Inverse problems in hydrodynamics lubrication: Parameter identification in the Reynold equation by using physics-informed neural networks

In this work, the inverse problems for hydrodynamic lubrication were solved by using the physics informed neural networks (PINNs) method. Both the conditions without and with the cavitation effects are studied. For the journal bearings without considering the cavitation effects, the eccentricity values can be accurately inverted using only 10 data points with a maximum error of less than 6%. For the problems with the mass-conserving cavitation, the geometry parameters for 1D conditions were estimated and accurate results can be obtained by also using 10 data points. While for the journal bearings with incompressible lubricants, the error was less than 3% with only 50 data points. For the ones with compressible lubricants, the eccentricity ratios can be estimated with 50 data points again, and the maximum error is less than 10%. In addition, the experimental oil pressure data were used to predict the journal bearing eccentricity, and the results were acceptable with only 9 oil pressure data points. The PINNs method presented two significant strengths: its ability to operate effectively with very sparse data points and its precision in delivering results, and it can provide a promising method for identifying unknown parameters in hydrodynamics lubrication with small data.