Pavan Pranjivan Mehta

I am a doctoral candidate in (applied) mathematics at SISSA, Italy. I hold two Master’s, namely, Applied Mathematics from Brown University and Thermal and Fluid Engineering from University of Manchester, with an undergraduate in Aeronautical Engineering. I was invited to the prestigious Isaac Newton Institute, Cambridge for my work on fractional calculus applied to turbulence.  

I have furthered the theory of fractional calculus by introducing vector calculus for variable order operators and general fractional calculus on finite intervals. As a result of fractional vector calculus, I have derived fractional Navier-Stokes equations from first principles, which involved me first formalizing the fractional Reynolds transport theorem. Notably, the fractional Cauchy stress tensor uses fractional stress-strain hypothesis, which was validated in the context of fractional Reynolds-averaged Navier-Stokes equations for transitional and separated flows too. 

For numerical solutions of fractional PDE, I introduced the Jacobi convolution series to develop spectral methods. Furthermore, I have developed machine learning algorithms, such as pointwise fractional Physics-informed Neural Networks for inverse problems, and general fractional Physics-informed Neural Networks. 

Also, I have worked on Uncertainty Quantification and Data Assimilation such as General Polynomial Chaos, Kriging (Gaussian Processes), anchored-ANOVA, POD for reduction and sensitivity analysis using Sobol indices.