AI optimizing HPC simulations (presentation from 6th EULAG Workshop)
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Krzysztof Rojek discusses adapting scientific codes for advanced computing architectures at the 6th International EULAG Users Workshop. The focus is on implementing mixed precision arithmetic to optimize performance and energy consumption in high-performance computing (HPC) platforms. The proposed methods and algorithms aim to reduce energy consumption by 33% while maintaining acceptable accuracy and improving computational speed across different architectures.
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AI optimizing HPC simulations (presentation from 6th EULAG Workshop)
- 1. Krzysztof Rojek, CTO, byteLAKE krojek@byteLAKE.com 6TH INTERNATIONAL EULAG USERS WORKSHOP MAY 29, 2018, 14:00-14:45
- 2. Area: Adaptation of a real-life scientific codes to the most advanced computing architectures. Challenge: Device architectures are constantly changing. Current architectures are very various. Our codes need to be very portable and flexible. Goal: Take HPC to the "Industry 4.0" by implementing smart techniques to optimize the codes in terms of performance and energy consumption. 2
- 3. Piz Daint (ranked 3-rd at top 500): GPU: NVIDIA Tesla P100 - PASCAL 1xGPU per node Single GPU design 5320 nodes (up to 36 used in this work) Calculation speed: float is 2x faster than double MICLAB: GPU: NVIDIA Tesla K80 - KEPLER 2xGPUs per node Dual GPU design 2 nodes (remaining nodes with Intel Xeon Phi) Calculation speed: float is 3x faster than double 3 Size of data transfer between nodes: 2x less using float than double No access to sudo user – it makes a problem when your code is based on DVFS Expectation: Mixed precision arithmetic allows us to reduce the energy consumption and execution time; It can be used in the real HPC platforms (without special access)
- 4. Stencil-based algorithm for numerical simulation of geophysical fluids flows on micro-to-planetary scales: 7 stencils (compressed into 4 kernels) – each depends on one or more others (343 flops-per-el.) Iterative algorithm – a single iteration represents one time step 11 matrices: x, xP – scalar quantity (i.e. temperature); input/output matrices between time steps v1, v2, v3, v1P, v2P, v3P – velocity vectors in i, j, and k directions h – density matrix cp, cn – temporary, intermediate matrices 4 xP x xPKernel 3 Kernel 2 Kernel 1 Kernel 0 xP v1P v2P cp xP cn v3P Outputs: (x,v1,v2,v3,h) (v1,v2,v3,h,xP) (x,h,xP,v1P,v2P,v3P) (x,h,v1P,v2P,v3P,cp,cn) Inputs:
- 5. Idea: Provide a highly parametrized code in order to easily map the algorithm onto GPU Mapping: Select the right values of given code parameters (configuration) in terms of desired criterion (Energy consumption) How to: We build the search space of possible configurations and prune it using our machine learning module (MLM) MLM: It is still the ongoing task. Here we propose to apply the modified random forest algorithm. 5
- 6. We can use different number of: Streams count (SPG) Nodes count (NDS) With different topologies: Topology of streams (TGP) Topology of nodes (TDS) 6 1x1 1x2 1x1 2x1 1x1 1x1 2x1 1x2 2x2 1x1 1x2 1x3 1x4 1x1 2x1 3x1 4x1 Stream/Node: 1 Topology: 1 Streams/Nodes: 2 Topologies: 2 Streams/Nodes: 4 Topologies: 3
- 7. 7 Synchronize domain Synchronize domain Synchronize domain Synchronize domain Synchronize domain Synchronize domain Synchronize domain Synchronize domain Kernel 0 Kernel 1 Kernel 2 Kernel 3 Data transfer Kernel 0 Kernel 1 Kernel 2 Kernel 3 Data transfer vs. Each stream works on distributed subdomains Computations are independent within a single time step Halo exchange is required after each time step Each stream share the same subdomain Computations depends on the neighboring streams Halo exchange is not required within a single node
- 8. By selecting the right strategy of halo exchanging we can focus on more parallelism or less operations We can use a different strategy within node and between nodes 8 Halo exchange cudaMemcpy Buffers GPU direct No GPU direct No-buffers Kernels Single kernel Two kernels
- 9. We takes into consideration also some basic parameters: CUDA block sizes for each of 4 kernels CUDA blocks are of size X times Y, where X*Y mod 32 = 0 X>=Y X mod 16 =0 X*Y <= 1024 X<=M and Y<=N, where NxMxL is a size of the grid Data alignment and padding within a range from 1 to 4096 B Align in: {1, 2, 4, 8, …, 4096} 9
