We leverage the computational singular perturbation (CSP) theory to develop an adaptive time-integration scheme for stiff chemistry based on a local, projection-based, reduced order model (ROM) freed of the fast time-scales. Its construction is such that artificial neural networks (ANN) can be plugged-in as cheap surrogates of the local projection basis, which is a state function, to alleviate the computational cost, without sacrificing the geometrical and physical foundation of the method. In fact, the solver relies on the synthetic basis in place of the more expensive on-the-fly calculated basis, i.e. the eigenvectors of the Jacobian matrix of the chemical source term, to define the local slow invariant manifold (SIM) and the projection matrix, then integrates explicitly the projected, i.e., non-stiff, chemical source term. We explore the feasibility of the ANN-accelerated CSP solver by training a set of ANNs to predict the projection basis vectors given the local chemical composition in a hydrogen/air homogeneous reactor problem. To enhance the smoothness of the basis vectors and reduce the reconstruction error, we introduce a constrained Jacobian formulation which removes the state heterogeneity due to the presence of temperature along with chemical species, and takes the derivatives enforcing the absolute enthalpy conservation. The test problem highlights the robustness of this ANN approach, arising from the relatively low requirements on the basis accuracy with respect to the requested integration accuracy.

An adaptive time-integration scheme for stiff chemistry based on computational singular perturbation and artificial neural networks / Malpica Galassi, Riccardo; Ciottoli, Pietro Paolo; Valorani, Mauro; Im, HONG GEUN. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - 451:(2022). [10.1016/j.jcp.2021.110875]

An adaptive time-integration scheme for stiff chemistry based on computational singular perturbation and artificial neural networks

Malpica Galassi, Riccardo
Primo
Membro del Collaboration Group
;
Ciottoli, Pietro Paolo
Secondo
Membro del Collaboration Group
;
Valorani, Mauro
Penultimo
Membro del Collaboration Group
;
Im, Hong G.
Ultimo
Membro del Collaboration Group
2022

Abstract

We leverage the computational singular perturbation (CSP) theory to develop an adaptive time-integration scheme for stiff chemistry based on a local, projection-based, reduced order model (ROM) freed of the fast time-scales. Its construction is such that artificial neural networks (ANN) can be plugged-in as cheap surrogates of the local projection basis, which is a state function, to alleviate the computational cost, without sacrificing the geometrical and physical foundation of the method. In fact, the solver relies on the synthetic basis in place of the more expensive on-the-fly calculated basis, i.e. the eigenvectors of the Jacobian matrix of the chemical source term, to define the local slow invariant manifold (SIM) and the projection matrix, then integrates explicitly the projected, i.e., non-stiff, chemical source term. We explore the feasibility of the ANN-accelerated CSP solver by training a set of ANNs to predict the projection basis vectors given the local chemical composition in a hydrogen/air homogeneous reactor problem. To enhance the smoothness of the basis vectors and reduce the reconstruction error, we introduce a constrained Jacobian formulation which removes the state heterogeneity due to the presence of temperature along with chemical species, and takes the derivatives enforcing the absolute enthalpy conservation. The test problem highlights the robustness of this ANN approach, arising from the relatively low requirements on the basis accuracy with respect to the requested integration accuracy.
combustion; multi-scale dynamical systems; model reduction; slow invariant manifold; Autoignition
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An adaptive time-integration scheme for stiff chemistry based on computational singular perturbation and artificial neural networks / Malpica Galassi, Riccardo; Ciottoli, Pietro Paolo; Valorani, Mauro; Im, HONG GEUN. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - 451:(2022). [10.1016/j.jcp.2021.110875]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1594755
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