brainpy.integrators.sde.SRK1W1
brainpy.integrators.sde.SRK1W1#
- class brainpy.integrators.sde.SRK1W1(f, g, dt=None, name=None, show_code=False, var_type=None, intg_type=None, wiener_type=None, state_delays=None)[source]#
Order 2.0 weak SRK methods for SDEs with scalar Wiener process.
This method has have strong orders \((p_d, p_s) = (2.0,1.5)\).
The Butcher table is:
\[\begin{split}\begin{array}{l|llll|llll|llll} 0 &&&&& &&&& &&&& \\ 3/4 &3/4&&&& 3/2&&& &&&& \\ 0 &0&0&0&& 0&0&0&& &&&&\\ \hline 0 \\ 1/4 & 1/4&&& & 1/2&&&\\ 1 & 1&0&&& -1&0&\\ 1/4& 0&0&1/4&& -5&3&1/2\\ \hline & 1/3& 2/3& 0 & 0 & -1 & 4/3 & 2/3&0 & -1 &4/3 &-1/3 &0 \\ \hline & &&&& 2 &-4/3 & -2/3 & 0 & -2 & 5/3 & -2/3 & 1 \end{array}\end{split}\]References
- 1
Rößler, Andreas. “Strong and weak approximation methods for stochastic differential equations—some recent developments.” Recent developments in applied probability and statistics. Physica-Verlag HD, 2010. 127-153.
- 2
Rößler, Andreas. “Runge–Kutta methods for the strong approximation of solutions of stochastic differential equations.” SIAM Journal on Numerical Analysis 48.3 (2010): 922-952.
- __init__(f, g, dt=None, name=None, show_code=False, var_type=None, intg_type=None, wiener_type=None, state_delays=None)[source]#
Methods
__init__
(f, g[, dt, name, show_code, ...])build
()cpu
()Move all variable into the CPU device.
cuda
()Move all variables into the GPU device.
load_state_dict
(state_dict[, warn])Copy parameters and buffers from
state_dict
into this module and its descendants.load_states
(filename[, verbose])Load the model states.
nodes
([method, level, include_self])Collect all children nodes.
register_implicit_nodes
(*nodes[, node_cls])register_implicit_vars
(*variables, ...)save_states
(filename[, variables])Save the model states.
set_integral
(f)Set the integral function.
state_dict
()Returns a dictionary containing a whole state of the module.
to
(device)Moves all variables into the given device.
tpu
()Move all variables into the TPU device.
train_vars
([method, level, include_self])The shortcut for retrieving all trainable variables.
tree_flatten
()Flattens the object as a PyTree.
tree_unflatten
(aux, dynamic_values)New in version 2.3.1.
unique_name
([name, type_])Get the unique name for this object.
vars
([method, level, include_self, ...])Collect all variables in this node and the children nodes.
Attributes
arguments
All arguments when calling the numer integrator of the differential equation.
dt
The numerical integration precision.
integral
The integral function.
name
Name of the model.
parameters
The parameters defined in the differential equation.
state_delays
State delays.
variables
The variables defined in the differential equation.