2020/10/17 by Roger Alexander Müller, Müller, Roger Alexander, Jonathan Laflamme-Janssen +5 · 1 voice
Computer Science · Physics and Astronomy · #Computational Physics and Python Applications #Gaussian Processes and Bayesian Inference #Model Reduction and Neural Networks #Modeling and Simulation Systems #cs.AI #cs.LG
paper · pdf · doi:10.48550/arxiv.2010.11270
openalex publication_date 2020/10/17 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
In this article we address the question whether it is possible to learn the\ndifferential equations describing the physical properties of a dynamical\nsystem, subject to non-conservative forces, from observations of its realspace\ntrajectory(ies) only. We introduce a network that incorporates a difference\napproximation for the second order derivative in terms of residual connections\nbetween convolutional blocks, whose shared weights represent the coefficients\nof a second order ordinary differential equation. We further combine this\nsolver-like architecture with a convolutional network, capable of learning the\nrelation between trajectories of coupled oscillators and therefore allows us to\nmake a stable forecast even if the system is only partially observed. We\noptimize this map together with the solver network, while sharing their\nweights, to form a powerful framework capable of learning the complex physical\nproperties of a dissipative dynamical system.\n