Scaling the “Memory Wall” for Multi-Dimensional Seismic Processing with Algebraic Compression on Cerebras CS-2 Systems

Ltaief, Hatem; Hong, Yuxi; Wilson, Leighton; Jacquelin, Mathias; Ravasi, Matteo; Keyes, David Elliot

doi:10.1145/3581784.3627042

Cited by 6 publications

(1 citation statement)

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“…Tile Low-Rank (TLR) matrix approximation (Amestoy et al, 2015); (Akbudak et al, 2017) simplifies the representative structure of the compressed data, making it amenable to supporting complex matrix operations on challenging hardware environments (Charara et al, 2018); (Keyes et al, 2020). TLR is therefore an excellent compromise between mathematical optimality and implementation complexity and has lately managed to penetrate a wide range of large-scale scientific applications (Abdulah et al, 2018); (Al-Harthi et al, 2020); (Cao et al, 2020); (Ltaief et al, 2021); (Hong et al, 2021); (Cao et al, 2021); Alomairy et al (2022), including geophysical processing (Hong et al, 2021); (Ltaief et al, 2023b,a). Compression capabilities of H-matrices in the context of seismic have been also reported in Jumah and Herrmann (2012).…”

Section: Related Workmentioning

confidence: 99%

High performance computing seismic redatuming by inversion with algebraic compression and multiple precisions

Hong,

Ltaief,

Ravasi

et al. 2024

The International Journal of High Performance Computing Applica

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We present a high-performance implementation of Seismic Redatuming by Inversion (SRI), which combines algebraic compression with mixed-precision (MP) computations. Seismic redatuming entails the repositioning of seismic data recorded at the surface of the Earth to a subsurface level closer to where reflections have originated. Marchenko-based redatuming is the best-in-class SRI method from a theoretical point of view because it can accurately handle full seismic wavefields with minimal data pre-processing. However, it requires intensive data movement, a large memory footprint, and extensive computations due to the need for manipulating large, formally dense, complex-valued frequency matrices in the bandwidth of the recorded seismic data. More precisely, at the heart of Marchenko modeling operator lies a Multi-Dimensional Convolution (MDC) operator, which requires the application of repeated complex-valued Matrix-Vector Multiplications (MVMs) with chosen set of seismic frequency matrices. SRI is deemed to be too time-consuming for realistic domain sizes and therefore industrially impractical. To alleviate these computational bottlenecks, we first improve the memory footprint of the MDC operator by using Tile Low-Rank Matrix-Vector Multiplications (TLR-MVMs); this exploits the low-rank nature of seismic recordings in the frequency domain, used as the kernel of the MDC modeling operator. MP computations are further introduced to increase the arithmetic intensity of the operators. We validate the numerical robustness of our synergistic approach on a benchmark 3D synthetic seismic dataset and demonstrate its use on various hardware architectures. We develop several FP32/FP16/INT8 MP TLR-MVM implementations with a limited and controllable impact on the overall accuracy of application. We achieve up to 63X memory footprint reduction and 12.5X performance speedup against the traditional dense MVM kernel on a single NVIDIA A100 GPU. Moreover, linear scalability is attained when deploying our implementation on eight A100 GPUs. Our implementations of the MDC operator integrate with the open-source PyLops framework for large-scale, matrix-free inverse problems.

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