  Quantization has proven effective in high-resolution and large-scale
simulations, which benefit from bit-level memory saving. However, identifying a
quantization scheme that meets the requirement of both precision and memory
efficiency requires trial and error. In this paper, we propose a novel
framework to allow users to obtain a quantization scheme by simply specifying
either an error bound or a memory compression rate. Based on the error
propagation theory, our method takes advantage of auto-diff to estimate the
contributions of each quantization operation to the total error. We formulate
the task as a constrained optimization problem, which can be efficiently solved
with analytical formulas derived for the linearized objective function. Our
workflow extends the Taichi compiler and introduces dithering to improve the
precision of quantized simulations. We demonstrate the generality and
efficiency of our method via several challenging examples of physics-based
simulation, which achieves up to 2.5x memory compression without noticeable
degradation of visual quality in the results. Our code and data are available
at https://github.com/Hanke98/AutoQuantizer.
