Update README.md

README.md

@@ -9,14 +9,14 @@ license: mit
 This repository contains the dataset for "Breakeven complexity: A new perspective on neural partial differential equation solvers".
 
 Dataset detail:
-- Navier-Stokes: field "u". 20,000 training trajectories and 1,000 test trajectories. Shape (N, res, res, T).
-- Kuramoto-Sivashinsky: field "u". 20,000 training trajectories and 1,000 test trajectories. Shape (N, res, res, T).
-- Gray-Scott: field "u" and "v". 20,000 training trajectories seperated equally into 10 files, and 1,000 test trajectories. Shape (N, res, res, T).
-- BreakFlow: field "velocity_x", ""velocity_y", "pressure", "vorticity", and "mask". 2,000 training trajectories and 50 test trajectories for each Reynolds bin. The combined folder is a shuffled collection of the data. The OOD(out of distribution) folder contrains train set of a shuffled collection of bin1 and bin2, and bin3 as test set. Shape (N, T, res, res).
+- Navier-Stokes: Simulated via [Exponax](https://fkoehler.site/exponax/). Contains field "u". 20,000 training trajectories and 1,000 test trajectories. Shape (N, res, res, T).
+- Kuramoto-Sivashinsky: Simulated via [Exponax](https://fkoehler.site/exponax/). Contains field "u". 20,000 training trajectories and 1,000 test trajectories. Shape (N, res, res, T).
+- Gray-Scott: Simulated via [Exponax](https://fkoehler.site/exponax/). Contains field "u" and "v". 20,000 training trajectories seperated equally into 10 files, and 1,000 test trajectories. Shape (N, res, res, T).
+- BreakFlow: Simulated via [PyFR](https://www.pyfr.org/). Contains field "velocity_x", ""velocity_y", "pressure", "vorticity", and "mask". 2,000 training trajectories and 50 test trajectories for each Reynolds bin. The combined folder is a shuffled collection of the data. The OOD(out of distribution) folder contrains train set of a shuffled collection of bin1 and bin2, and bin3 as test set. Shape (N, T, res, res).
 
 Here are time matching statistics for the datasets:
 
-**Navier-Stokes**
+# Navier-Stokes 
 | Resolution | nRMSE | Time (seconds) |
 | :--- | :--- | :--- |
 | **10** | 0.710526 | 0.020756 |
@@ -31,7 +31,7 @@ Here are time matching statistics for the datasets:
 | **100** | 0.001344 | 0.043408 |
 | **256** | 0.000000 | 0.043537 |
 
-**Kuramoto-Sivashinsky 1D**
+# Kuramoto-Sivashinsky 1D
 | Resolution | nRMSE | Time (seconds) |
 | :--- | :--- | :--- |
 | **8** | 0.840487 | 0.000209 |
@@ -64,7 +64,7 @@ Here are time matching statistics for the datasets:
 | **62** | 0.000412 | 0.000373 |
 | **64** | 0.000000 | 0.000310 |
 
-**Kuramoto-Sivashinsky 2D**
+# Kuramoto-Sivashinsky 2D
 | Resolution | nRMSE | Time (seconds) |
 | :--- | :--- | :--- |
 | **54** | 0.504471 | 0.015612 |
@@ -79,7 +79,7 @@ Here are time matching statistics for the datasets:
 | **100** | 0.000704 | 0.030900 |
 | **256** | 0.000000 | 0.066734 |
 
-**Kuramoto-Sivashinsky 3D**
+# Kuramoto-Sivashinsky 3D
 | Resolution | nRMSE | Time (seconds) |
 | :--- | :--- | :--- |
 | **48** | 0.439662 | 1.144816 |
@@ -92,7 +92,7 @@ Here are time matching statistics for the datasets:
 | **62** | 0.012842 | 2.050640 |
 | **64** | 0.000000 | 2.711006 |
 
-**Gray-Scott**
+# Gray-Scott
 | Resolution | nRMSE | Time (seconds) |
 | :--- | :--- | :--- |
 | **10** | 0.803211 | 0.037729 |
@@ -120,7 +120,7 @@ Here are time matching statistics for the datasets:
 | **230** | 0.002240 | 0.473417 |
 | **256** | 0.000000 | 0.475097 |
 
-**BreakFlow Combined**
+# BreakFlow Combined
 | Resolution | nRMSE | Time (seconds) |
 | :--- | :--- | :--- |
 | **1.0000** | 0.000000 | 136.90 |
@@ -145,7 +145,7 @@ Here are time matching statistics for the datasets:
 | **16.0000** | 0.310202 | 15.66 |
 | **19.0274** | 0.331415 | 15.00 |
 
-**BreakFlow Bin1**
+# BreakFlow Bin1
 | Resolution | nRMSE | Time (seconds) |
 | :--- | :--- | :--- |
 | **1.0000** | 0.000000 | 95.00 |
@@ -193,7 +193,7 @@ Here are time matching statistics for the datasets:
 | **13.4543** | 0.314424 | 13.52 |
 | **16.0000** | 0.314749 | 13.80 |
 
-**BreakFlow Bin3 and OOD**
+# BreakFlow Bin3 and OOD
 | Resolution | nRMSE | Time (seconds) |
 | :--- | :--- | :--- |
 | **1.0000** | 0.000000 | 167.48 |