Learning second order coupled differential equations that are subject to non-conservative forces

• URL: http://arxiv.org/abs/2010.11270v2
• Date: Thu, 29 Jul 2021 11:33:52 GMT
• Title: Learning second order coupled differential equations that are subject to non-conservative forces
• Authors: Roger Alexander M\"uller, Jonathan Laflamme-Janssen, Jaime Camacaro, Carolina Bessega
• Abstract summary: We introduce a network that incorporates a difference approximation for the second order derivative in terms of residual connections between convolutional blocks. We optimize this map together with the solver network, while sharing their weights, to form a powerful framework capable of learning the complex physical properties of a dissipative dynamical system.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this article we address the question whether it is possible to learn the differential equations describing the physical properties of a dynamical system, subject to non-conservative forces, from observations of its realspace trajectory(ies) only. We introduce a network that incorporates a difference approximation for the second order derivative in terms of residual connections between convolutional blocks, whose shared weights represent the coefficients of a second order ordinary differential equation. We further combine this solver-like architecture with a convolutional network, capable of learning the relation between trajectories of coupled oscillators and therefore allows us to make a stable forecast even if the system is only partially observed. We optimize this map together with the solver network, while sharing their weights, to form a powerful framework capable of learning the complex physical properties of a dissipative dynamical system.

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