Evaluating Liquid Neural Networks on a Behavioral Cloning Quadrotor Control Problem

Abstract

This paper evaluates Liquid Neural Networks (LNNs) on an energy-optimal quadrotor control benchmark formulated as a behavioral cloning problem. Several LNN variants, including ordinary differential equation (ODE)-based formulations and closed-form continuous-time (CfC) models, are compared against classical recurrent architectures and a reference multilayer perceptron (MLP). Results show that ODE-based LNNs achieve the strongest closed-loop performance among recurrent models, demonstrating robustness to discretization effects and partial observability while maintaining stable behavior across network sizes. In contrast, CfC variants provide competitive performance under nominal conditions but degrade more significantly under scaling, revealing limitations of its closed-form approximation. While the MLP baseline achieves superior steady-state accuracy and lowest inference latency, it is less reliable under degraded observability and numerical perturbations. Overall, the results emphasize complementary trade-offs between continuous-time recurrent models and feedforward architectures, suggesting that LNNs are particularly well-suited for control tasks involving temporal uncertainty or limited state information.