Stencil kernels dominate a range of scientific applications  including seismic and medical imaging, image processing, and neural networks. Temporal blocking is a performance optimisation that aims to reduce the required memory bandwidth of stencil computations by re-using data from the cache for multiple time steps. It has already been shown to be beneficial for this class of algorithms. However, optimising stencils for practical applications remains challenging. These computations often include sparsely located operators , not aligned with the computational grid ("off-the-grid"). For example, our work is motivated by sources that inject a wavefieldand measurements interpolating grid values . The resulting data dependencies make the adoption of temporal blocking much more challenging. We propose a methodology to inspect these data dependencies and reorder the computation, leading to performance gains in stencil codes where temporal blocking has not been applicable. We implement this novel scheme in the Devito domain-specific compiler toolchain. Devito implements a domain-specific language embedded in Python to generate optimised partial differential equation solvers using the finite-difference method from high-level symbolic problem definitions. We evaluate our scheme using isotropic acoustic, anisotropic acoustic  and isotropic elastic wave propagators of industrial significance. Performance evaluation, after auto-tuning,  shows that this enables substantial performance improvement through temporal blocking , over highly-optimised vectorized spatially-blocked code of up to 1.6x.
Stencil kernels dominate a range of scientific applications , including seismic and medical imaging, image processing, and neural networks. Temporal blocking is a performance optimization that aims to reduce the required memory bandwidth of stencil computations by re-using data from the cache for multiple time steps. It has already been shown to be beneficial for this class of algorithms. However, applying temporal blocking to practical applications' stencils remains challenging. These computations often consist of sparsely located operators not aligned with the computational grid ("off-the-grid"). Our work is motivated by modeling problems in which source injections result in wavefields that must then be measured at receivers by interpolation from the grided wavefield . The resulting data dependencies make the adoption of temporal blocking much more challenging. We propose a methodology to inspect these data dependencies and reorder the computation, leading to performance gains in stencil codes where temporal blocking has not been applicable. We implement this novel scheme in the Devito domain-specific compiler toolchain. Devito implements a domain-specific language embedded in Python to generate optimized partial differential equation solvers using the finite-difference method from high-level symbolic problem definitions. We evaluate our scheme using isotropic acoustic, anisotropic acoustic , and isotropic elastic wave propagators of industrial significance. After auto-tuning, performance evaluation shows that this enables substantial performance improvement through temporal blocking over highly-optimized vectorized spatially-blocked code of up to 1.6x.
A
,
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optimisation
optimization
R
optimising stencils for practical applications
applying temporal blocking to practical applications' stencils
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include
consist of
D
,
R
For example, our
Our
R
sources that inject a wavefieldand measurements interpolating grid values
modeling problems in which source injections result in wavefields that must then be measured at receivers by interpolation from the grided wavefield
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optimised
optimized
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,
R
Performance evaluation, after
After
A
performance evaluation
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, over highly-optimised
over highly-optimized