Model reduction of chemical kinetics via decomposition: SPVF theory and ILDM-based initial data projection

This study outlines and discusses model reduction problems. The concept of Singularly Perturbed Vector Fields (SPVF) is revisited as a framework for handling the decomposition of motions and, in particular, for addressing the fundamental problem of initial-data consistency in reduced models. This issue arises because the initial conditions generally do not lie on the slow invariant manifold that approximates the reduced system. To address this, this study demonstrates how the method of Intrinsic Low-Dimensional Manifolds (ILDMs) can be employed both to approximate the slow manifold and to generate consistent initial data. Two classical benchmark examples in model reduction theory are examined to verify and discuss the approach. The Lindemann mechanism is used to illustrate how SPVF theory reconciles the standard asymptotic limits and thereby captures both pressure dependence and variations in reaction order. The Michaelis–Menten model serves as a key example where standard reduction approaches–such as QSSA and PEA–may fail under certain asymptotic conditions. The SPVF framework provides a systematic way to understand these limitations by clarifying the asymptotic structure and its parameter dependencies. Meanwhile the ILDM method not only offers an efficient way to approximate the slow manifold but also supplies consistent initial data projection procedure, ensuring a physically and mathematically sound reduced system.