The Finite-Volume Dynamical Core on GPUs within GEOS-5 William Putman Global Modeling and Assimilation Office NASA GSFC 9/8/11 Programming weather, climate, and earth-system models on heterogeneous multi-core platforms- Boulder, CO

Outline Motivation Motivation Test advection kernel Test advection kernel Approach in GEOS-5 Approach in GEOS-5 Design for FV development Design for FV development Early results Early results Status/future Status/future Motivation Motivation Test advection kernel Test advection kernel Approach in GEOS-5 Approach in GEOS-5 Design for FV development Design for FV development Early results Early results Status/future Status/future Development Platform Development Platform NASA Center for Climate Simulation GPU Cluster 32 Compute Nodes 2 Hex-core 2.8 GHz Intel Xeon Westmere Processors 48 GB of memory per node 2 NVidia M2070 GPUs dedicated x16 PCIe Gen2 connection Infiniband QDR Interconnect 64 Graphical Processing Units 1 Tesla GPU (M2070) 448 CUDA cores ECC Memory 6 GB of GDDR5 memory 515 Gflop/s of double precision floating point performance (peak) 1.03 Tflop/s of single precision floating point performance (peak) 148 GB/sec memory bandwidth 1 PCIe x16 Gen2 system interface

We are pushing the resolution of global models into the 10- to 1-km range GEOS-5 can fit a 5-day forecast at 10-km within the 3-hour window required for operations using 12,000 Intel Westmere cores At current cloud-permitting resolutions (10- to 3-km) required scaling of 300,000 cores is reasonable (though not readily available) To get to global cloud resolving (1-km or finer) requires order 10-million cores Weak scaling of cloud-permitting GEOS-5 model indicates need for accelerators ~90% of those computations are in the dynamics Motivation Global Cloud Resolving GEOS-6 Motivation Global Cloud Resolving GEOS-6 PDF of Average Convective Cluster Brightness Temperature 3.5-km GEOS-5 Simulated Clouds

The ultimate target: the FV dynamical core – accounts for ~ 90% of the compute cycles at high-resolution (1- to 10-km) The D-grid Shallow water routines are as costly as the non- hydrostatic dynamics (thus first pieces to attack) An offline Cuda C demonstration kernel was developed for the 2-D advection scheme Data Transfers from Host to the Device cost about 10-15% Fermi GPGPU 16x 32-core Streaming Multiprocessors Fermi GPGPU 16x 32-core Streaming Multiprocessors For a 512x512 domain, the benchmark revealed up to 80x speedup Caveats: Written entirely on the GPU (no data transfers) Single CPU to Single GPU speedup compares Cuda C to C code Motivation Idealized FV advection kernel Motivation Idealized FV advection kernel CUDA Profiler – Used to profile

Fermi GPGPU 16x 32-core Streaming Multiprocessors Fermi GPGPU 16x 32-core Streaming Multiprocessors The Finite-Volume kernel performs 2-dimensional advection on a 256x256 mesh Blocks on the GPU are used to decompose the mesh in a similar fashion to MPI domain decomposition Optimal distribution of blocks improve occupancy on the GPU Targeting 100% Occupancy and threads in multiples of the Warp size (32) Best performance with 16, 32 or 64 threads in the Y-direction Fermi – Compute 2.0 CUDA device: [Tesla M2050] Occupancy - the amount of shared memory and registers used by each thread block, or the ratio of active warps to the maximum number of warps available Warp – A collection of 32 threads CUDA Profiler – Used to profile and compute occupancy Motivation Idealized FV advection kernel - tuning Motivation Idealized FV advection kernel - tuning Total Number of Threads

Approach GEOS-5 Modeling Framework and the FV 3 dycore Approach GEOS-5 Modeling Framework and the FV 3 dycore Earth System Modeling Framework (ESMF) GEOS-5 uses a fine-grain component design with light-weight ESMF components used down to the parameterization level A hierarchical topology is used to create Composite Components, defining coupling (relations) between parents and children components As a result, implementation of GEOS-5 residing entirely on GPUs is unrealistic, we must have data exchanges to the CPU for ESMF component connections Flexible Modeling System (FMS) Component based modeling framework developed and implemented at GFDL The MPP layer provides a uniform interface to different message-passing libraries, used for all MPI communication in FV The GPU implementation of FV will extend out to this layer and exchange data for halo updates between GPU and CPU fv_dynamics dyn_core Halo Updates do 1,npz c_sw geopk NH column based Halo Updates do 1,npz d_sw geopk NH column based Halo Updates Tracer advection Vertical remapping PGI Cuda Fortran – CPU and GPU code co-exist in the same code-base (#ifdef _CUDA)

1.8x - 1.3x Speedup Approach Single Precision FV cubed Approach Single Precision FV cubed FV was converted to single precision prior to beginning GPU development

