DecTree v1.0 – Chemistry speedup in reactive transport simulations: purely data-driven and physics-based surrogates

Abstract

Abstract. The computational costs associated with coupled reactive transport simulations are mostly due to the chemical subsystem: replacing it with a pre-trained statistical surrogate is a promising strategy to achieve decisive speedups at the price of small accuracy losses and thus to extend the scale of problems which can be handled. We introduce a hierarchical coupling scheme in which full physics, equation-based geochemical simulations are partially replaced by surrogates. Errors on mass balance resulting from multivariate surrogate predictions effectively assess the accuracy of multivariate regressions at runtime: inaccurate surrogate predictions are rejected and the more expensive equation-based simulations are run instead. Gradient boosting regressors such as xgboost, not requiring data standardization and being able to handle Tweedie distributions, proved to be a suitable emulator. Finally, we devise a surrogate approach based on geochemical knowledge, which overcomes the issue of robustness when encountering previously unseen data, and which can serve as basis for further development of hybrid physics-AI modelling.

<tt>POET</tt> (v0.1): Speedup of Many-Cores Parallel Reactive Transport Simulations with Fast DHT-Lookups

“…In current POET's version we chose a rather simplistic approach for the coupling of chemistry, in which all "state variables" defining completely the chemical problem (aqueous concentrations and mineral amounts) and the corresponding outputs are saved. It is possible to spare DHT space by recasting the results of the chemical problem in terms of the actually independent variables (i.e., storing reaction rates within the time step along with pH and pe and the ∆t, and to back-calculate the changes in total elemental concentrations (De Lucia and Kühn, 2021), possibly in combination with scaling relationships such as those proposed by Klein et al (2013) andDe Lucia et al (2015), which could also be beneficial in case of spatial heterogeneity not only of porosity and water saturation, but for the chemical process itself. This is however a quite complex task, since the particular definition of kinetic laws and the choice of the relationships used to update parameters such as specific reactive surfaces, which we did not consider in the present work, directly affect how the "chemical heterogeneity" can be treated to optimize the speedup through a DHT.…”

“…times slower. This speedup puts the use of DHT in the same tier with other acceleration strategies such as surrogate modelling (Jatnieks et al, 2016;Laloy and Jacques, 2019;Prasianakis et al, 2020;De Lucia and Kühn, 2021) and the on demand machine learning approach of REAKTORO (Leal et al, 2020;Kyas et al, 2020). In particular, the caching via DHT is an algorithm which, once implemented in the coupled simulator and tuned for the problem at hand, does not require training of complex surrogates but it works out-of-the-box.…”

“…In the next development steps, along with the above mentioned technical improvements resulting from the reimplementation in native C++ of some R routines, we envisage notably the adoption of geochemical surrogate models for chemistry (De Lucia et al, 2017;De Lucia and Kühn, 2021), which the interface to high-level language R makes straightforward. This will allow a direct comparison between surrogate and POET's DHT as well as their composition.…”

“…Surrogate models are statistical multivariate regressors which are trained in advance on an ensemble of geochemical simulations spanning the expected parameter space encountered during the coupled simulations. Regressors commonly employed to this goal are Artificial Neural Networks (Laloy and Jacques, 2019;Guérillot and Bruyelle, 2020;Prasianakis et al, 2020;Lu et al, 2020), RandomForest (Lu et al, 2020), xgboost (De Lucia andKühn, 2021), Gaussian Processes (Laloy and Jacques, 2019).…”

“…The chemical problem solved throughout the present work derives from Engesgaard and Kipp (1992) and is commonly used, with different variants, in the reactive transport community (e.g., Shao et al, 2009;De Lucia et al, 2017;Damiani et al, 2020;Leal et al, 2020;De Lucia and Kühn, 2021). A MgCl 2 solution enters a domain whose pore water is at thermodynamic equilibrium with calcite.…”