Table 5.

Discovery of identities in Navier–Stokes equations using threshold sparse Bayesian regression with threshold 0.1. Here, 202 data are used. Result 1, Result 4, Result 5, Result 8 have the smallest error bars, and they are equivalent to the identity ∂u₁/∂x + ∂u₂/∂y = 0.

result	1	2	3	4	5	6	7
u1∂u1/∂x	1			1.000		−0.396
u1∂u1/∂y		1
u1∂u2/∂x		2.271	1			−0.349	−0.231
u1∂u2/∂y	1.000	−0.909		1		0.993
u2∂u1/∂x		1.746			1
u2∂u1/∂y		−0.608				1	−0.204
u2∂u2/∂x		4.997	0.154			−1.223	1
u2∂u2/∂y					1.000	−0.575
ν∂2u1/∂x2		−3.389	−0.632			0.676	−0.534
ν∂2u1/∂y2		−1.366
ν∂2u2/∂x2		2.455				−0.613	0.657
ν∂2u2/∂y2		−7.156	−0.351			2.774	−1.111
∂(p/ρ)/∂x			−0.100			0.209
∂(p/ρ)/∂y		−1.008					−0.294
error bar  × 103	0.000	1110.362	183.139	0.000	0.000	3139.186	127.743

result	8	9	10	11	12	13	14
u1∂u1/∂x			−1.179
u1∂u1/∂y			−0.220
u1∂u2/∂x		−0.388				−1.290	0.721
u1∂u2/∂y							−0.640
u2∂u1/∂x	1.000		−0.478
u2∂u1/∂y		0.119		−0.193	0.203	0.533
u2∂u2/∂x		−0.387	−2.059	0.770	−0.468	−0.867	−1.043
u2∂u2/∂y	1						0.581
ν∂2u1/∂x2		1	2.436	−0.745	0.232	−0.441	0.489
ν∂2u1/∂y2			1			−0.463
ν∂2u2/∂x2		−0.317	−1.002	1	−0.128	−0.274	−1.515
ν∂2u2/∂y2		0.463	3.272	−0.521	1	1.233	−0.116
∂(p/ρ)/∂x			−0.796			1
∂(p/ρ)/∂y		0.128	0.370	−0.473			1
error bar × 103	0.000	189.638	332.790	88.404	48.410	358.041	1081.667