Corpus ID: 220424445

Learning Differential Equations that are Easy to Solve

@article{Kelly2020LearningDE,
  title={Learning Differential Equations that are Easy to Solve},
  author={Jacob Kelly and J. Bettencourt and M. Johnson and D. Duvenaud},
  journal={ArXiv},
  year={2020},
  volume={abs/2007.04504}
}
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… Expand
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References

SHOWING 1-10 OF 47 REFERENCES
Scalable Gradients for Stochastic Differential Equations
How to train your neural ODE
Neural Ordinary Differential Equations
Augmented Neural ODEs
Neural Differential Equations for Single Image Super-resolution
Latent Ordinary Differential Equations for Irregularly-Sampled Time Series
FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models
Deep Neural Networks Motivated by Partial Differential Equations
Sensitivity and Generalization in Neural Networks: an Empirical Study
...
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4
5
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