ECCOMAS 2024

Reversible Random Number Generators for Adjoint Monte Carlo Simulation of Kinetic Equations

  • Løvbak, Emil (Karlsruhe Institute of Technology)
  • Vandewalle, Stefan (KU Leuven)
  • Samaey, Giovanni (KU Leuven)

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Kinetic equations model particles subject to transport and collision effects. Of the many application domains in which they are used, we consider the modeling of neutral particles in the scrap-off-layer, i.e., outer region of tokamak fusion reactors. For reactor design, these equations are part of a set of PDE constraints for the optimization problem to be solved. Solving this problem requires both the ability to simulate the PDE, as well as to compute the corresponding gradient of the objective function to the design parameters [2]. These kinetic equations are typically simulated using particle-based Monte Carlo methods, which introduce noise to the simulation outputs and, consequently, the objective function being minimized. Care must then be taken when computing the gradient of the objective function to its design parameters, to ensure convergence. The discrete-adjoint method computes the gradient through a simulation that retraces the original particle trajectories backwards in time [1]. For complex simulations, however, storing these trajectories requires a large amount of memory. In this work, we tackle this memory issue by recomputing reversed trajectories from scratch. To this end, we use a reversible random number generator [3], i.e., one that can step both forwards and backwards through its sequence at identical cost. We demonstrate that this approach significantly reduces the memory required in a straightforward implementation of a simplified 1D coupled plasma-neutral model. [1] R. Caflisch, D. Silantyev, Y. Yang, Adjoint DSMC for nonlinear Boltzmann equation constrained optimization. Journal of Computational Physics 439, pp. 110404 (2021) [2] W. Dekeyser, M. Blommaert, K. Ghoos, N. Horsten, P. Börner, G. Samaey, M. Baelmans, Divertor design through adjoint approaches and efficient code simulation strategies. Contributions to Plasma Physics 58 (6-8), pp 643–651 (2018) [3] E. Løvbak, F. Blondeel, A. Lee, L. Vanroye, A. Van Barel and G. Samaey, Reversible random number generation for adjoint Monte Carlo simulation of the heat equation. In Review, arXiv:2302.02778 (2023)