Inverse Heat Transfer: Fundamentals and Applications

By M. Ozisik, H. Orlande, A. Kassab. 2000

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Inverse Problems in Heat Transfer (2009, background): “Finally, in section 2.6, directions for further investigation in the use of spectral methods for stochastic inverse problems are suggested.”
Inverse and Optimization Problems in Heat Transfer (2006, methodology): “If the objective function U(x) is twice differentiable, the Hessian is symmetric, and we can write ( ) hxxhx )(D)( 2 kkk UUU +∇≅+∇ (3.1.9) A necessary condition for the minimization of the objective function is that its gradient vanishes.”
Estimation of dimensionless parameters of Luikov's system for heat and mass transfer in capillary porous media (2002, methodology): “Such an automatic control of the damping parameter makes the Levenberg–Marquardt method a quite robust and stable estimation procedure, so that it does not require the use of the Discrepancy Principle in the stopping criterion to become stable, like the conjugate gradient method [13, 14].”
Physics-Informed Neural Networks for Heat Transfer Problems (2021, methodology): “In a typical CFD setup, this would require a tedious data assimilation method [31,32] blended in with ﬂow and heat transfer solvers and may take extremely long times to converge, if it could converge at all.”