Abstract: An apparatus for solving time-continuous differential equations is disclosed. The apparatus includes a group of hybrid integrators interconnected to each other. Each one of the hybrid integrators includes an analog integrator, a conversion logic and multiple digital registers. The analog integrator generates an analog output, and the conversion logic along with the digital registers converts the analog output to a digital output. The analog output and the digital output are then combined to yield an integrated output. The integrated output is fed to the hybrid integrators within the group.

Abstract: An apparatus for solving time-continuous differential equations is disclosed. The apparatus includes a group of hybrid integrators interconnected to each other. Each one of the hybrid integrators includes an analog integrator, a conversion logic and multiple digital registers. The analog integrator generates an analog output, and the conversion logic along with the digital registers converts the analog output to a digital output. The analog output and the digital output are then combined to yield an integrated output. The integrated output is fed to the hybrid integrators within the group.

Abstract: The present invention is a fully connected feed forward network that includes at least one hidden layer 16. The hidden layer 16 includes nodes 20 in which the output of the node is fed back to that node as an input with a unit delay produced by a delay device 24 occurring in the feedback path 22 (local feedback). Each node within each layer also receives a delayed output (crosstalk) produced by a delay unit 36 from all the other nodes within the same layer 16. The node performs a transfer function operation based on the inputs from the previous layer and the delayed outputs. The network can be implemented as analog or digital or within a general purpose processor. Two teaching methods can be used: (1) back propagation of weight calculation that includes the local feedback and the crosstalk or (2) more preferably a feed forward gradient decent which immediately follows the output computations and which also includes the local feedback and the crosstalk.