README.md

metadata

license: mit

This repository contains the dataset for "Breakeven complexity: A new perspective on neural partial differential equation solvers".

Dataset detail:

• Navier-Stokes: Simulated via Exponax. Contains field "u". 20,000 training trajectories and 1,000 test trajectories. Shape (N, res, res, T).
• Kuramoto-Sivashinsky: Simulated via Exponax. Contains field "u". 20,000 training trajectories and 1,000 test trajectories. Shape (N, res, res, T).
• Gray-Scott: Simulated via 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. 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

Resolution	nRMSE	Time (seconds)
10	0.710526	0.020756
20	0.274556	0.020724
30	0.079504	0.022734
40	0.036205	0.025200
50	0.018495	0.027116
60	0.009136	0.032884
70	0.005968	0.036457
80	0.003813	0.041083
90	0.002139	0.041915
100	0.001344	0.043408
256	0.000000	0.043537

Kuramoto-Sivashinsky 1D

Resolution	nRMSE	Time (seconds)
8	0.840487	0.000209
10	0.694043	0.000236
12	0.579952	0.000225
14	0.579953	0.000234
16	0.576410	0.000200
18	0.590125	0.000230
20	0.590130	0.000318
22	0.516423	0.000243
24	0.430445	0.000232
26	0.430447	0.000254
28	0.320877	0.000243
30	0.188443	0.000238
32	0.188440	0.000237
34	0.076120	0.000240
36	0.046457	0.000212
38	0.046294	0.000243
40	0.023428	0.000240
42	0.011915	0.000250
44	0.011915	0.000243
46	0.006401	0.000256
48	0.003399	0.000243
50	0.003400	0.000251
52	0.001929	0.000369
54	0.001090	0.000250
56	0.001089	0.000250
58	0.000658	0.000290
60	0.000426	0.000262
62	0.000412	0.000373
64	0.000000	0.000310

Kuramoto-Sivashinsky 2D

Resolution	nRMSE	Time (seconds)
54	0.504471	0.015612
60	0.217395	0.017008
64	0.148039	0.017242
70	0.070031	0.017442
74	0.045836	0.019862
80	0.015524	0.021907
84	0.004999	0.023360
90	0.001333	0.023940
94	0.000871	0.027558
100	0.000704	0.030900
256	0.000000	0.066734

Kuramoto-Sivashinsky 3D

Resolution	nRMSE	Time (seconds)
48	0.439662	1.144816
50	0.444682	1.199737
52	0.171244	1.654107
54	0.073160	1.338130
56	0.074237	1.356794
58	0.031996	1.912379
60	0.013426	1.338568
62	0.012842	2.050640
64	0.000000	2.711006

Gray-Scott

Resolution	nRMSE	Time (seconds)
10	0.803211	0.037729
20	0.722904	0.041896
30	0.635374	0.047774
40	0.587572	0.051580
50	0.546942	0.061180
60	0.453108	0.068281
70	0.326739	0.074282
80	0.245069	0.081521
90	0.180130	0.101329
100	0.129753	0.114296
110	0.091766	0.131567
120	0.064967	0.143684
130	0.045852	0.172376
140	0.034773	0.189323
150	0.024973	0.213734
160	0.016908	0.224823
170	0.015451	0.361601
180	0.014250	0.283169
190	0.010380	0.354393
200	0.003622	0.379086
210	0.002213	0.383786
220	0.002397	0.425519
230	0.002240	0.473417
256	0.000000	0.475097

BreakFlow Combined

Coarse size	nRMSE	Time (seconds)
1.0000	0.000000	136.90
1.0443	0.128982	116.90
1.0905	0.129075	112.56
1.1388	0.130949	108.54
1.1892	0.131635	106.62
1.4142	0.148803	80.38
1.6818	0.161297	61.96
2.0000	0.183323	45.88
2.3784	0.185847	42.64
2.8284	0.188891	41.28
3.3636	0.222432	28.84
4.0000	0.225344	27.60
4.7568	0.240020	26.86
5.6569	0.240704	26.84
6.7272	0.271237	17.96
8.0000	0.276092	17.64
9.5137	0.288030	15.78
11.3137	0.292035	15.72
13.4543	0.307576	15.68
16.0000	0.310202	15.66
19.0274	0.331415	15.00

BreakFlow Bin1

Coarse size	nRMSE	Time (seconds)
1.0000	0.000000	95.00
1.0443	0.002162	90.68
1.0905	0.002408	87.58
1.1388	0.002191	84.58
1.1892	0.002310	82.16
1.4142	0.002670	62.50
1.6818	0.004234	48.10
2.0000	0.006039	36.38
2.3784	0.007088	33.78
2.8284	0.007740	32.42
3.3636	0.017143	23.14
4.0000	0.018088	22.24
4.7568	0.019215	21.78
5.6569	0.022276	21.58
6.7272	0.042654	14.48
8.0000	0.048285	14.26
9.5137	0.063298	12.96
11.3137	0.072127	12.88
13.4543	0.092477	12.86
16.0000	0.093449	12.78

BreakFlow Bin2

Coarse size	nRMSE	Time (seconds)
1.0000	0.000000	99.24
1.0443	0.054530	96.30
1.0905	0.058209	92.84
1.1388	0.048698	89.30
1.1892	0.055428	87.10
1.4142	0.081105	66.50
1.6818	0.088567	51.16
2.0000	0.123205	39.36
2.3784	0.126006	36.22
2.8284	0.125205	35.32
3.3636	0.179135	24.54
4.0000	0.179902	24.02
4.7568	0.199868	23.18
5.6569	0.211182	23.32
6.7272	0.250170	16.12
8.0000	0.255241	15.60
9.5137	0.285511	13.48
11.3137	0.278287	13.66
13.4543	0.314424	13.52
16.0000	0.314749	13.80

BreakFlow Bin3

Coarse size	nRMSE	Time (seconds)
1.0000	0.000000	167.48
1.0443	0.330253	163.74
1.0905	0.332230	157.28
1.1388	0.336337	151.76
1.1892	0.337167	150.62
1.4142	0.362633	112.16
1.6818	0.391089	86.62
2.0000	0.420725	61.88
2.3784	0.424446	57.90
2.8284	0.433728	56.10
3.3636	0.471017	38.82
4.0000	0.478041	36.52
4.7568	0.500976	35.62
5.6569	0.488654	35.62
6.7272	0.520888	23.28
8.0000	0.524751	23.08
9.5137	0.515281	20.32
11.3137	0.525692	20.64
13.4543	0.515828	20.64
16.0000	0.522407	20.40