Randomized physics-informed machine learning for uncertainty quantification in high-dimensional inverse problems
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Engineering topics
Publications and source records attributed to Barajas-Solano, David.
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This AI4ESP white paper is the outcome of an open ideation session led by PNNL that numerous institutions participated in. The leadership team included Amy Goldman, Huiying Ren, Tim Scheibe, and James Stegen. The white paper is broken into two sections: (1) A summary of the ideation session, and (2) a short summary of a ‘meta idea’ that emerged from combining multiple ideas spanning the three primary focal area themes articulated in BER’s AI4ESP guidance: A - Data Acquisition and Assimilation, B - Predictive Modeling, and C - Insight from Complex Data. The white paper, therefore, has two goals. The first section is meant to be a resource for innovating around how to pursue open, community-based ideation in virtual environments. The second section is meant as an example of the kinds of ‘meta ideas’ that can emerge from bringing diverse ideas together in a single shared space. We consider the second section to be a submission to BER’s request for white papers around AI4ESP.
We present an Eulerian stochastic advection–diffusion–reaction (SADR) model and use it to explain incomplete mixing typically observed in transport experiments with bimolecular reactions. Unlike traditional advection– dispersion–reaction (ADR) models, the SADR model describes mechanical and diffusive mixing as two separate processes. In the SADR model, mechanical mixing is driven by random advective velocity whose variance is given by the coefficient of mechanical dispersion. The diffusive mixing is modeled as a Fickian diffusion process with the effective diffusion coefficient. We demonstrate that the sum of the two coefficients is equal to the dispersion coefficient, but only the effective diffusion coefficient contributes to the mixing-controlled reactions. We use experimental results of Gramling et al. * * to show that for transport and bimolecular reactions in porous media, the SADR model is significantly more accurate than the ADR model, which overestimates the concentration of the reaction product by as much as 60%. We also show that the SADR model predicts an experimentally observed bell- shaped spatial distribution of the reactive product concentration, while the ADR model results in a concentration distribution with an unphysical kink.