Sharp CFL stability and temporal-dispersion optimization of symmetric splitting schemes for time-domain Maxwell equations
arXiv:2608.22315
2026
Dynamics
2 ideas extracted · analyzed Aug 29, 2026
What the math gives to ML
The paper develops a coefficient-design principle for explicit palindromic splitting of skew-generated, energy-preserving dynamics. Its transferable asset is the separation between maximizing a real-coefficient stability interval and canceling leading phase error with complex-conjugate coefficients. This suggests stable recurrent or state-space neural blocks built from exact shear substeps rather than Euler residual updates. The most practical first experiment is a two-field Hamiltonian-style SSM with a learned skew coupling and a step-size bound based on the coupling spectral norm.
Ideas from this paper
✗ Mechanism failed
2026
Replace an explicit Euler residual update for a skew-coupled hidden state with a five-stage palindromic composition of exact shear maps. Use a=1/4, the unique real coefficient maximizing the analyzed spectral CFL interval, and adapt the step size from an estimate of the learned coupling operator's spectral norm.
Useful7/10
Difficulty5/10
Novelty6/10
Unverified
2026
Use the complex-conjugate palindromic coefficient that cancels the leading temporal phase defect of oscillatory modes. Implement complex arithmetic directly or use an exactly equivalent doubled-real state, then project the final state to its real component for real-valued prediction tasks.
Useful5/10
Difficulty6/10
Novelty7/10