Neural Lagrangian Schr\"odinger bridge
- URL: http://arxiv.org/abs/2204.04853v1
- Date: Mon, 11 Apr 2022 03:32:17 GMT
- Title: Neural Lagrangian Schr\"odinger bridge
- Authors: Takeshi Koshizuka and Issei Sato
- Abstract summary: We study population dynamics using continuous normalizing flows (CNFs) and dynamic optimal transport.
We formulate the Lagrangian Schr"odinger bridge (LSB) problem and propose to solve it using neural SDE with regularization.
Our experiments show that our solution to the LSB problem can approximate the dynamics at the population level.
- Score: 25.157282476221482
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Population dynamics is the study of temporal and spatial variation in the
size of populations of organisms and is a major part of population ecology. One
of the main difficulties in analyzing population dynamics is that we can only
obtain observation data with coarse time intervals from fixed-point
observations due to experimental costs or other constraints. Recently, modeling
population dynamics by using continuous normalizing flows (CNFs) and dynamic
optimal transport has been proposed to infer the expected trajectory of samples
from a fixed-point observed population. While the sample behavior in CNF is
deterministic, the actual sample in biological systems moves in an essentially
random yet directional manner. Moreover, when a sample moves from point A to
point B in dynamical systems, its trajectory is such that the corresponding
action has the smallest possible value, known as the principle of least action.
To satisfy these requirements of the sample trajectories, we formulate the
Lagrangian Schr\"odinger bridge (LSB) problem and propose to solve it
approximately using neural SDE with regularization. We also develop a model
architecture that enables faster computation. Our experiments show that our
solution to the LSB problem can approximate the dynamics at the population
level and that using the prior knowledge introduced by the Lagrangian enables
us to estimate the trajectories of individual samples with stochastic behavior.
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