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[solver] Proposal: add classic tableau option for dopri5 #158

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[solver] Proposal: add classic tableau option for dopri5 #158

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153b242
add classic dp5 tableau and test
Zymrael Mar 28, 2021
6de13ec
fix tol in DETEST
Zymrael Mar 28, 2021
4bd6a7a
rm cache
Zymrael Mar 28, 2021
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4 changes: 2 additions & 2 deletions tests/DETEST/run.py
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Original file line number Diff line number Diff line change
Expand Up @@ -22,8 +22,8 @@ def __call__(self, t, y):
def main():

sol = dict()
for method in ['dopri5', 'adams']:
for tol in [1e-3, 1e-6, 1e-9]:
for method in ['dopri5', 'classic_dopri5']:
for tol in [1e-3, 1e-4, 1e-5, 1e-6]:
print('======= {} | tol={:e} ======='.format(method, tol))
nfes = []
times = []
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54 changes: 39 additions & 15 deletions torchdiffeq/_impl/dopri5.py
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Original file line number Diff line number Diff line change
@@ -1,18 +1,39 @@
import torch
from .rk_common import _ButcherTableau, RKAdaptiveStepsizeODESolver

alpha=torch.tensor([1 / 5, 3 / 10, 4 / 5, 8 / 9, 1., 1.], dtype=torch.float64)
beta=[
torch.tensor([1 / 5], dtype=torch.float64),
torch.tensor([3 / 40, 9 / 40], dtype=torch.float64),
torch.tensor([44 / 45, -56 / 15, 32 / 9], dtype=torch.float64),
torch.tensor([19372 / 6561, -25360 / 2187, 64448 / 6561, -212 / 729], dtype=torch.float64),
torch.tensor([9017 / 3168, -355 / 33, 46732 / 5247, 49 / 176, -5103 / 18656], dtype=torch.float64),
torch.tensor([35 / 384, 0, 500 / 1113, 125 / 192, -2187 / 6784, 11 / 84], dtype=torch.float64),
]
c_sol=torch.tensor([35 / 384, 0, 500 / 1113, 125 / 192, -2187 / 6784, 11 / 84, 0], dtype=torch.float64)


_CLASSIC_DORMAND_PRINCE_SHAMPINE_TABLEAU = _ButcherTableau(
alpha=alpha, beta=beta, c_sol=c_sol,
c_error=torch.tensor([
35 / 384 - 5179 / 57600,
0,
500 / 1113 - 7571 / 16695,
125 / 192 - 393 / 640,
-2187 / 6784 - -92097 / 339200,
11 / 84 - 187 / 2100,
-1 / 40,
], dtype=torch.float64),
)

DPS_C_MID = torch.tensor([
6025192743 / 30085553152 / 2, 0, 51252292925 / 65400821598 / 2, -2691868925 / 45128329728 / 2,
187940372067 / 1594534317056 / 2, -1776094331 / 19743644256 / 2, 11237099 / 235043384 / 2
], dtype=torch.float64)


_DORMAND_PRINCE_SHAMPINE_TABLEAU = _ButcherTableau(
alpha=torch.tensor([1 / 5, 3 / 10, 4 / 5, 8 / 9, 1., 1.], dtype=torch.float64),
beta=[
torch.tensor([1 / 5], dtype=torch.float64),
torch.tensor([3 / 40, 9 / 40], dtype=torch.float64),
torch.tensor([44 / 45, -56 / 15, 32 / 9], dtype=torch.float64),
torch.tensor([19372 / 6561, -25360 / 2187, 64448 / 6561, -212 / 729], dtype=torch.float64),
torch.tensor([9017 / 3168, -355 / 33, 46732 / 5247, 49 / 176, -5103 / 18656], dtype=torch.float64),
torch.tensor([35 / 384, 0, 500 / 1113, 125 / 192, -2187 / 6784, 11 / 84], dtype=torch.float64),
],
c_sol=torch.tensor([35 / 384, 0, 500 / 1113, 125 / 192, -2187 / 6784, 11 / 84, 0], dtype=torch.float64),
alpha=alpha, beta=beta, c_sol=c_sol,
c_error=torch.tensor([
35 / 384 - 1951 / 21600,
0,
Expand All @@ -24,13 +45,16 @@
], dtype=torch.float64),
)

DPS_C_MID = torch.tensor([
6025192743 / 30085553152 / 2, 0, 51252292925 / 65400821598 / 2, -2691868925 / 45128329728 / 2,
187940372067 / 1594534317056 / 2, -1776094331 / 19743644256 / 2, 11237099 / 235043384 / 2
], dtype=torch.float64)


class Dopri5Solver(RKAdaptiveStepsizeODESolver):
order = 5
tableau = _DORMAND_PRINCE_SHAMPINE_TABLEAU
mid = DPS_C_MID


class ClassicDopri5Solver(RKAdaptiveStepsizeODESolver):
order = 5
tableau = _CLASSIC_DORMAND_PRINCE_SHAMPINE_TABLEAU
mid = DPS_C_MID


3 changes: 2 additions & 1 deletion torchdiffeq/_impl/odeint.py
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Original file line number Diff line number Diff line change
@@ -1,6 +1,6 @@
import torch
from torch.autograd.functional import vjp
from .dopri5 import Dopri5Solver
from .dopri5 import ClassicDopri5Solver, Dopri5Solver
from .bosh3 import Bosh3Solver
from .adaptive_heun import AdaptiveHeunSolver
from .fehlberg2 import Fehlberg2
Expand All @@ -13,6 +13,7 @@
SOLVERS = {
'dopri8': Dopri8Solver,
'dopri5': Dopri5Solver,
'classic_dopri5': ClassicDopri5Solver,
'bosh3': Bosh3Solver,
'fehlberg2': Fehlberg2,
'adaptive_heun': AdaptiveHeunSolver,
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