Approach Domain Decomposition (MPI and GPU) Approach Domain Decomposition (MPI and GPU) MPI Decomposition – 2D in X,Y GPU blocks distributed in X,Y within the decomposed domain

Bottom-up development Target kernels for 1D and 2D advection will be developed at the lowest level of FV (tp_core module) fxppm/fyppm xtp/ytp fv_tp_2d The advection kernels are reused throughout the c_sw and d_sw routines (the Shallow Water equations) delp/pt/vort advection At the dyn_core layer halo regions will be exchanged between the host and the device The device data is centrally located and maintained at a high level (fv_arrays) to maintain object oriented approach (and we can pin this memory as needed) Test-driven development Offline test modules have been created to develop GPU kernels for tp_core Easily used to validate results with the CPU code Improve development time by avoiding costly rebuilds of full GEOS-5 code-base Approach GEOS-5 Modeling Framework and the FV dycore Approach GEOS-5 Modeling Framework and the FV dycore

π 1D flux-form operators Directionally split Cross-stream inner-operators The value at the edge is an average of two one-sided 2nd order extrapolations across edge discontinuities Positivity for tracers Fitting by Cubic Polynomial to find the value on the other edge of the cell - vanishing 2nd derivative - local mean = cell mean of left/right cells ORD=7 details ( 4th order and continuous before monotonicity )… Sub-Grid PPM Distribution Schemes Details of the Implementation The FV advection scheme (PPM) Details of the Implementation The FV advection scheme (PPM)

Details of the Implementation Serial offline test kernel for 2D advection (fv_tp_2d with PGI Cuda Fortran) Details of the Implementation Serial offline test kernel for 2D advection (fv_tp_2d with PGI Cuda Fortran) GPU Code istat = cudaMemcpy(q_device, q, NX*NY) call copy_corners_dev >>() call xtp_dev >>() call intermediateQj_dev >>() call ytp_dev >>() call copy_corners_dev >>() call ytp_dev >>() call intermediateQi_dev >>() call xtp_dev >>() call yflux_average_dev >>() call xflux_average_dev >>() istat = cudaMemcpy(fy, fy_device, NX*NY) istat = cudaMemcpy(fx, fx_device, NX*NY) ! Compare fy/fx bit-wise reproducible to CPU code

GPU Code istat = cudaMemcpyAsync(qj_device, q, NX*NY, stream(2)) istat = cudaMemcpyAsync(qi_device, q, NX*NY, stream(1)) call copy_corners_dev >>() call xtp_dev >>() call intermediateQj_dev >>() call ytp_dev >>() call copy_corners_dev >>() call ytp_dev >>() call intermediateQi_dev >>() call xtp_dev >>() call yflux_average_dev >>() call xflux_average_dev >>() istat = cudaMemcpyAsync(fy, fy_device, NX*NY, stream(2)) istat = cudaMemcpyAsync(fx, fx_device, NX*NY, stream(1)) Data is copied back to the host for export, but the GPU work can continue… Details of the Implementation Serial offline test kernel for 2D advection (fv_tp_2d with PGI Cuda Fortran) Details of the Implementation Serial offline test kernel for 2D advection (fv_tp_2d with PGI Cuda Fortran)

GPU Code call getCourantNumbersY(…stream(2)) call getCourantNumbersX(…stream(1)) call fv_tp_2d(delp…) call update_delp(delp,fx,fy,…) call update_KE_Y(…stream(2)) call update_KE_X(…stream(1)) call divergence_damping() call compute_vorticity() call fv_tp_2d(vort…) call update_uv(u,v,fx,fy,…) istat = cudaStreamSynchronize(stream(2)) istat = cudaStreamSynchronize(stream(1)) istat = cudaMemcpy(delp, delp_dev, NX*NY) istat = cudaMemcpy( u, u_dev, NX*(NY+1)) istat = cudaMemcpy( v, v_dev, (NX+1)*NY) CPU Time 6 coresD_SW coresD_SW GPU Time 6 GPUsD_SW GPUsD_SW Speedup 6 GPUs: 6 cores 16.2x 6 GPUs : 36 cores 4.6x 36 GPUs : 36 cores 10.2x Times for a 1-day 28-km Shallow Water Test Case Details of the Implementation D_SW – Asynchronous multi-stream Details of the Implementation D_SW – Asynchronous multi-stream

Status - Summary Most of D_SW is implemented on GPU Preliminary results are being generated (but need to be studied more) C_SW routine is similar to D_SW, but has not been touched yet Data transfers between host and device are done asynchronously when possible Most data transfers will move up to the dyn_core level as implementation progresses, improving performance Higher-level operations in dyn_core will be tested with pragmas (Kerr - GFDL) Non-hydrostatic core must be tackled (column based) Strong scaling potential?