added Ralston and EulerHeun

patrick-kidger · Aug 4, 2024 · 0433920 · 0433920
1 parent b4211df
commit 0433920
Showing 1 changed file with 38 additions and 36 deletions.
diff --git a/docs/devdocs/sde_example.ipynb b/docs/devdocs/sde_example.ipynb
@@ -643,42 +643,44 @@
    "metadata": {},
    "source": [
     "```\n",
-    "+----------------+-------+------------+----------------------------------+-------------------+----------------+------------------------------------------+\n",
-    "|                | SDE   | Lévy       | Strong/weak order per noise type | VF evaluations    | Embedded error | Recommended for                          |\n",
-    "|                | type  | area       +---------+-------------+----------+-------+-----------+ estimation     | (and other notes)                        |\n",
-    "|                |       |            | General | Commutative | Additive | Drift | Diffusion |                |                                          |\n",
-    "+----------------+-------+------------+---------+-------------+----------+-------+-----------+----------------+------------------------------------------+\n",
-    "| Euler          | Itô   | BM only    | 0.5/1.0 | 0.5/1.0     | 1.0/1.0  | 1     | 1         | No             | Itô SDEs when a cheap solver is needed   |\n",
-    "+----------------+-------+------------+---------+-------------+----------+-------+-----------+----------------+------------------------------------------+\n",
-    "| Heun           | Strat | BM only    | 0.5/1.0 | 1.0/1.0     | 1.0/1.0  | 2     | 2         | Yes            | Stratonovich SDEs without space-time LA. |\n",
-    "|                |       |            |         |             |          |       |           |                | Has weak order 2 for constant noise.     |\n",
-    "+----------------+-------+------------+---------+-------------+----------+-------+-----------+----------------+------------------------------------------+\n",
-    "| ItoMilstein    | Itô   | BM only    | 0.5/1.0 | 1.0/1.0     | 1.0/1.0  | 1     | 1 + deriv | No             | Better than Euler for Itô SDEs, but      |\n",
-    "|                |       |            |         |             |          |       |     ative |                | comuptes the derivative of diffusion VF  |\n",
-    "+----------------+-------+------------+---------+-------------+----------+-------+-----------+----------------+------------------------------------------+\n",
-    "| Stratonovich   | Strat | BM only    | 0.5/1.0 | 1.0/1.0     | 1.0/1.0  | 1     | 1 + deriv | No             | For commutative Stratonovich SDEs when   |\n",
-    "| Milstein       |       |            |         |             |          |       |     ative |                | space-time Lévy area is not available.   |\n",
-    "|                |       |            |         |             |          |       |           |                | Computes derivative of diffusion VF.     |\n",
-    "+----------------+-------+------------+---------+-------------+----------+-------+-----------+----------------+------------------------------------------+\n",
-    "| ReversibleHeun | Strat | BM only    | 0.5/1.0 | 1.0/1.0     | 1.0/1.0  | 1     | 1         | Yes            | When a reversible solver is needed, e.g. |\n",
-    "|                |       |            |         |             |          |       |           |                | for Neural SDEs. This method is FSAL.    |\n",
-    "+----------------+-------+------------+---------+-------------+----------+-------+-----------+----------------+------------------------------------------+\n",
-    "| Midpoint       | Strat | BM only    | 0.5/1.0 | 1.0/1.0     | 1.0/1.0  | 2     | 2         | Yes            | Usually Heun should be preferred.        |\n",
-    "+----------------+-------+------------+---------+-------------+----------+-------+-----------+----------------+------------------------------------------+\n",
-    "| ShARK          | Addit | space-time | /       | /           | 1.5/2.0  | 2     | 2         | Yes            | Additive noise SDEs                      |\n",
-    "+----------------+-------+------------+---------+-------------+----------+-------+-----------+----------------+------------------------------------------+\n",
-    "| SRA1           | Addit | space-time | /       | /           | 1.5/2.0  | 2     | 2         | Yes            | Only slightly worse than ShARK           |\n",
-    "+----------------+-------+------------+---------+-------------+----------+-------+-----------+----------------+------------------------------------------+\n",
-    "| SEA            | Addit | space-time | /       | /           | 1.0/1.0  | 1     | 1         | No             | Cheap solver for additive noise SDEs     |\n",
-    "+----------------+-------+------------+---------+-------------+----------+-------+-----------+----------------+------------------------------------------+\n",
-    "| SPaRK          | Strat | space-time | 0.5/1.0 | 1.0/1.0     | 1.5/2.0  | 3     | 3         | Yes            | General SDEs when embedded error         |\n",
-    "|                |       |            |         |             |          |       |           |                | estimation is needed                     |\n",
-    "+----------------+-------+------------+---------+-------------+----------+-------+-----------+----------------+------------------------------------------+\n",
-    "| GeneralShARK   | Strat | space-time | 0.5/1.0 | 1.0/1.0     | 1.5/2.0  | 2     | 3         | No             | General SDEs when embedded error         |\n",
