We present a continuous modelling framework for simulating the dynamics of metabolic-regulatory networks (MRNs), designed to overcome the scalability limitations of traditional hybrid models. Hybrid approaches, often based on Boolean logic to represent regulatory interactions, become computationally intractable as the number of regulatory proteins increases, due to an exponential growth in discrete modes and transitions. To address this, our framework replaces discrete logic with smooth Hill functions, enabling the approximation of switch-like regulatory behaviour without introducing combinatorial complexity. This continuous formulation maintains the biological interpretability of hybrid models while greatly enhancing computational efficiency. Parameter estimation, a common bottleneck in continuous models, is simplified in our approach by requiring fewer kinetic parameters than typical hybrid models. We further employ sparse-based system identification, a data-driven technique that efficiently infers network dynamics by selecting a minimal set of nonlinear terms. This method avoids exhaustive search procedures and yields interpretable kinetic models. Applied to MRNs, our framework demonstrates the ability to capture essential regulatory mechanisms with reduced complexity and improved scalability.

Dynamic Programming suffers from the curse of dimensionality due to large state and action spaces, a challenge further compounded by uncertainties in the environment. To mitigate these issue, we explore an off-policy based Temporal Difference Approximate Dynamic Programming approach that preserves contraction mapping when projecting the problem into a subspace of selected features, accounting for the probability distribution of the perturbed transition probability matrix. We further demonstrate how this Approximate Dynamic Programming approach can be implemented as a particular variant of the Temporal Difference learning algorithm, adapted for handling perturbations. To validate our theoretical findings, we provide a numerical example using a Markov Decision Process corresponding to a resource allocation problem.