Quantum-based Molecular Dynamics Simulations Using Tensor Cores

Finkelstein, Joshua M.; Smith, Justin S.; Mniszewski, Susan M.; Barros, Kipton; Negre, Christian F. A.; Rubensson, Emanuel H.; Niklasson, Anders M. N.

doi:10.48550/arxiv.2107.02737

Cited by 2 publications

(4 citation statements)

References 104 publications

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“…We develop two types of implementations: cutlass halfhalf and cutlass tf32tf32. We use the mma.sync.aligned.m16n8k8 PTX instruction, which computes matmul- (16,8,8) and addition using FP16 Tensor Cores. We call this implementation cutlass halfhalf.…”

Section: Incorporating Our Methods Into Cutlassmentioning

confidence: 99%

“…In this case, m 13 • • • m 0 bits decide whether we round-up in Eq. (8). We show the mantissa length kept by Eqs.…”

Section: Expectation Of Mantissa Lengthmentioning

confidence: 99%

“…For single-precision matrix-matrix multiplication, Markidis et al propose a method to improve the accuracy of Tensor Core computation by using auxiliary FP16 variables to account for the truncated bits [17]. Markidis' method and its extensions are used for FFT [27], QR Factorization [22], and quantum-based molecular dynamics simulations [8]. However, the use of auxiliary FP16 variables alone is not sufficient to fully recover the FP32 accuracy.…”

Section: Introductionmentioning

confidence: 99%

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Recovering single precision accuracy from Tensor Cores while surpassing the FP32 theoretical peak performance

Ootomo¹,

Yokota²

2022

Preprint

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Tensor Core is a mixed-precision matrix-matrix multiplication unit on NVIDIA GPUs with a theoretical peak performance of more than 300 TFlop/s on Ampere architectures. Tensor Cores were developed in response to the high demand of dense matrix multiplication from machine learning. However, many applications in scientific computing such as preconditioners for iterative solvers and low-precision Fourier transforms can exploit these Tensor Cores. To compute a matrix multiplication on Tensor Cores, we need to convert input matrices to half-precision, which results in loss of accuracy. To avoid this, we can keep the mantissa loss in the conversion using additional half-precision variables and use them for correcting the accuracy of matrix-matrix multiplication. Even with this correction, the use of Tensor Cores yields higher throughput compared to FP32 SIMT Cores. Nevertheless, the correcting capability of this method alone is limited, and the resulting accuracy cannot match that of a matrix multiplication on FP32 SIMT Cores. We address this problem and develop a high accuracy, high performance, and low power consumption matrix-matrix multiplication implementation using Tensor Cores, which exactly matches the accuracy of FP32 SIMT Cores while achieving superior throughput. The implementation is based on NVIDIA's CUTLASS. We found that the key to achieving this accuracy is how to deal with the rounding inside Tensor Cores and underflow probability during the correction computation. Our implementation achieves 51TFlop/s for a limited exponent range using FP16 Tensor Cores and 33TFlop/s for full exponent range of FP32 using TF32 Tensor Cores on NVIDIA A100 GPUs, which outperforms the theoretical FP32 SIMT Core peak performance of 19.5TFlop/s.

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Section: Incorporating Our Methods Into Cutlassmentioning

confidence: 99%

“…In this case, m 13 • • • m 0 bits decide whether we round-up in Eq. (8). We show the mantissa length kept by Eqs.…”

Section: Expectation Of Mantissa Lengthmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Recovering single precision accuracy from Tensor Cores while surpassing the FP32 theoretical peak performance

Ootomo¹,

Yokota²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…For single-precision matrix-matrix multiplication, Markidis et al propose a method to improve the accuracy of Tensor Core computation by using auxiliary FP16 variables to account for the truncated bits (Markidis et al, 2018). Markidis' method and its extensions are used for FFT (Sorna et al, 2018), QR Factorization (Ootomo and Yokota, 2020), and quantum-based molecular dynamics simulations (Finkelstein et al, 2021). However, the use of auxiliary FP16 variables alone is not sufficient to fully recover the FP32 accuracy.…”

Section: Introductionmentioning

confidence: 99%

Recovering single precision accuracy from Tensor Cores while surpassing the FP32 theoretical peak performance

Ootomo

Yokota

2022

The International Journal of High Performance Computing Applica

View full text Add to dashboard Cite

Tensor Core is a mixed-precision matrix–matrix multiplication unit on NVIDIA GPUs with a theoretical peak performance of more than 300 TFlop/s on Ampere architectures. Tensor Cores were developed in response to the high demand of dense matrix multiplication from machine learning. However, many applications in scientific computing such as preconditioners for iterative solvers and low-precision Fourier transforms can exploit these Tensor Cores. To compute a matrix multiplication on Tensor Cores, we need to convert input matrices to half-precision, which results in loss of accuracy. To avoid this, we can keep the mantissa loss in the conversion using additional half-precision variables and use them for correcting the accuracy of matrix–matrix multiplication. Even with this correction, the use of Tensor Cores yields higher throughput compared to FP32 SIMT Cores. Nevertheless, the correcting capability of this method alone is limited, and the resulting accuracy cannot match that of a matrix multiplication on FP32 SIMT Cores. We address this problem and develop a high accuracy, high performance, and low power consumption matrix–matrix multiplication implementation using Tensor Cores, which exactly matches the accuracy of FP32 SIMT Cores while achieving superior throughput. The implementation is based on NVIDIA’s CUTLASS. We found that the key to achieving this accuracy is how to deal with the rounding inside Tensor Cores and underflow probability during the correction computation. Our implementation achieves 51 TFlop/s for a limited exponent range using FP16 Tensor Cores and 33 TFlop/s for full exponent range of FP32 using TF32 Tensor Cores on NVIDIA A100 GPUs, which outperforms the theoretical FP32 SIMT Core peak performance of 19.5 TFlop/s.

show abstract

Quantum-based Molecular Dynamics Simulations Using Tensor Cores

Cited by 2 publications

References 104 publications

Recovering single precision accuracy from Tensor Cores while surpassing the FP32 theoretical peak performance

Recovering single precision accuracy from Tensor Cores while surpassing the FP32 theoretical peak performance

Recovering single precision accuracy from Tensor Cores while surpassing the FP32 theoretical peak performance

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