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.

Software To solve ODE initial value problems numerically, we use the implicit Adams method implemented in LSODE and VODE and interfaced through the package. Being an implicit method, it has better guarantees than explicit methods such as Runge-Kutta but requires solving a nonlinear optimization problem at every step.

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  Software, Differential, Solving, Equations, Ordinary, Neural, Neural ordinary differential equations

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