DDE-Find: Learning Delay Differential Equations from Noisy, Limited Data
<|reference_start|>DDE-Find: Learning Delay Differential Equations from Noisy, Limited Data: Delay Differential Equations (DDEs) are a class of differential equations that can model diverse scientific phenomena. However, identifying the parameters, especially the time delay, that make a DDE's predictions match experimental results can be challenging. We introduce DDE-Find, a data-driven framework for learning a DDE's parameters, time delay, and initial condition function. DDE-Find uses an adjoint-based approach to efficiently compute the gradient of a loss function with respect to the model parameters. We motivate and rigorously prove an expression for the gradients of the loss using the adjoint. DDE-Find builds upon recent developments in learning DDEs from data and delivers the first complete framework for learning DDEs from data. Through a series of numerical experiments, we demonstrate that DDE-Find can learn DDEs from noisy, limited data.<|reference_end|>
@article{stephany2024dde-find:,
    title={DDE-Find: Learning Delay Differential Equations from Noisy, Limited Data},
    author={Robert Stephany},
    journal={arXiv preprint arXiv:2405.02661},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.02661},
    primaryClass={cs.LG}
}