Future work

• Advised by Dr. Shiwei Lan

  • improve recovery of \(a(\cdot)\) in the inverse heat (filtering out-of-range prediction, smoothing)
  • build inference of \(u(t,x;\theta), a(x;\theta)\) from PINN, based on residual and regression losses
  • combine the optimization method Ensemble Kalman filter with gradient based method

• Advised by Dr. Kookjin Lee

  • low-rank approximation of large matrices in MLP with adapted rank-selection in low-rank optimization [DLRT 2022]
  • Fourier neural operator [Li, Kovachki, Stuart and Anandkumar] for inverse heat

• Application: Phoenix area temperature prediction based on car sensors (Prof. Alex Mahalov)