# Differentiable Physics

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.

TactoHand unifies contact, proximity and 3D vertex force into dense fields on the hand surface inferred from monocular video, removing the need for the specialized hardware that tactile collection requires. A temporal transformer aggregates visual evidence across frames, and a differentiable rigid-body layer ties predicted forces to observed object motion. On HOCap, excluded from training, contact Macro-F1 reaches 50.5 against 18.0 for HACO, and physics supervision lowers the temporal variant's rollout position error from 5.7 cm to 3.3 cm.

TactoHand unifies contact, proximity and 3D vertex force into dense fields on the hand surface inferred from monocular video, removing the need for the specialized hardware that tactile collection requires. A temporal transformer aggregates visual evidence across frames, and a differentiable rigid-body layer ties predicted forces to observed object motion. On HOCap, excluded from training, contact Macro-F1 reaches 50.5 against 18.0 for HACO, and physics supervision lowers the temporal variant's rollout position error from 5.7 cm to 3.3 cm.