Assessing physics-informed neural network performance with sparse noisy velocity data

The utilization of data in physics-informed neural network (PINN) may be considered as a necessity as it allows the simulation of more complex cases with a significantly lower computational cost. However, doing so would also make it prone to any issue with the data quality, including its noise. This study would primarily focus on developing a special loss function in the PINN to allow an effective utilization of noisy data. However, a study regarding the data location and amount was also conducted in order to allow a better data utilization in PINN. This study was conducted on a lid-driven cavity flow at Re = 200, 1000, and 5000 with a dataset of less than 100 velocity data and a maximum noise of 10% of the maximum velocity. The results show that by ensuring the data are distributed in a certain configuration, it has zero noise, and by using as much data as possible, the computational cost of PINN can be significantly reduced compared to without using any data at all. For Re = 200, it is 7.4 faster by using data, and this speedup is potentially higher for higher Re cases. For the noise in particular, it does not only make the PINN more inaccurate but also necessitate the usage of more data as this is the only way to make it more accurate. This issue though is capable to be solved with our new method, which only uses the data as an approximate solution, and the governing equation would figure out the details. This method was also shown to be capable to improve the PINN accuracy with the potential to almost completely eliminating the noise effect.