Equivariant Spectral Submanifolds Enhance Physics-Informed Reduced Models.

Creating accurate reduced-order models for complex nonlinear systems is crucial for efficient simulation and analysis, especially in scientific and engineering domains. While Spectral Submanifold (SSM) reduction offers a mathematically sound method, its computational cost can be prohibitive for high-dimensional systems. This research introduces a novel extension called equivariant spectral submanifold (eSSM) reduction. The core idea is to explicitly integrate the inherent symmetries of the full-order model into the reduction process. The paper establishes the mathematical basis, showing that SSMs naturally exhibit equivariance and that the resulting reduced dynamics inherit these symmetries. Building on this foundation, an equivariant SSM reduction algorithm is developed. This algorithm leverages symmetries to achieve significantly faster computations and enhance the robustness of the reduced models. The advantages of eSSM are demonstrated through several benchmark problems, including a test case from the Common Task Framework for Science, highlighting its potential for more efficient and reliable modeling.