Autonomic communications aim at easing the burden of managing complex and dynamic networks, and designing adaptive, self-turning and self-stabilizing networks to provide much needed flexibility and functional scalability. With the ever-increasing number of multicast applications made recently, considerable efforts have been focused on the design of adaptive flow control schemes for autonomic multicast services. The main difficulties in designing an adaptive flow controller for autonomic multicast service are caused by heterogeneous multicast receivers, especially those with large propagation delays, since the feedback arriving at the source is somewhat outdated and can be harmful to the control operations.To tackle the preceding problem, this article describes a novel, adaptive, and autonomic multicast scheme, the so-called Proportional, Integrative, Derivative plus Neural Network (PIDNN) predictive technique, which consists of two components: the Proportional Integrative plus Derivative (PID) controller and the Back Propagation BP Neural Network (BPNN). In this integrated scheme, the PID controllers are located at the next upstream main branch nodes of the multicast receivers, and have explicit rate algorithms to regulate the receiving rates of the receivers; while the BPNN is located at the multicast source, and predicts the available bandwidth of those longer delay receivers to compute the expected rates of the longer delay receivers. The ultimate sending rate of the multicast source is the maximum of the aforesaid receiving rates that can be accommodated by its participating branches. This network-assisted property is different from the existing control schemes, in that the PIDNN controller can release the irresponsiveness of a multicast flow caused by those long propagation delays from the receivers. By using BPNN, this active scheme makes the control more responsive to the receivers with longer propagation delay. Thus the rate adaptation can be performed in a timely manner, for the sender to respond to network congestion quickly. We analyze the theoretical aspects of the proposed algorithm, show how the control mechanism can be used to design a controller to support multirate multicast transmission based on feedback of explicit rates, and verify this matching using simulations. Simulation results demonstrate that the proposed PIDNN controller avoids overflow of multicast traffic, and performs better than the existing scheme PNN [Tan et al, 2005] and the multicast schemes based on control theory. Moreover, it also performs well in the sense that it achieves high link utilization, quick response, good scalability, high unitary throughput, intra-session fairness and inter-session fairness.