1 research outputs found
SNODE: Spectral Discretization of Neural ODEs for System Identification
This paper proposes the use of spectral element methods
\citep{canuto_spectral_1988} for fast and accurate training of Neural Ordinary
Differential Equations (ODE-Nets; \citealp{Chen2018NeuralOD}) for system
identification. This is achieved by expressing their dynamics as a truncated
series of Legendre polynomials. The series coefficients, as well as the network
weights, are computed by minimizing the weighted sum of the loss function and
the violation of the ODE-Net dynamics. The problem is solved by coordinate
descent that alternately minimizes, with respect to the coefficients and the
weights, two unconstrained sub-problems using standard backpropagation and
gradient methods. The resulting optimization scheme is fully time-parallel and
results in a low memory footprint. Experimental comparison to standard methods,
such as backpropagation through explicit solvers and the adjoint technique
\citep{Chen2018NeuralOD}, on training surrogate models of small and
medium-scale dynamical systems shows that it is at least one order of magnitude
faster at reaching a comparable value of the loss function. The corresponding
testing MSE is one order of magnitude smaller as well, suggesting
generalization capabilities increase.Comment: Published as a conference paper at ICLR 202