# dlode45

Deep learning solution of nonstiff ordinary differential equation (ODE)

*Since R2021b*

## Syntax

## Description

The neural ordinary differential equation (ODE) operation returns the solution of a specified ODE.

The `dlode45`

function applies the neural ODE operation to `dlarray`

data.
Using `dlarray`

objects makes working with high
dimensional data easier by allowing you to label the dimensions. For example, you can label
which dimensions correspond to spatial, time, channel, and batch dimensions using the
`"S"`

, `"T"`

, `"C"`

, and
`"B"`

labels, respectively. For unspecified and other dimensions, use the
`"U"`

label. For `dlarray`

object functions that operate
over particular dimensions, you can specify the dimension labels by formatting the
`dlarray`

object directly, or by using the `DataFormat`

option.

**Note**

This function applies the neural ODE operation to `dlarray`

data in
deep learning models defined as functions or in custom layer functions. If you want to
apply the neural ODE operation within a `dlnetwork`

object or `Layer`

array, use
`neuralODELayer`

.
To solve ODEs for other workflows, use `ode45`

.

specifies additional options using one or more name-value arguments. For example, `Y`

= dlode45(___,`Name=Value`

)```
Y
= dlode45(odefun,tspan,Y0,theta,GradientMode="adjoint")
```

integrates the system of
ODEs given by `odefun`

and computes gradients by solving the associated
adjoint ODE system.

## Examples

## Input Arguments

## Output Arguments

## Algorithms

## References

[1] Chen, Ricky T. Q., Yulia Rubanova, Jesse Bettencourt, and David Duvenaud. “Neural Ordinary Differential Equations.” Preprint, submitted June 19, 2018. https://arxiv.org/abs/1806.07366.

[2] Dormand, J. R., and P. J. Prince.
“A Family of Embedded Runge-Kutta Formulae.” *Journal of Computational and Applied
Mathematics* 6, no. 1 (March 1980): 19–26. https://doi.org/10.1016/0771-050X(80)90013-3.

[3] Shampine, Lawrence F., and Mark W. Reichelt. “The MATLAB ODE Suite.” SIAM Journal on Scientific Computing 18, no. 1 (January 1997): 1–22. https://doi.org/10.1137/S1064827594276424.

[4] Kidger, Patrick, Ricky T. Q. Chen, and Terry Lyons. “‘Hey, That’s Not an ODE’: Faster ODE Adjoints via Seminorms.” arXiv, May 10, 2021. https://doi.org/10.48550/arXiv.2009.09457.

## Extended Capabilities

## Version History

**Introduced in R2021b**