# JAX-WAVE

In a heterogeneous medium, making a wave field take a prescribed shape at a set time means working backward to an initial pressure distribution, and previously every target and every medium required a fresh numerical inversion. JAX-WAVE trains a shared neural network to map the desired terminal field and a known wave-speed map directly to a bounded initial pressure, with training signal supplied by a differentiable finite-difference time-domain solver and no pre-optimized control labels. On an independent confirmation set, three trained models reach 25.24% error on unseen geometric targets and 4.77% on unseen reachable targets; within a 5 ms median online budget the learned map cuts mean error by 45% relative to accelerated numerical inversion on the heterogeneous benchmark.

In a heterogeneous medium, making a wave field take a prescribed shape at a set time means working backward to an initial pressure distribution, and previously every target and every medium required a fresh numerical inversion. JAX-WAVE trains a shared neural network to map the desired terminal field and a known wave-speed map directly to a bounded initial pressure, with training signal supplied by a differentiable finite-difference time-domain solver and no pre-optimized control labels. On an independent confirmation set, three trained models reach 25.24% error on unseen geometric targets and 4.77% on unseen reachable targets; within a 5 ms median online budget the learned map cuts mean error by 45% relative to accelerated numerical inversion on the heterogeneous benchmark.