-    "|                |       |            |         |             |          |       |           |                | estimaiton is not needed                 |\n",
-    "+----------------+-------+------------+---------+-------------+----------+-------+-----------+----------------+------------------------------------------+\n",
-    "| SlowRK         | Strat | space-time | 0.5/1.0 | 1.5/2.0     | 1.5/2.0  | 2     | 5         | No             | Commutative noise SDEs.                  |\n",
-    "+----------------+-------+------------+---------+-------------+----------+-------+-----------+----------------+------------------------------------------+\n",
+    "+----------------+-------+------------+------------------------------------+-------------------+----------------+------------------------------------------+\n",
+    "|                | SDE   | Lévy       | Strong/weak order (per noise type) | VF evaluations    | Embedded error | Recommended for                          |\n",
+    "|                | type  | area       +----------+--------------+----------+-------+-----------+ estimation     | (and other notes)                        |\n",
+    "|                |       |            | General  | Commutative  | Additive | Drift | Diffusion |                |                                          |\n",
+    "+----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+\n",
+    "| Euler          | Itô   | BM only    | 0.5/1.0  | 0.5/1.0      | 1.0/1.0  | 1     | 1         | No             | Itô SDEs when a cheap solver is needed.  |\n",
+    "+----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+\n",
+    "| Heun           | Strat | BM only    | 0.5/1.0  | 1.0/1.0      | 1.0/1.0  | 2     | 2         | Yes            | Standard solver for Stratonovich SDEs.   |\n",
+    "+----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+\n",
+    "| EulerHeun      | Strat | BM only    | 0.5/1.0  | 0.5/1.0      | 1.0/1.0  | 1     | 2         | No             | Stratonovich SDEs with expensive drift.  |\n",
+    "+----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+\n",
+    "| ItoMilstein    | Itô   | BM only    | 0.5/1.0  | 1.0/1.0      | 1.0/1.0  | 1     | 1         | No             | Better than Euler for Itô SDEs, but      |\n",
+    "|                |       |            |          |              |          |       |           |                | comuptes the derivative of diffusion VF. |\n",
+    "+----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+\n",
+    "| Stratonovich   | Strat | BM only    | 0.5/1.0  | 1.0/1.0      | 1.0/1.0  | 1     | 1         | No             | For commutative Stratonovich SDEs when   |\n",
+    "| Milstein       |       |            |          |              |          |       |           |                | space-time Lévy area is not available.   |\n",
+    "|                |       |            |          |              |          |       |           |                | Computes derivative of diffusion VF.     |\n",
+    "+----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+\n",
+    "| ReversibleHeun | Strat | BM only    | 0.5/1.0  | 1.0/1.0      | 1.0/1.0  | 2     | 2         | Yes            | When a reversible solver is needed.      |\n",
+    "+----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+\n",
+    "| Midpoint       | Strat | BM only    | 0.5/1.0  | 1.0/1.0      | 1.0/1.0  | 2     | 2         | Yes            | Usually Heun should be preferred.        |\n",
+    "+----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+\n",
+    "| Ralston        | Strat | BM only    | 0.5/1.0  | 1.0/1.0      | 1.0/1.0  | 2     | 2         | Yes            | Usually Heun should be preferred.        |\n",
+    "+----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+\n",
+    "| ShARK          | Strat | space-time | /        | /            | 1.5/2.0  | 2     | 2         | Yes            | Additive noise SDEs.                     |\n",
+    "+----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+\n",
+    "| SRA1           | Strat | space-time | /        | /            | 1.5/2.0  | 2     | 2         | Yes            | Only slightly worse than ShARK.          |\n",
+    "+----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+\n",
+    "| SEA            | Strat | space-time | /        | /            | 1.0/1.0  | 1     | 1         | No             | Cheap solver for additive noise SDEs.    |\n",
+    "+----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+\n",
+    "| SPaRK          | Strat | space-time | 0.5/1.0  | 1.0/1.0      | 1.5/2.0  | 3     | 3         | Yes            | General SDEs when embedded error         |\n",
+    "|                |       |            |          |              |          |       |           |                | estimation is needed.                    |\n",
+    "+----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+\n",
+    "| GeneralShARK   | Strat | space-time | 0.5/1.0  | 1.0/1.0      | 1.5/2.0  | 2     | 3         | No             | General SDEs when embedded error         |\n",
+    "|                |       |            |          |              |          |       |           |                | estimaiton is not needed.                |\n",
+    "+----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+\n",
+    "| SlowRK         | Strat | space-time | 0.5/1.0  | 1.5/2.0      | 1.5/2.0  | 2     | 5         | No             | Commutative noise SDEs.                  |\n",
+    "+----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+\n",
     "```"
    ]
   }