%0 Generic %1 kelly2020learning %A Kelly, Jacob %A Bettencourt, Jesse %A Johnson, Matthew James %A Duvenaud, David %D 2020 %K deep-implicit-learning from:adulny neural-ode %T Learning Differential Equations that are Easy to Solve %U http://arxiv.org/abs/2007.04504 %X 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.

@misc{kelly2020learning, abstract = {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.}, added-at = {2021-03-26T12:02:28.000+0100}, author = {Kelly, Jacob and Bettencourt, Jesse and Johnson, Matthew James and Duvenaud, David}, biburl = {https://www.bibsonomy.org/bibtex/29e2a50f9d2b4e897018292299587be5a/adulny}, description = {[2007.04504] Learning Differential Equations that are Easy to Solve}, interhash = {e8fd802e0240e7969e0e57ab7eecb682}, intrahash = {9e2a50f9d2b4e897018292299587be5a}, keywords = {deep-implicit-learning from:adulny neural-ode}, note = {cite arxiv:2007.04504}, timestamp = {2021-03-26T12:02:28.000+0100}, title = {Learning Differential Equations that are Easy to Solve}, url = {http://arxiv.org/abs/2007.04504}, year = 2020 }