Compositional neural-network modeling of complex analog circuits

We introduce CompNN, a compositional method for the construction of a neural-network (NN) capturing the dynamic behavior of a complex analog multiple-input multiple-output (MIMO) system. CompNN first learns for each input/output pair (i, j), a small-sized nonlinear auto-regressive neural network with exogenous input (NARX) representing the transfer-function h
_ij
. The training dataset is generated by varying input i of the MIMO, only. Then, for each output j, the transfer functions h
_ij
are combined by a time-delayed neural network (TDNN) layer, f
_j
. The training dataset for f
_j
is generated by varying all MIMO inputs. The final output is f = (f
₁
, ..., f
_n
). The NNs parameters are learned using Levenberg-Marquardt back-propagation algorithm. We apply CompNN to learn an NN abstraction of a CMOS band-gap voltage-reference circuit (BGR). First, we learn the NARX NNs corresponding to trimming, load-jump and line-jump responses of the circuit. Then, we recompose the outputs by training the second layer TDNN structure. We demonstrate the performance of our learned NN in the transient simulation of the BGR by reducing the simulation-time by a factor of 17 compared to the transistor-level simulations. CompNN allows us to map particular parts of the NN to specific behavioral features of the BGR. To the best of our knowledge, CompNN is the first method to learn the NN of an analog integrated circuit (MIMO system) in a compositional fashion.