# IDRIS Hackathon

Team CosmoStat

## What are we trying to do?

• The Universe is difficult to describe analytically, for many applications in Cosmology, we need to simulate it!

• In our case we rely on a class of simple N-body simulations, based on a Particle-Mesh scheme. We alternate between:
• Interpolating particles on a 3D grid
• Computing forces on the grid by 3D Fast Fourier-Transform
• There are existing codes for such simulations in C/Python (FastPM). Rely on the PFFT library:
• MPI-based, can scale to grids of size 20480^3

• What we want to develop, are differentiable simulations, i.e. where we can compute gradients of the output with respect to parameters

Example of reconstructing the initial conditions of the Universe by gradient descent

## FlowPM: Distributed PM Solver in TensorFlow

``````import tensorflow as tf
import numpy as np
import flowpm

cosmo = flowpm.cosmology.Planck15()
stages = np.linspace(0.1, 1.0, 10, endpoint=True)

initial_conditions = flowpm.linear_field(32,          # size of the cube
100,         # Physical size of the cube
ipklin,      # Initial power spectrum
batch_size=16)

# Sample particles
state = flowpm.lpt_init(cosmo, initial_conditions, a0=0.1)
# Evolve particles down to z=0
final_state = flowpm.nbody(cosmo, state, stages, 32)
# Retrieve final density field
final_field = flowpm.cic_paint(tf.zeros_like(initial_conditions), final_state[0])``````

FlowPM on single-GPU

## Scaling up: Mesh TensorFlow

• With a single GPU, 16GB of RAM can run an approximate 128^3 simulation => Far from enough for practical applications

• We adopted the Mesh TensorFlow framework for model parallelism.
``````#A simple 2 layer fully connected network
#y=Relu(xw+bias)v

#Define dimensions
batch = mtf.Dimension("batch", b)
io = mtf.Dimension("io", d_io)
hidden = mtf.Dimension("hidden", d_h)
# x.shape == [batch, io]
#Get tensors
w = mtf.get_variable("w", shape=[io, hidden])
bias = mtf.get_variable("bias", shape=[hidden])
v = mtf.get_variable("v", shape=[hidden, io])
#Define operations
h = mtf.relu(mtf.einsum(x, w, output_shape=[batch, hidden]) + bias)
y = mtf.einsum(h, v, output_shape=[batch, io])``````
``````

batch = mtf.Dimension("batch", b)
io = mtf.Dimension("io", d_io)
hidden = mtf.Dimension("hidden", d_h)
#Define mesh dimensions and layout
mesh_shape = [("processor_rows", 2), ("processor_cols", 2)]
layout_rules = [("batch", "processor_rows"),
("hidden", "processor_cols")]``````

## And it works!

Comparison of distributed simulation on 4 GPUs

But... we are hitting performance and scalability issues

## The problem with Mesh TensorFlow on GPU clusters

• Mesh TensorFlow is designed for Google's TPU pods
• SIMD mesh implementation relying on TPU-specific collectives

• For GPUs, Mesh TensorFlow ships with what's called "DevicePlacementMeshImpl"
``````gpus = tf.config.experimental.list_logical_devices('GPU')
if gpus:
# Replicate your computation on multiple GPUs
c = []
for gpu in gpus:
with tf.device(gpu.name):
a = tf.constant([[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0]])
b = tf.constant([[1.0, 2.0],
[3.0, 4.0],
[5.0, 6.0]])
c.append(tf.matmul(a, b))

with tf.device('/CPU:0'):

print(matmul_sum)``````

## Limitations of Device Placement

• How it works:
• One master TensorFlow process defines and runs the compute graph
• One client TensorFlow process per node just exposes its GPUs over network

• Limitations:
• A very large and complex graph is executed by a single process

• Inter-process comms happen through the gRPC layer
``````  # Resolve the cluster from SLURM environment
cluster = tf.distribute.cluster_resolver.SlurmClusterResolver(
port_base=8822,
gpus_per_node=FLAGS.gpus_per_node,

cluster_spec = cluster.cluster_spec()
# Create a server for all mesh members
server = tf.distribute.Server(cluster_spec, "mesh",

# Only he master job takes care of the graph building,
# everyone else can just chill for now
server.join()

# Otherwise we are the main task, let's define the devices
mesh_devices = [
]
print("List of devices", mesh_devices)

mesh_impl = mtf.placement_mesh_impl.PlacementMeshImpl(
mesh_shape, layout_rules, mesh_devices)``````

# The goal: SPMD Mesh TensorFlow using NCCL

• Level I: Use Horovod as the interface layer between NCCL and TensorFlow

• Level II: Implement a Mesh TensorFlow backend on modified Horovod

• Level III:Implement and Benchmark distributed FlowPM on new Mesh TF

## Level I: Horovod

• Since late last year Horovod includes all2all collectives based on NCCL. BUT, only supports one global communicator.

• With Myriam and Jin, we worked on a PR to include support for multiple communicators.
``````from mpi4py import MPI
import horovod.tensorflow as hvd

# This will be our baseline world communicator
comm = MPI.COMM_WORLD
# Split COMM_WORLD into subcommunicators
subcomm = MPI.COMM_WORLD.Split(color=MPI.COMM_WORLD.rank % 2,
key=MPI.COMM_WORLD.rank)

# Initialize horovod with an array of communicators
hvd.init(comm=[comm, subcomm])
[....]
# AlltoAll over the WORLD communicator
hvd.alltoall(a, communicator_id=0)

# AlltoAll over second (splitted) communicator
hvd.alltoall(a, communicator_id=1)``````

## Level I goals

• Further test implementation (check for deadlocks in particular), and try to get PR approved for merging in Horovod.

• [Very Optional] Implement missing collectives like shifts along one mesh axis

## Level II: Mesh TensorFlow

• We already have a prototype here of a Horovod-based Mesh TensorFlow backend, already runs but with limited functionality)

``````
mesh_impl = HvdSimdMeshImpl(mtf.convert_to_shape(mesh_shape),
mtf.convert_to_layout_rules(layout_rules))

# And internally, HvdSimdMeshImpl essentially does:

# Use MPI to define needed communicators
cart_comm = MPI.COMM_WORLD.Create_cart(dims=dims,
periods=[False]*len(dims))

[...]

# Initializing horovod with our set of communicators
hvd.init(comm=[c for _, c in comms.items()])

# When collectives are called:

t = hvd.alltoall(t, communicator_id=self._comms_id[name_dim])``````

## Level II goals

• Finish and test Mesh TF Horovod implementation

• Benchmark and optimize main ops needed for simulation: FFT3D and halo exchange

GPU utilisation for 3D FFT in device placement Mesh TF

## Level III: FlowPM and Mesh TF applications

• We have never have been able to run FlowPM simulations on grids larger than 1024^3, so we want to test the scaling of our end-application under the new backend

• Some recent functionalities of FlowPM are not yet distributed, in particular Gravitational Lensing. They should be reimplemented in Mesh TF, and tested and optimized for the new backend

• Our lab is also working on 3D brain imaging with NeuroSpin, we have a prototype Mesh TF reconstruction code that can be transfered to new backend

## Level III goals

• Benchmark final application

• Implement missing Mesh TF FlowPM components

• [Bonus goal] Proof of Concept of 3D brain imaging with Mesh TF model parallelism on new backend

By eiffl

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