VDMD: A Data-Driven Time Eigenvalue Method for Radiation Transport

We present the Variable Dynamic Mode Decomposition (VDMD). VDMD is an extension of the Dynamic Mode Decomposition which is novel in permitting a variable time step size, and demonstrate the application of VDMD to data from radiation transport simulation. VDMD can computing time-eigenvalues of an operator, can providing a time step size recommendation, and can form a low rank linear operator capable of advancing the system while only requiring simulation output data, the size of each time step, and knowledge of the time integration method used for the simulation. We show VDMD performing these feats on neutronics data generated from a variety of numerical methods, where an entire spectrum of time eigenvalues are recovered to sub-pcm precision. Compressed methods with VDMD allow large multiphysics, multi-timescale simulations to be post-processed with VDMD. We consider simulations of the Opacity-on-NIF experiment being analyzed with VDMD using only a minute fraction, roughly 1/22,000th, of available simulation data to draw conclusions regarding complicated multi-physics phenomena. Finally, a novel semi-analytic technique for solving the thermal radiation diffusion equation with an arbitrary boundary condition in curvilinear coordinates is derived and shown, where supersonic, diverging thermal radiation can be semi-analytically modeled in ICF capsules and hohlraums.