We propose a physics-informed neural network (PINN) framework for the discovery of slow invariant manifolds (SIMs) in general fast/slow dynamical systems described by ordinary differential equations. Unlike existing machine learning approaches that construct black-box surrogate models through regression and/or rely on a priori identification of fast and slow variables, our method simultaneously decomposes the vector field into its fast and slow components and provides an explicit functional representation of the SIM. This decomposition is achieved by learning a transformation of the state variables that separates them into fast and slow coordinates. This enables the derivation of a SIM functional expressed explicitly in terms of the fast variables. The SIM is obtained by solving the invariance equation arising from Geometric Singular Perturbation Theory (GSPT) using a single-layer feedforward neural network trained with symbolic differentiation. We evaluate the performance of the proposed PINN-based approach on three benchmark systems: the Michaelis-Menten kinetics, the target-mediated drug disposition (TMDD) model, and a fully competitive substrate-inhibitor (fCSI) mechanism. We also compare our results against classical GSPT-based reduction methods, including the quasi-steady-state approximation (QSSA), the partial equilibrium approximation (PEA), and the computational singular perturbation (CSP) method with one and two iterations. Our findings demonstrate that the proposed PINN framework yields SIM approximations with accuracy comparable to or exceeding that of traditional methods, particularly near the boundaries of the SIM, where classical approaches tend to lose precision. REFERENCES [1] Patsatzis, D., Fabiani, G., Russo, L. and Siettos, C., 2024. Slow invariant manifolds of singularly perturbed systems via physics-informed machine learning. SIAM Journal on Scientific Computing, 46(4), C297-C322. [2] Patsatzis, D. G., Russo, L., & Siettos, C., 2024. Slow Invariant Manifolds of Fast-Slow Systems of ODEs with Physics-Informed Neural Networks. SIAM Journal on Applied Dynamical Systems 23 (4), 3077-3122