Abstract:a b s t r a c tRecent years have seen a growing interest in using data-driven (machine-learning) techniques for the construction of cheap surrogate models of turbulent subgrid scale stresses. These stresses display complex spatio-temporal structures, and constitute a difficult surrogate target. In this paper we propose a datapreprocessing step, in which we derive alternative subgrid scale models which are virtually exact for a user-specified set of spatially integrated quantities of interest. The unclosed comp… Show more
“…The primary interest often lies in predicting the large-scale coherent structures. Therefore, developing computationally efficient reduced order models with suitable parameterizations and forecasting the statistics of the leading a few resolved modes, which still correspond to a relatively high-dimensional PDF for direct numerical simulations, have more practical significance in more realistic applications [29,1,20,41,5,3,22,42,12]. The PIDD-CG algorithm can facilitate the development of efficient statistical reduced order models as well as accelerating the associated statistical forecast.…”
A new ensemble forecast algorithm, named as the physics-informed data-driven algorithm with conditional Gaussian statistics (PIDD-CG), is developed to predict the time evolution of the probability density functions (PDFs) of complex turbulent systems with partial observations. The PIDD-CG algorithm integrates a unique multiscale statistical closure model with an extremely efficient nonlinear data assimilation scheme to represent the PDF as a mixture of conditional statistics, which overcomes the curse of dimensionality for high-dimensional systems. The multiscale features in the time evolution of each conditional statistics ensemble member effectively captured by an appropriate combination of physics-informed analytic formulae and recurrent neural networks. An information metric is adopted as the loss function for the latter to more accurately calibrate the key turbulent signals with strong fluctuations. The proposed algorithm succeeds in forecasting both the transient and statistical equilibrium non-Gaussian PDFs of strongly turbulent systems with intermittency, regime switching and extreme events.
“…The primary interest often lies in predicting the large-scale coherent structures. Therefore, developing computationally efficient reduced order models with suitable parameterizations and forecasting the statistics of the leading a few resolved modes, which still correspond to a relatively high-dimensional PDF for direct numerical simulations, have more practical significance in more realistic applications [29,1,20,41,5,3,22,42,12]. The PIDD-CG algorithm can facilitate the development of efficient statistical reduced order models as well as accelerating the associated statistical forecast.…”
A new ensemble forecast algorithm, named as the physics-informed data-driven algorithm with conditional Gaussian statistics (PIDD-CG), is developed to predict the time evolution of the probability density functions (PDFs) of complex turbulent systems with partial observations. The PIDD-CG algorithm integrates a unique multiscale statistical closure model with an extremely efficient nonlinear data assimilation scheme to represent the PDF as a mixture of conditional statistics, which overcomes the curse of dimensionality for high-dimensional systems. The multiscale features in the time evolution of each conditional statistics ensemble member effectively captured by an appropriate combination of physics-informed analytic formulae and recurrent neural networks. An information metric is adopted as the loss function for the latter to more accurately calibrate the key turbulent signals with strong fluctuations. The proposed algorithm succeeds in forecasting both the transient and statistical equilibrium non-Gaussian PDFs of strongly turbulent systems with intermittency, regime switching and extreme events.
“…To address the more fundamental model-form uncertainty, we are currently investigating the use of data-driven stochastic surrogates to replace traditional deterministic parametrizations; see e.g. [ 55 , 56 ] for recent results. Figure 7 A Tube Map showing the VECMA components used in the climate application.…”
We present the VECMA toolkit (VECMAtk), a flexible software environment for single and multiscale simulations that introduces directly applicable and reusable procedures for verification, validation (V&V), sensitivity analysis (SA) and uncertainty quantication (UQ). It enables users to verify key aspects of their applications, systematically compare and validate the simulation outputs against observational or benchmark data, and run simulations conveniently on any platform from the desktop to current multi-petascale computers. In this sequel to our paper on VECMAtk which we presented last year [
1
] we focus on a range of functional and performance improvements that we have introduced, cover newly introduced components, and applications examples from seven different domains such as conflict modelling and environmental sciences. We also present several implemented patterns for UQ/SA and V&V, and guide the reader through one example concerning COVID-19 modelling in detail.
This article is part of the theme issue ‘Reliability and reproducibility in computational science: implementing verification, validation and uncertainty quantification
in silico
’.
“…to keep Qireffalse(tfalse)−Qifalse(tfalse) small for all times during training, where Qiref is the reference QoI computed from the high-resolution training data. We skip details for the sake of brevity, and refer to [26] for more technical information, or to [27] for the code and a practical tutorial.…”
Section: Case Studiesmentioning
confidence: 99%
“…We generate a database of training data by solving the Gray–Scott equations for u and v at a high spatial resolution of 512 × 512 nodes. Instead of creating a surrogate for the spatially dependent subgrid-scale terms, we create the so-called reduced surrogates [ 26 ]. These are specifically geared towards predicting global (i.e.…”
Section: Case Studiesmentioning
confidence: 99%
“…This shows the PDFs of the four QoIs, for both the high spatial resolution simulation (with no subgrid-scale terms), and the low-resolution model ( 6.2 ) with reduced surrogates. As this is the training phase, these reduced surrogates are informed directly from the training data [ 26 ]. Note that the two PDFs for each Q i are practically indistinguishable from each other, confirming the accuracy of the reduced surrogate during the training phase.…”
Uncertainty quantification (UQ) is a key component when using computational models that involve uncertainties, e.g. in decision-making scenarios. In this work, we present uncertainty quantification patterns (UQPs) that are designed to support the analysis of uncertainty in coupled multi-scale and multi-domain applications. UQPs provide the basic building blocks to create tailored UQ for multiscale models. The UQPs are implemented as generic templates, which can then be customized and aggregated to create a dedicated UQ procedure for multiscale applications. We present the implementation of the UQPs with multiscale coupling toolkit Multiscale Coupling Library and Environment 3. Potential speed-up for UQPs has been derived as well. As a proof of concept, two examples of multiscale applications using UQPs are presented.
This article is part of the theme issue ‘Reliability and reproducibility in computational science: implementing verification, validation and uncertainty quantification
in silico
’.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
