Lie Classification and Symmetry-Preserving Reduced-Order Modeling of Nonlinear Electrostatic MEMS

High-fidelity continuum models of electrostatically actuated MEMS accurately capture distributed electromechanical interactions but are computationally expensive for repeated simulation, optimization, and real-time applications. This work develops a physics-informed reduced-order modeling framework based on Lie symmetry classification for a nonlinear electrostatic MEMS microplate governed by a fourth-order integro-partial differential equation. The continuum model is recast as an extended canonical system separating local differential operators from nonlocal stretching and capacitive contributions. Lie group classification of the complete boundary value problem shows that the electrostatic singularity, constitutive coefficients, fixed geometry, and clamped boundary conditions suppress nontrivial continuous spatial symmetries in the generic bounded problem, while time translation survives only in the autonomous subclass. The discrete reflection invariances of the centered rectangular device are treated separately to identify invariant functional subspaces for Galerkin projection. A symmetry-preserving reduced-order model is then constructed in the even-even subspace, retaining bending, geometric stretching, pre-stress, capacitive feedback, dielectric inhomogeneity, and fringing field effects. Numerical verification against the high-fidelity continuum model shows close agreement with the FOM for static and transient responses while preserving reflection symmetry and remaining robust under parameter variations. For the nominal configuration, the monomodal Lie-ROM predicts a pull-in voltage of 127.73V versus 128.21V for the FOM, corresponding to an absolute relative error of 0.37% and a signed error of -0.37%. The monomodal formulation substantially reduces computational cost and consistently outperforms a classical lumped-parameter approximation, providing an interpretable and efficient basis for parametric analysis, design optimization, control-oriented modeling, and future digital twin applications.