Anamnesic Neural Differential Equations with Orthogonal Polynomial
Projections
- URL: http://arxiv.org/abs/2303.01841v1
- Date: Fri, 3 Mar 2023 10:49:09 GMT
- Title: Anamnesic Neural Differential Equations with Orthogonal Polynomial
Projections
- Authors: Edward De Brouwer and Rahul G. Krishnan
- Abstract summary: We propose PolyODE, a formulation that enforces long-range memory and preserves a global representation of the underlying dynamical system.
Our construction is backed by favourable theoretical guarantees and we demonstrate that it outperforms previous works in the reconstruction of past and future data.
- Score: 6.345523830122166
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Neural ordinary differential equations (Neural ODEs) are an effective
framework for learning dynamical systems from irregularly sampled time series
data. These models provide a continuous-time latent representation of the
underlying dynamical system where new observations at arbitrary time points can
be used to update the latent representation of the dynamical system. Existing
parameterizations for the dynamics functions of Neural ODEs limit the ability
of the model to retain global information about the time series; specifically,
a piece-wise integration of the latent process between observations can result
in a loss of memory on the dynamic patterns of previously observed data points.
We propose PolyODE, a Neural ODE that models the latent continuous-time process
as a projection onto a basis of orthogonal polynomials. This formulation
enforces long-range memory and preserves a global representation of the
underlying dynamical system. Our construction is backed by favourable
theoretical guarantees and in a series of experiments, we demonstrate that it
outperforms previous works in the reconstruction of past and future data, and
in downstream prediction tasks.
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