state)

10 Jun. 2021: Hannah Christensen (Oxford)

24 Jun. 2021: Federica Gugole (CWI)