Speeding up reactive transport simulations in cement systems by surrogate geochemical modeling: deep neural networks and k-nearest neighbors

Abstract

This study investigates how reactive transport (RT) simulation can be accelerated by replacing the geochemical solver the RT code by a surrogate model or emulator, considering either a trained deep neural network (DNN) or a k-nearest neighbor (kNN) regressor. We focus on 2D leaching of hardened cement paste under diffusive or advective-dispersive transport conditions, a solid solution representation of the calcium silicate hydrates and either 4 or 7 chemical components, and use the HPx reactive transport code as baseline. We find that after training, both our DNN-based and kNN-based codes, called HPx py -DNN and HPx py -kNN, can make quite accurate predictions for the simpler 4-components cement system while providing either a 4.2 to 6.8 (DNN) or 2.8 to 5.0 (kNN) speedup factor compared to HPx with parallelized geochemical calculations over 4 cores. Benchmarking against single-threaded HPx, these speedup factors become 16.2 to 24.5 and 10.8 to 18.0 for HPx py -DNN and HPx py -kNN, respectively. For the more complex 7-components cement system, no emulator that is globally accurate over the full space of possible geochemical conditions could be devised, neither using DNNs nor kNN. Instead we therefore build "local" emulators that are only valid over a relevant fraction of the input parameter space. This is achieved by running a computationally cheap full RT simulation for which case-specific computational requirements control what domain size and time period can be used, to create a first set of training points. This initial training set is then augmented by kernel density sampling to provide more input diversity while simultaneously honoring as much as possible the complex between-input dependencies. The resulting training set is then either used to train the DNN emulator or serves as training base for the kNN emulator. Our results indicate that this strategy works to some extent but does no longer deliver nearperfect predictions, as both the HPx py -DNN and HPx py -kNN outputs show discrepancies in some of the emulated time series of 2D concentration profiles compared to the baseline. Nevertheless, these deviations can presumably be smoothed out to some extent using post-filtering. Although smaller than for the 4-components system, the speedups achieved for this 7-component system remain attractive: 4.0 to 4.7 (13.4 to 16.3) and 2.4 to 2.9 (7.9 to 10.0) compared to four-threaded (single-threaded) HPx for HPx py -DNN and HPx py -kNN, respectively. Defining the maximum possible speedup as the computational gain in RT simulation that would be obtained if the geochemical calculations would come at no cost, we find that HPx py -DNN achieves a close to optimal speedup while HPx py -kNN provides half the maximum possible speedup. How to improve both accuracy and speedup for the considered cement systems and other problems will be the scope of future work.

An emulation-based approach for interrogating reactive transport models

“…Ours is not the first work to apply emulators to RTM simulations. Notably, a rich vein of research based around replacing the geochemical solver in RTMs with an emulator has emerged over the past few years (see Laloy and Jacques (2021) and Kyas et al (2022), among others). However, the work presented here is less concerned with speeding up individual RTM simulations as it is with developing new methods to explore geochemical parameter spaces.…”