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Neural Ordinary Differential Equations

Neural Ordinary Differential EquationsRicky T. Q. Chen*, Yulia Rubanova*, Jesse Bettencourt*, David DuvenaudUniversity of Toronto, Vector Institute AbstractWe introduce a new family of deep Neural network models. Instead of specifying adiscrete sequence of hidden layers, we parameterize the derivative of the hiddenstate using a Neural network. The output of the network is computed using a black-box Differential equation solver. These continuous-depth models have constantmemory cost, adapt their evaluation strategy to each input, and can explicitly tradenumerical precision for speed.

Algorithm 1 shows how to construct the necessary dynamics, and call an ODE solver to compute all gradients at once. Algorithm 1 Reverse-mode derivative of an ODE initial value problem Input: dynamics parameters θ, start time t0, stop time t1, final state z(t1), loss …

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