An Online-Learned Neural Network Chemical Solver for Stable Long-Term Global Simulations of Atmospheric Chemistry

A major computational barrier in global modeling of atmospheric chemistry is the numerical integration of the coupled kinetic equations describing the chemical mechanism. Machine-learned (ML) solvers can offer order-of-magnitude speedup relative to conventional implicit solvers, but past implementations have suffered from fast error growth and only run for short simulation times (<1 month). A successful ML solver for global models must avoid error growth over year-long simulations and allow for re-initialization of the chemical trajectory by transport at every time step. Here we explore the capability of a neural network solver equipped with an autoencoder to achieve stable full-year simulations of tropospheric oxidant chemistry in the global 3-D GEOS-Chem model, replacing its standard mechanism (228 species) by the Super-Fast mechanism (12 species) to avoid the curse of dimensionality. We find that online training of the ML solver within GEOS-Chem is essential for accuracy, whereas offline training from archived GEOS-Chem inputs/outputs produces large errors. After online training we achieve stable 1-year simulations with five-fold speedup compared to the standard implicit Rosenbrock solver with global tropospheric normalized mean biases of -0.3% for ozone, 1% for hydrogen oxide radicals, and -5% for nitrogen oxides. The ML solver captures the diurnal and synoptic variability of surface ozone at polluted and clean sites. There are however large regional biases for ozone and NOx under remote conditions where chemical aging leads to error accumulation. These regional biases remain a major limitation for practical application, and ML emulation would be more difficult in a more complex mechanism.

Stable solvers for real-time Complex Langevin

This study explores the potential of modern implicit solvers for stochastic partial differential equations in the simulation of real-time complex Langevin dynamics. Not only do these methods offer asymptotic stability, rendering the issue of runaway solution moot, but they also allow us to simulate at comparatively large Langevin time steps, leading to lower computational cost. We compare different ways of regularizing the underlying path integral and estimate the errors introduced due to the finite Langevin time steps. Based on that insight, we implement benchmark (non-)thermal simulations of the quantum anharmonic oscillator on the canonical Schwinger-Keldysh contour of short real-time extent.

Performance analysis of fully explicit and fully implicit solvers within a spectral element shallow-water atmosphere model

Explicit Runge–Kutta methods and implicit multistep methods utilizing a Newton–Krylov nonlinear solver are evaluated for a range of configurations of the shallow-water dynamical core of the spectral element community atmosphere model to evaluate their computational performance. These configurations are designed to explore the attributes of each method under different but relevant model usage scenarios including varied spectral order within an element, static regional refinement, and scaling to the largest problem sizes. This analysis is performed within the shallow-water dynamical core option of a full climate model code base to enable a wealth of simulations for study, with the aim of informing solver development within the more complete hydrostatic dynamical core used for climate research. The limitations and benefits to using explicit versus implicit methods, with different parameters and settings, are discussed in light of the trade-offs with Message Passing Interface (MPI) communication and memory and their inherent efficiency bottlenecks. Given the performance behavior across the configurations analyzed here, the recommendation for future work using the implicit solvers is conditional based on scale separation and the stiffness of the problem. For the regionally refined configurations, the implicit method has about the same efficiency as the explicit method, without considering efficiency gains from a preconditioner. The potential for improvement using a preconditioner is greatest for higher spectral order configurations, where more work is shifted to the linear solver. Initial simulations with OpenACC directives to utilize a Graphics Processing Unit (GPU) when performing function evaluations show improvements locally, and that overall gains are possible with adjustments to data exchanges.

ASIS v1.0: an adaptive solver for the simulation of atmospheric chemistry

This article reports on the development and tests of the adaptive semi-implicit scheme (ASIS) solver for the simulation of atmospheric chemistry. To solve the ordinary differential equation systems associated with the time evolution of the species concentrations, ASIS adopts a one-step linearized implicit scheme with specific treatments of the Jacobian of the chemical fluxes. It conserves mass and has a time-stepping module to control the accuracy of the numerical solution. In idealized box-model simulations, ASIS gives results similar to the higher-order implicit schemes derived from the Rosenbrock's and Gear's methods and requires less computation and run time at the moderate precision required for atmospheric applications. When implemented in the MOCAGE chemical transport model and the Laboratoire de Météorologie Dynamique Mars general circulation model, the ASIS solver performs well and reveals weaknesses and limitations of the original semi-implicit solvers used by these two models. ASIS can be easily adapted to various chemical schemes and further developments are foreseen to increase its computational efficiency, and to include the computation of the concentrations of the species in aqueous-phase in addition to gas-phase chemistry.

ASIS v1.0: an adaptative solver for the simulation of atmospheric chemistry

This article reports on the development and tests of the Adaptative Semi-Implicit Scheme (ASIS) solver for the simulation of atmospheric chemistry. To solve the Ordinary Differential Equation systems associated with the time evolution of the species concentrations, ASIS adopts a one step linearized implicit scheme with specific treatments of the Jacobian of the chemical fluxes. It conserves mass and has a time stepping module to control the accuracy of the numerical solution. In idealized box model simulations ASIS gives results similar to the higher order implicit schemes derived from the Rosenbrock's and Gear's methods. When implemented in the MOCAGE CTM and the LMD Mars GCM the ASIS solver performs well and reveals weaknesses and limitations of the original semi-implicit solvers used by these two models. ASIS can be easily adapted to various chemical schemes and further developments are foreseen to increase its computational efficiency, and to include the computation of the concentrations of the species in aqueous phase in addition to gas phase chemistry.