Learning second order coupled differential equations that are subject to non-conservative forces
This work addresses the challenge of modeling complex physical systems with non-conservative forces, which is incremental as it builds on existing methods for learning differential equations.
The authors tackled the problem of learning second-order coupled differential equations for dissipative dynamical systems from observed trajectories, introducing a network that combines a solver-like architecture with a convolutional network to enable stable forecasting even with partial observations.
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.