An official website of the United States government
Abstract The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance, that include fracturing or damage of the solid phase, require a nonlinear description of the large deformations that can occur. This paper presents a variational energy‐based continuum mechanics framework to model large‐deformation poroelasticity. The approach begins from the total free energy density that is additively composed of the free energy of the components. A variational procedure then provides the balance of momentum, fluid transport balance, and pressure relations. A numerical approach based on finite elements is applied to analyze the behavior of saturated and unsaturated porous media using a nonlinear constitutive model for the solid skeleton. Examples studied include the Terzaghi and Mandel problems; a gas–liquid phase‐changing fluid; multiple immiscible gases; and unsaturated systems where we model injection of fluid into soil. The proposed variational approach can potentially have advantages for numerical methods as well as for combining with data‐driven models in a Bayesian framework.
more »
« less
Black Box Variational Bayesian Model Averaging
For many decades now, Bayesian Model Averaging (BMA) has been a popular framework to systematically account for model uncertainty that arises in situations when multiple competing models are available to describe the same or similar physical process. The implementation of this framework, however, comes with a multitude of practical challenges including posterior approximation via Markov chain Monte Carlo and numerical integration. We present a Variational Bayesian Inference approach to BMA as a viable alternative to the standard solutions which avoids many of the aforementioned pitfalls. The proposed method is “black box” in the sense that it can be readily applied to many models with little to no model-specific derivation. We illustrate the utility of our variational approach on a suite of examples and discuss all the necessary implementation details. Fully documented Python code with all the examples is provided as well.
more »
« less
- PAR ID:
- 10338221
- Date Published:
- Journal Name:
- The American Statistician
- ISSN:
- 0003-1305
- Page Range / eLocation ID:
- 1 to 12
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
In this paper, we summarize some recent advances related to the energetic variational approach (EnVarA), a general variational framework of building thermodynamically consistent models for complex fluids, by some examples. Particular focus will be placed on how to model systems involving chemo-mechanical couplings and non-isothermal effects.more » « less
-
The BUQEYE collaboration (Bayesian Uncertainty Quantification: Errors in Your effective field theory) presents a pedagogical introduction to projection-based, reduced-order emulators for applications in low-energy nuclear physics. The term emulator refers here to a fast surrogate model capable of reliably approximating high-fidelity models. As the general tools employed by these emulators are not yet well-known in the nuclear physics community, we discuss variational and Galerkin projection methods, emphasize the benefits of offline-online decompositions, and explore how these concepts lead to emulators for bound and scattering systems that enable fast and accurate calculations using many different model parameter sets. We also point to future extensions and applications of these emulators for nuclear physics, guided by the mature field of model (order) reduction. All examples discussed here and more are available as interactive, open-source Python code so that practitioners can readily adapt projection-based emulators for their own work.more » « less
-
To guide the selection of probabilistic solar power forecasting methods for day-ahead power grid operations, the performance of four methods, i.e., Bayesian model averaging (BMA), Analog ensemble (AnEn), ensemble learning method (ELM), and persistence ensemble (PerEn) is compared in this paper. A real-world hourly solar generation dataset from a rooftop solar plant is used to train and validate the methods under clear, partially cloudy, and overcast weather conditions. Comparisons have been made on a one-year testing set using popular performance metrics for probabilistic forecasts. It is found that the ELM method outperforms other methods by offering better reliability, higher resolution, and narrower prediction interval width under all weather conditions with a slight compromise in accuracy. The BMA method performs well under overcast and partially cloudy weather conditions, although it is outperformed by the ELM method under clear conditions.more » « less
-
Group fairness is measured via parity of quantitative metrics across different protected demographic groups. In this paper, we investigate the problem of reliably assessing group fairness metrics when labeled examples are few but unlabeled examples are plentiful. We propose a general Bayesian framework that can augment labeled data with unlabeled data to produce more accurate and lower-variance estimates compared to methods based on labeled data alone. Our approach estimates calibrated scores (for unlabeled examples) of each group using a hierarchical latent variable model conditioned on labeled examples. This in turn allows for inference of posterior distributions for an array of group fairness metrics with a notion of uncertainty. We demonstrate that our approach leads to significant and consistent reductions in estimation error across multiple well-known fairness datasets, sensitive attributes, and predictive models. The results clearly show the benefits of using both unlabeled data and Bayesian inference in assessing whether a prediction model is fair or not.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1080/00031305.2022.2058611
