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Paper · 2206.04843 · 2022

Neural Laplace: Learning diverse classes of differential equations in the Laplace domain

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 13 functions out of this paper's own repositories and ran 10 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
samholt/neurallaplace canonical 7 of 9
vanderschaarlab/neurallaplace canonical 3 of 4
FunctionStatusWhere it lives
basic_collate_fn Ran samholt/neurallaplace/experiments/baseline_models/data_utils.py
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create_classifier Ran samholt/neurallaplace/experiments/baseline_models/ode_models.py
code served (permissive licence) · get_code("fc9a64735be0911c")
dde_ramp_loading_time_sol Ran samholt/neurallaplace/experiments/datasets.py
code served (permissive licence) · get_code("55f4cfe6a29a744b")
dde_ramp_loading_time_sol Ran vanderschaarlab/neurallaplace/experiments/datasets.py
code served (permissive licence) · get_code("b633769ffe59821d")
get_device Ran samholt/neurallaplace/experiments/baseline_models/data_utils.py
code served (permissive licence) · get_code("012fddf9316ca0e7")
integro_de Ran samholt/neurallaplace/experiments/datasets.py
code served (permissive licence) · get_code("ce33d657a3e3f286")
split_last_dim Ran vanderschaarlab/neurallaplace/experiments/baseline_models/data_utils.py
code served (permissive licence) · get_code("132869b5387d420e")
split_last_dim Ran samholt/neurallaplace/experiments/baseline_models/data_utils.py
code served (permissive licence) · get_code("20591e4d72a66e22")
stiffvdp Ran samholt/neurallaplace/experiments/datasets.py
code served (permissive licence) · get_code("4a27044555a5bac2")
stiffvdp Ran vanderschaarlab/neurallaplace/experiments/datasets.py
code served (permissive licence) · get_code("0bedd0e434f01ebf")
create_LatentODE_model Not yet run samholt/neurallaplace/experiments/baseline_models/ode_models.py
code served (permissive licence) · get_code("08c0cfca21c35cc8")
create_LatentODE_model Not yet run vanderschaarlab/neurallaplace/experiments/baseline_models/ode_models.py
code served (permissive licence) · get_code("3641153c7a8fad48")
get_mask Not yet run samholt/neurallaplace/experiments/baseline_models/ode_models.py
code served (permissive licence) · get_code("b97f87bade2026b7")

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Abstract

Neural Ordinary Differential Equations model dynamical systems with ODEs learned by neural networks. However, ODEs are fundamentally inadequate to model systems with long-range dependencies or discontinuities, which are common in engineering and biological systems. Broader classes of differential equations (DE) have been proposed as remedies, including delay differential equations and integro-differential equations. Furthermore, Neural ODE suffers from numerical instability when modelling stiff ODEs and ODEs with piecewise forcing functions. In this work, we propose Neural Laplace, a unified framework for learning diverse classes of DEs including all the aforementioned ones. Instead of modelling the dynamics in the time domain, we model it in the Laplace domain, where the history-dependencies and discontinuities in time can be represented as summations of complex exponentials. To make learning more efficient, we use the geometrical stereographic map of a Riemann sphere to induce more smoothness in the Laplace domain. In the experiments, Neural Laplace shows superior performance in modelling and extrapolating the trajectories of diverse classes of DEs, including the ones with complex history dependency and abrupt changes.

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