ArrheniusActiveSubspace

Use Arrhenius.jl to compute active subspace

Active subspace is an elegant approach for uncertainty quantification of combustion models, by exploring the low-dimensional structure in the model parameter space. It identifies the subspace using the sensitivity information of the quantity of interest. It is historically challenging to compute the sensitivity for ignition delay. Thanks to recent advances in the sensitivity algorithms and the auto-differentiation in Arrhenius.jl, we are now able to compute the sensitivity quite efficiently.

sensBVP

The core functionally is the function of sensBVP_mthread(ts, pred, p) located in the file sensitivity.jl. It exploits following computational techniques:

• auto-differentiation
• banded matrix
• multi-thread paralleliration
• sensBVP method

The following plot shows the Eigen spectrum and summary plot with sensitivities calculated by sensBVP method.

• n-heptane (631 species 4846 reactions)

  4846-parameters is probably the most complex mechanism uncertainty quantification that existing. It takes 14 hours for 85 samples on 16-threads workstation.

• n-heptane (41 species 168 reactions)

• methane (53 species 325 reactions)

• hydrogen

sensBF

Sensitivity can also be calculated by brute-forece method, which is also implemented in sensBF_mthreads function. To obtain active subspace, one can only solve sensitivities for sensitive or important reactions, when using brute-force method.

The following plot shows the Eigen spectrum for the H2 model under 1200 K, 10 atm, equivalence ratio of one, with sensitivities calculated by brute-force method.

Get started

Install all relevent packages imported in header.jl and run main.jl. Specify the fuel you want to run at input.yaml

Roadmap

• Two-stages pipleline: select active parameters with local sensitivities and then compute active subspace within active variables. This could greatly reduce the computational cost of evaluating the parameter Jacobian and the cost of solving the linear systems. (Easy)

• Exploiting the sparsity of the two Jacobians, especially the parameter Jacobian, which is very sparse for large mechanisms. (Medium)

• Investigate the downsampling straightgies and the effect of ignition temperature (Easy)

References

active subspace

• Ji, Weiqi, Zhuyin Ren, Youssef Marzouk, and Chung K. Law. "Quantifying kinetic uncertainty in turbulent combustion simulations using active subspaces." Proceedings of the Combustion Institute 37, no. 2 (2019): 2175-2182.
• Ji, Weiqi, Jiaxing Wang, Olivier Zahm, Youssef M. Marzouk, Bin Yang, Zhuyin Ren, and Chung K. Law. "Shared low-dimensional subspaces for propagating kinetic uncertainty to multiple outputs." Combustion and Flame 190 (2018): 146-157.
• Su, Xingyu, Weiqi Ji, and Zhuyin Ren. "Uncertainty analysis in mechanism reduction via active subspace and transition state analyses." Combustion and Flame 227 (2021): 135-146.

Sensitiivty of ignition delay

• Gururajan, Vyaas, and Fokion N. Egolfopoulos. "Direct sensitivity analysis for ignition delay times." Combustion and Flame 209 (2019): 478-480.[sensBVP method]

• Ji, Weiqi, Zhuyin Ren, and Chung K. Law. "Evolution of sensitivity directions during autoignition." Proceedings of the Combustion Institute 37, no. 1 (2019): 807-815.

Auto-differentiation

• Revels, Jarrett, Miles Lubin, and Theodore Papamarkou. "Forward-mode automatic differentiation in Julia." arXiv preprint arXiv:1607.07892 (2016).