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Adjoint DSMC for nonlinear Boltzmann equation constrained optimization
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DOI：10.1016/j.jcp.2021.110404.png)
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Abstract
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Applications for kinetic equations such as optimal design and inverse problems often involve finding unknown parameters through gradient-based optimization algorithms. Based on the adjoint-state method, we derive two different frameworks for approximating the gradient of an objective functional constrained by the nonlinear Boltzmann equation. While the forward problem can be solved by the DSMC method, it is difficult to efficiently solve the high-dimensional continuous adjoint equation obtained by the optimize-then-discretize approach. This challenge motivates us to propose an adjoint DSMC method following the discretize-then-optimize approach for Boltzmann-constrained optimization. We also analyze the properties of the two frameworks and their connections. Several numerical examples are presented to demonstrate their accuracy and efficiency. (C) 2021 Elsevier Inc. All rights reserved.
Keywords:
Boltzmann equation
Direct simulation Monte Carlo methods
DSMC
Optimization
Adjoint-state method
Linear Boltzmann equation
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