Optimization of Weight Function for (3+1)d Phonon Propagation in Weyl Fermion Sea Expressed by Clifford Algebra Using Elman Rnn and Echo State Network

We modify the lattice simulation of (3+1)D Quantum Chromo Dynamics using fixed point actions by replacing Dirac fermions to Weyl fermions expressed by biquaternions. Paths of phonons are described by the weight function of eigenfunctions. The optimization is performed by using Elman Recurrent Neural Network and the Echo State Networks. Numerical results of the two optimizations are compared. We compare in lower dimensional systems the Time-Reversal based Nonlinear Elastic Wave Spectroscopy and the theory based on Quaternion Field Theory.