Trajectories

Determistic Trajectory with Euler's method

Simulates the deterministic trajectory of the cells using Euler's method: $$ \operatorname{state}(t + \Delta t) = \operatorname{state}(t) + {d \operatorname{state} \over dt} \Delta t. $$

Parameters:

Name	Type	Description	Default
`cells`	`CellPopulation`	CellPopulation.	required
`time_range`	`1D torch.Tensor`	Time points at which the cells state should be evaluated.	required

Returns:

Type	Description
`torch.Tensor`	torch.Tensor: Trajectory of shape (n_time_points, n_cells, n_genes, *state_dim)

Determistic Trajectory with solver

Simulates the deterministic trajectory of the cells using the torchdiffeq solver.

Parameters:

Name	Type	Description	Default
`cells`	`CellPopulation`	CellPopulation.	required
`time_range`	`1D torch.Tensor`	Time points at which the cells state should be evaluated.	required
`method`	`str`	argument for the solver.	`'dopri5'`

Returns:

Type	Description
`torch.Tensor`	torch.Tensor: Trajectory of shape (n_time_points, n_cells, n_genes, *state_dim)

Stochastic Trajectory

Simulates stochastic trajectories of the cell using the tau-leaping method, which is a variation of the Gillespie algorithm: $$ \operatorname{state}(t + \Delta t) = \operatorname{state}(t) + \operatorname{Pois}[\Delta t \cdot (\operatorname{production rates})] - \operatorname{Pois}[\Delta t \cdot (\operatorname{decay rates})]. $$

Parameters:

Name	Type	Description	Default
`cells`	`CellPopulation`	CellPopulation.	required
`time_range`	`1D torch.Tensor`	Time points at which the cells state should be evaluated.	required

Returns:

Type	Description
	torch.Tensor: Trajectory of shape (n_time_points, n_cells, n_genes, *state_dim)