A chaotic system with measurable state variables fewer than the degrees of freedom of the system is identified with the Artificial Neural Network (ANN) method combined with dynamic training. Instead of using the usual method of Sum of Square Errors (SSE), the identified models are validated with the return maps (embedded trajectories), the largest Lyapunov exponent, and the correlation dimension when there is no exogenous input, and bifurcation diagram when there is an exogenous input. This method is demonstrated for nonisothermal, irreversible, first-order, series reaction A -> B -> C in a CSTR.