Creating ultra-stable jammed packings by training on pressure

Disordered materials are highly trainable because of their rugged energy landscapes. The idea of training is to evolve the physical properties of the microscopic constituents in a given system until a macroscopic state with desired emergent properties is achieved. Here, we train packings of soft harmonic spheres based on their per-particle pressures. First, the pressure on each particle is measured and then the radius of each particle is changed proportional to the inverse of its pressure, (i.e. particles with larger pressure get slightly smaller and particles with smaller pressure grow slightly larger). This process is repeated iteratively until pressure fluctuations disappear from the system. The final trained packings have a much lower energy and are mechanically ultra-stable regardless of original (untrained) packings' distance from the instability. This training process moves the critical packing fraction to a higher value and engraves a memory of training in the system that does not disappear under decompression.