Monotone systems, originating from real-world (e.g., biological or chemical)
applications, are a class of dynamical systems that preserves a partial order
of system states over time. In this work, we introduce a feedforward neural
networks (FNNs)-based method to learn the dynamics of unknown stable nonlinear
monotone systems. We propose the use of nonnegative neural networks and batch
normalization, which in general enables the FNNs to capture the monotonicity
conditions without reducing the expressiveness. To concurrently ensure
stability during training, we adopt an alternating learning method to
simultaneously learn the system dynamics and corresponding Lyapunov function,
while exploiting monotonicity of the system.~The combination of the
monotonicity and stability constraints ensures that the learned dynamics
preserves both properties, while significantly reducing learning errors.
Finally, our techniques are evaluated on two complex biological and chemical
systems