Balanced truncation for model reduction of biological oscillators

Model reduction is a central problem in mathematical biology. Reduced order models enable modeling of a biological system at different levels of complexity and the quantitative analysis of its properties, like sensitivity to parameter variations and resilience to exogenous perturbations. However, available model reduction methods often fail to capture a diverse range of nonlinear behaviors observed in biology, such as multistability and limit cycle oscillations. The paper addresses this need using differential analysis. This approach leads to a nonlinear enhancement of classical balanced truncation for biological systems whose behavior is not restricted to the stability of a single equilibrium. Numerical results suggest that the proposed framework may be relevant to the approximation of classical models of biological systems.

Comparison of two model reduction approaches of an industrial drying process

Dynamic models have proven to be helpful for determining the residual water content in combustible biomass. However, these models often require partial differential equations, which render simulations impracticable when several thousand particles need to be considered, such as in the drying of wood chips. Reduced-order models help to overcome this problem. We compare proper orthogonal decomposition (POD) based to balanced truncation based reduced-order models. Both reduced models are lean enough for an application to systems with many particles, but the model based on balanced truncation shows more accurate results.

Model reduction of unstable systems based on balanced truncation algorithm

Model reduction of a system is an approximation of a higher-order system to a lower-order system while the dynamic behavior of the system is almost unchanged. In this paper, we will discuss model order reduction (MOR) strategies for unstable systems, in which the method based on the balanced truncation algorithm will be focused on. Since each MOR algorithm has its strengths and weakness, practical applications should be suitable for each specific requirement. Simulation results will demonstrate the correctness of the algorithms.