Zero Coordinate Shift: Whetted Automatic Differentiation for Physics-informed Operator Learning. (arXiv:2311.00860v1 [cs.LG])

Automatic differentiation (AD) is a critical step in physics-informed machine
learning, required for computing the high-order derivatives of network output
w.r.t. coordinates. In this paper, we present a novel and lightweight algorithm
to conduct such AD for physics-informed operator learning, as we call the trick
of Zero Coordinate Shift (ZCS). Instead of making all sampled coordinates leaf
variables, ZCS introduces only one scalar-valued leaf variable for each spatial
or temporal dimension, leading to a game-changing performance leap by
simplifying the …

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