Porous media exhibit intriguing responses when shocked, such as the anomalous response region where higher pressure behind the shock-front leads to a less dense material behind the shock [1]. In addition, shock wave speed is far slower in porous materials than in fully dense materials, with the wave speed varying smoothly as a function of porosity. By controlling the distribution of porosity in materials, a variable shock speed can be achieved, allowing precise control of the wave shape. This can be leveraged to control interfacial instabilities (e.g. Richtmyer-Meshkov [2-7]), generate heat, or reshape shocks (e.g. concentrate, diffuse). Figure 1 illustrates a simulation of porous media under shock conditions. However, anticipating which porosity distribution will optimize such objectives is difficult due to the computational cost and highly non-linear behavior of hydrodynamic simulations. An additional challenge is the limitless variations of potential porosity distributions in these structures. We propose to limit the potential search space by parameterizing porosity fields to the first few Fourier modes. A supervised deep learning model can then be trained on thousands of simulation results. The model is designed as a surrogate to efficiently apply constrained optimization onto the complicated physics, which enables optimal porosity distributions for desired interface control to be quickly discovered. The deep learning model is trained in an autoregressive method to predict the next time-step from a temporal sequence of pressure, velocity, and temperature full-field data. Feeding predictions as input, a sequence is recursively continued to achieve subsequent temporal predictions. The optimized porosity distributions are showcased and discussed. This work demonstrates the tremendous power of machine learning approaches for shock compression of condensed matter. Several possible future directions will be summarized. References This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. Lawrence Livermore National Security, LLC. We gratefully acknowledge the LLNL Lab Directed Research and Development Program for funding support of this research under Project No. 21-SI-006 and Project No. 24-ERD-005.