  Insect flight is a strongly nonlinear and actuated dynamical system. As such,
strategies for understanding its control have typically relied on either
model-based methods or linearizations thereof. Here we develop a framework that
combines model predictive control on an established flight dynamics model and
deep neural networks (DNN) to create an efficient method for solving the
inverse problem of flight control. We turn to natural systems for inspiration
since they inherently demonstrate network pruning with the consequence of
yielding more efficient networks for a specific set of tasks. This bio-inspired
approach allows us to leverage network pruning to optimally sparsify a DNN
architecture in order to perform flight tasks with as few neural connections as
possible, however, there are limits to sparsification. Specifically, as the
number of connections falls below a critical threshold, flight performance
drops considerably. We develop sparsification paradigms and explore their
limits for control tasks. Monte Carlo simulations also quantify the statistical
distribution of network weights during pruning given initial random weights of
the DNNs. We demonstrate that on average, the network can be pruned to retain
approximately 7% of the original network weights, with statistical
distributions quantified at each layer of the network. Overall, this work shows
that sparsely connected DNNs are capable of predicting the forces required to
follow flight trajectories. Additionally, sparsification has sharp performance
limits.

Quantitative Methods