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2 results on '"multi-scale dynamical systems"'

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

Author

Malpica Galassi, Riccardo, Ciottoli, Pietro Paolo, Valorani, Mauro, and Im, Hong G.

Subjects
*TIME integration scheme, *ARTIFICIAL neural networks, *SINGULAR perturbations, *COMPUTATIONAL chemistry, *INVARIANT manifolds
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. • Stiffness in kinetics ODE can be removed by projecting out the fast timescales. • The CSP solver explicitly integrates the local non-stiff (slow) reduced order model. • The slow system is evolved with a pace larger than that provided by implicit solvers. • ANNs are employed to provide a surrogate model for the projection basis. • The integration scheme is robust to the basis reconstruction errors. [ABSTRACT FROM AUTHOR]

Published
2022
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2. Glycolysis in saccharomyces cerevisiae: Algorithmic exploration of robustness and origin of oscillations.

Author

Kourdis, Panayotis D. and Goussis, Dimitris A.

Subjects
*GLYCOLYSIS, *SACCHAROMYCES cerevisiae, *ROBUST control, *OSCILLATIONS, *DYNAMICAL systems, *INVARIANT manifolds
Abstract

Abstract: The glycolysis pathway in saccharomyces cerevisiae is considered, modeled by a dynamical system possessing a normally hyperbolic, exponentially attractive invariant manifold, where it exhibits limit cycle behavior. The fast dissipative action simplifies considerably the exploration of the system’s robustness, since its dynamical properties are mainly determined by the slow dynamics characterizing the motion along the limit cycle on the slow manifold. This manifold expresses a number of equilibrations among components of the cellular mechanism that have a non-negligible projection in the fast subspace, while the motion along the slow manifold is due to components that have a non-negligible projection in the slow subspace. The characteristic time scale of the limit cycle can be directly altered by perturbing components whose projection in the slow subspace contributes to its generation. The same effect can be obtained indirectly by perturbing components whose projection in the fast subspace participates in the generated equilibrations, since the slow manifold will thus be displaced and the slow dynamics must adjust. Along the limit cycle, the characteristic time scale exhibits successively a dissipative and an explosive nature (leading towards or away from a fixed point, respectively). Depending on their individual contribution to the dissipative or explosive nature of the characteristic time scale, the components of the cellular mechanism can be classified as either dissipative or explosive ones. Since dissipative/explosive components tend to diminish/intensify the oscillatory behavior, one would expect that strengthening a dissipative/explosive component will diminish/intensify the oscillations. However, it is shown that strengthening dissipative (explosive) components might lead the system to amplified oscillations (fixed point). By employing the Computational Singular Perturbation method, it is demonstrated that such a behavior is due to the constraints imposed by the slow manifold. [Copyright &y& Elsevier]

Published
2013
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