Nonintrusive reduced‐order modeling of parametrized time‐dependent partial differential equations

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Data-driven reduced order modeling for time-dependent problems (2019, methodology): “the RB method for linear evolution equations [16], the POD-based reduced-order fluid/structure modeling [24], the nonlinear ROM based on local reduced-order bases [3], the dynamic mode decomposition [21], several developments of the RB method for complex models [22, 34, 40], recently proposed struct”
Digital Twin: Values, Challenges and Enablers From a Modeling Perspective (2019, background): “5) have emerged recently with the democratization of computational power, explosion of archival data, and advances in ML algorithms [294]–[304].”
Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems (2019, methodology): “, via gappy POD [5, 6], or using radial basis 21 functions [7], a neural network [8, 9, 10] or a nearest-neighbors method [10].”
Non-intrusive reduced order modelling of the Navier-Stokes equations (2015, methodology): “[20] proposed a non-intrusive Radial Basis Function (RBF) reduced-order modelling method for approximating the solutions of nonlinear time-dependent parameterized partial differential equations (Burgers’ equation and a parameterized convection–reaction–diffusion problem).”
Non‐intrusive reduced‐order modelling of the Navier–Stokes equations based on RBF interpolation (2015, methodology): “This method is verified and validated by Burgers equation and convection–diffusion–reaction problems [38, 39].”