In plain words: When a neural network defines how a system changes over time, simulating it gets slower as training goes on. A penalty on how wiggly the solution's derivatives are keeps the equations cheap to solve, cutting simulation time sharply with almost no loss in accuracy.
Abstract · Learning Differential Equations that are Easy to Solve
Differential equations parameterized by neural networks become expensive to solve numerically as training progresses. We propose a remedy that encourages learned dynamics to be easier to solve. Specifically, we introduce a differentiable surrogate for the time cost of standard numerical solvers, using higher-order derivatives of solution trajectories. These derivatives are efficient to compute with Taylor-mode automatic differentiation. Optimizing this additional objective trades model performance against the time cost of solving the learned dynamics. We demonstrate our approach by training substantially faster, while nearly as accurate, models in supervised classification, density estimation, and time-series modelling tasks.
Jacob Kelly, Jesse Bettencourt, Matthew James Johnson, David Duvenaud
arXiv:2007.04504 · cs.LG, stat.ML · submitted Jul 9, 2020 · updated Oct 22, 2020
abstract · pdf · html
https://github.com/verdverm/go-pge/raw/master/pge_gecco2013....
https://github.com/verdverm/pypge