Defined in tensorflow/contrib/integrate/python/ops/

ODE integration on a fixed grid (with no step size control).

Useful in certain scenarios to avoid the overhead of adaptive step size control, e.g. when differentiation of the integration result is desired and/or the time grid is known a priori to be sufficient.


  • func: Function that maps a Tensor holding the state y and a scalar Tensor t into a Tensor of state derivatives with respect to time.
  • y0: N-D Tensor giving starting value of y at time point t[0].
  • t: 1-D Tensor holding a sequence of time points for which to solve for y. The initial time point should be the first element of this sequence, and each time must be larger than the previous time. May have any floating point dtype.
  • dt: 0-D or 1-D Tensor providing time step suggestion to be used on time integration intervals in t. 1-D Tensor should provide values for all intervals, must have 1 less element than that of t. If given a 0-D Tensor, the value is interpreted as time step suggestion same for all intervals. If passed None, then time step is set to be the t[1:] - t[:-1]. Defaults to None. The actual step size is obtained by insuring an integer number of steps per interval, potentially reducing the time step.
  • method: One of 'midpoint' or 'rk4'.
  • name: Optional name for the resulting operation.


  • y: (N+1)-D tensor, where the first dimension corresponds to different time points. Contains the solved value of y for each desired time point in t, with the initial value y0 being the first element along the first dimension.


  • ValueError: Upon caller errors.