  This paper proposes a new method that combines check-pointing methods with
error-controlled lossy compression for large-scale high-performance
Full-Waveform Inversion (FWI), an inverse problem commonly used in geophysical
exploration. This combination can significantly reduce data movement, allowing
a reduction in run time as well as peak memory. In the Exascale computing era,
frequent data transfer (e.g., memory bandwidth, PCIe bandwidth for GPUs, or
network) is the performance bottleneck rather than the peak FLOPS of the
processing unit. Like many other adjoint-based optimization problems, FWI is
costly in terms of the number of floating-point operations, large memory
footprint during backpropagation, and data transfer overheads. Past work for
adjoint methods has developed checkpointing methods that reduce the peak memory
requirements during backpropagation at the cost of additional floating-point
computations. Combining this traditional checkpointing with error-controlled
lossy compression, we explore the three-way tradeoff between memory, precision,
and time to solution. We investigate how approximation errors introduced by
lossy compression of the forward solution impact the objective function
gradient and final inverted solution. Empirical results from these numerical
experiments indicate that high lossy-compression rates (compression factors
ranging up to 100) have a relatively minor impact on convergence rates and the
quality of the final solution.
