Algorithm 1.

Overview over the deep learning algorithm described in this section

1:	Load observed data
2:	Initialize deep learning models, optimization model, learning rate strategy
3:	for n_epochs do
4:	$\text{mean\_loss}\leftarrow 0$
5:	while $\text{t}$, $\overrightarrow{x}=\text{load\_batch}()$ do
6:	if ${\sigma }_{\text{Aux}}$ is True then
7:	$t\leftarrow \left[0\right]+t$
8:	$\overrightarrow{x}\leftarrow [\overrightarrow{x}(t=0)]+\overrightarrow{x}$
9:	end if
10:	$\hat{\overrightarrow{x}}=\text{model.predict}(\mathrm{t})$
11:	Compute ${ℒ}_{Data}$	▷ Equation 27
12:	Compute ${ℒ}_{ODE}$ iff ${\sigma }_{\mathrm{O}\mathrm{D}\mathrm{E}}$	▷ Equation 28
13:	Compute ${ℒ}_{Aux}$ iff ${\sigma }_{\text{Aux}}$	▷ Equation 29
14:	Compute ${ℒ}_{\overrightarrow{\hat{p}}}$, ${ℒ}_{\overrightarrow{\hat{x}}}$ iff ${\sigma }_{\overrightarrow{\hat{p}}}$	▷ Equations 30,31
15:	$ℒ\leftarrow {\lambda }_{\text{Data}}{ℒ}_{Data}+{\sigma }_{ODE}{\lambda }_{\mathrm{O}\mathrm{D}\mathrm{E}}{ℒ}_{ODE}+{\sigma }_{\text{Aux}}{\lambda }_{\text{Aux}}{ℒ}_{Aux}{\sigma }_{\hat{x}}{ℒ}_{\hat{x}}+{\sigma }_p{ℒ}_p$
16	Compute ${\nabla }_{\overrightarrow{\theta }}ℒ$
17:	if clip_gradients then
18	clip_gradients$({\nabla }_{\overrightarrow{\theta }}ℒ)$
19:	end if
20:	optimization_step()
21:	$\text{mean\_loss}\leftarrow \text{mean\_loss}\mathrm{s}+ℒ$
22:	end while
23:	register_lr(mean_loss)	▷ Reduces LR if necessary
24:	end for
25:	Save results