- 10. Assumption: We believe that we can find a really good configuration by testing about 5000 configurations from the search space (more that this is too expensive) We consider two possible approaches: Positive: Find good solutions and eliminate groups that seem to be worse than ours Risk: When we find a branch with a good solution we can eliminate other branches (also quite good) that should be worse. In fact we can eliminate a branch containing the best solution. Negative: Find bad solutions and eliminate them Risk: When we find branches with bad solutions we can eliminate them although the worst one can be still in (the best one also is there). Fact: We test random branches (we may not select the best or the worst one); we are searching for the suboptimal solution. 10
- 11. Precision: DOUBLE Diameter: 28.0 L2 norm: 0.0746 Diffusion error: 1.7503 Phase error: 0.7576 11 Halo exchange (xP or x)
- 12. Precision: DOUBLE Diameter: 28.0 L2 norm: 0.0746 Diff. err.: 1.7503 Phase err.: 0.7576 Precision: FLOAT Diameter: 28.0 L2 norm: 0.1301 Diff. err.: 2.2439 Phase err.: 7.5919 12 FloatDouble
- 13. Goal: Reduce the energy consumption Condition: Keep the accuracy at a high level (1% loss is acceptable) Assumptions: The proposed method is intended to iterative algorithms Dynamic approach, self adaptable to a particular simulation Self adaptation is done based on the short training stage (the first 11 time steps) 13 1. Change the i-th matrix from DP to SP 2. Execute a single time step 3. Measure Energy and Accuracy 4. Restore the i-th matrix to DP Training stage: Traditional approach based on static selection of precision arithmetic is less flexible and may be too restrictive for some simulations
- 14. 14 0 10 20 30 40 50 60 70 80 90 100 0/4 1/4 2/4 3/4 4/4 ENERGYCONSUMPTION[%] PART OF A SINGLE SOLID BODY ROTATION Change the precision of the i-th matrix from DP to SP 0 10 20 30 40 50 60 70 80 90 100 0/4 1/4 2/4 3/4 4/4 ACCURACYLOSS[%] PART OF A SINGLE SOLID BODY ROTATION DOUBLE Change the precision of the i-th matrix from DP to SP Should be minimizedShould be maximized ΔE ΔA
- 15. 15 Assumptions: ΔE – should be maximized ΔA – should be minimized Conclusion: R=ΔE/ΔA – the higher, the better Method: We estimate the R ratio for each matrix and set matrices with the highest R from double to float This step is repeated until the accuracy loss is lower than 1% Set the matrices with the highest R to float until the accuracy loss<1% Sort them decreasing by R Calculate R=ΔE/ΔA for each matrix The higher, the better
- 16. Precision: DOUBLE Diameter: 28.0 L2 norm: 0.0746 Diff. err.: 1.7503 Phase err.: 0.7576 Precision: MIXED Diameter: 28.0 L2 norm: 0.0749 Diff. err.: 1.7504 Phase err.: 0.7576 16 Float group: x, xP, v3, h, v1P,v3P Double group: v1, v2, v2P, cp, cn Double
- 17. 17 Double Mixed The proposed method was also validated for the other tests The difference between L2 norms for double and mixed precision is 0.00001 The phase is 44.2135 for both cases
- 18. Test: 512x512x512 – 3909 time steps 18 Double 1 335.48 44 Mixed 1 255.02 1.32 35 19.79 Double 32 27.52 71 Mixed 24 21.65 1.27 48 32.63 Conclusion: Energy consumption is reduced by 33% Best performance 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 1 6 11 16 21 26 31 36 Gflop/s # of nodes Double Mixed
- 19. Test: 512x512x512 – 3909 time steps 19 Double 1/2 533.65 80 Mixed 1/2 352.18 1.51 53 34.00 Double 4/8 144.83 87 Mixed 4/8 96.04 1.51 57 33.66 Conclusion: Energy consumption is reduced by 33% Best performance 0 200 400 600 800 1000 1200 1400 1600 1800 2000 1 2 3 4 Gflop/s # of GPUs – 2 GPUs per node Double Mixed
- 20. The developed implementation of MPDATA is very flexible and portable The proposed method allows us to automate the code adaptation even for a very large number of possible configurations Mixed precision arithmetic allows us to reduce the energy consumption and execution time It can be used in the real HPC platforms without special access to the machine It has an effect on the computation speed, data transfer, and scalability of the application The proposed method allows us to reduce the energy consumption by 33% without loss in accuracy It has also improved the performance by the factor of 1.27 for Piz Daint and 1.51 for MICLAB in relation to double precision arithmetic 20
- 21. We build Artificial Intelligence software and integrate that into products. We port and optimize algorithms for parallel, CPU+GPU architectures. We design and optimize algorithms for HPC supercomputers. byteLAKE We are specialists in: www.byteLAKE.com Machine Learning Deep Learning Computer Vision High Performance Computing Heterogeneous Computing Edge Computing Our mission: help industries transform for the era of Artificial Intelligence. We combine business and academia. Our team consists of experts schooled by Fortune 500 corporations as well as PhD researchers.
- 22. 22 Areas of Our Expertise Computer Vision Deep Learning Machine Learning Learning Optimization AI for Edge Devices HPC Expertise Consultancy Proof of Concept