The discovery of governing equations from data is revolutionizing the development of some research fields, where the scientific data are abundant, but the well-characterized quantitative descriptions are probably scarce. We proposed to combine molecular simulations and machine learning to discover the governing equations for fluid dynamics [9], as shown in Fig 5. The prediction from data-driven discovery not only provides the right form of governing equation, but also determines the accurate values of transport coefficients such as viscosity and diffusion. This strategy is expected to help discover constitutive relationships and establish governing equations for nonequilibrium flows and complex fluids [10].

Fig. 5. Data-driven discovery of governing equations based on molecular simulations.

[9] J. Zhang*, and W. Ma, "Data-driven discovery of governing equations for fluid dynamics based on molecular simulation," Journal of Fluid Mechanics 892, A5 (2020).