id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
cord-248848-p7jv79ae	Lee, Kookjin	Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems	2020-10-28		.txt	text/plain	6965	424	53	We emphasize that our approach is closely related to [63] , where neural networks are trained to approximate the action of the first-order time-integration scheme applied to latent dynamics and, at each time step, the neural networks take a set of problem-specific parameters as well as reduced state as an input. PNODEs still can learn multiple trajectories, which are characterized by the ODE parameters, even if the same initial states are given for different ODE parameters, which is not achievable with NODEs. Furthermore, the proposed framework is significantly simpler than the common neural network settings for NODEs when they are used to learn latent dynamics: the sequence-to-sequence architectures as in [9, 61, 74, 45, 46] , which require that a (part of) sequence is fed into the encoder network to produce a context vector, which is then fed into the NODE decoder network as an initial condition.	./cache/cord-248848-p7jv79ae.txt	./txt/cord-248848-p7jv79ae.txt