extrap_expratedecay¶
- extrap_expratedecay(sample: Tensor, sample_at: Tensor, prev_data: Tensor, next_data: Tensor, step_time: float, *, rate_constant: float, **kwargs) tuple[Tensor, Tensor][source]¶
Extrapolates out assuming exponential decay dynamics, parameterized by a rate constant.
\[\begin{split}\begin{align*} X(0) &= X(t_s) \exp \left( \lambda t_s \right) \\ X(\Delta t) &= X(t_s) \exp \left( -\lambda (\Delta t - t_s) \right) \end{align*}\end{split}\]- Parameters:
sample (torch.Tensor) – sample from which to extrapolate, \(X(t=t_s)\)
sample_at (torch.Tensor) – relative time at which to sample data, \(t_s\).
prev_data (torch.Tensor) – most recent observation prior to sample time, \(D(t=0)\).
next_data (torch.Tensor) – most recent observation subsequent to sample time, \(D(t=\Delta t)\).
step_time (float) – length of time between the prior and subsequent observations, \(\Delta t\).
rate_constant (float) – rate constant of exponential decay, \(\lambda\).
- Returns:
extrapolated data at neighboring steps, \((X(t=0), X(t=\Delta t))\).
- Return type: