  We propose a method for training ordinary differential equations by using a
control-theoretic Lyapunov condition for stability. Our approach, called
LyaNet, is based on a novel Lyapunov loss formulation that encourages the
inference dynamics to converge quickly to the correct prediction.
Theoretically, we show that minimizing Lyapunov loss guarantees exponential
convergence to the correct solution and enables a novel robustness guarantee.
We also provide practical algorithms, including one that avoids the cost of
backpropagating through a solver or using the adjoint method. Relative to
standard Neural ODE training, we empirically find that LyaNet can offer
improved prediction performance, faster convergence of inference dynamics, and
improved adversarial robustness. Our code available at
https://github.com/ivandariojr/LyapunovLearning .
