Projection-based model order reduction onto an SVD-learned subspace reproduces water QMD trajectories with visual agreement to high-fidelity DFT, but only within the sampled configuration domain.
Theory and numerics of subspace approximation of eigenvalue problems
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abstract
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to mitigate the computational burden associated with high-fidelity systems. We provide general error estimates under non-simple eigenvalue conditions, establishing some theoretical foundations for understanding the convergence behavior of subspace approximations. Numerical examples, including problems with one-dimensional to three-dimensional spatial domain and one-dimensional to two-dimensional parameter domain, are presented to demonstrate the efficacy of reduced basis method in handling parametric variations in boundary conditions and coefficient fields to achieve significant computational savings while maintaining high accuracy, making them promising tools for practical applications in large-scale eigenvalue computations.
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Model Order Reduction for Quantum Molecular Dynamics
Projection-based model order reduction onto an SVD-learned subspace reproduces water QMD trajectories with visual agreement to high-fidelity DFT, but only within the sampled configuration domain.