Example 2: Rimu with MPI

In this example, we will demonstrate using Rimu with MPI.

A runnable script for this example is located here. Run it with mpirun julia BHM-example-mpi.jl.

We start by importing Rimu and Rimu.RMPI, which contains MPI-related functionality.

using Rimu
using Rimu.RMPI

We will compute the ground-state of a Bose-Hubbard model in momentum space with 10 particles in 10 sites.

First, we define the Hamiltonian. We want to start from an address with zero momentum.

address = BoseFS(10, 5 => 10)

BoseFS{10,10}(0, 0, 0, 0, 10, 0, 0, 0, 0, 0)

We will set the interaction strength u to 6. The hopping strength t defaults to 1.0.

hamiltonian = HubbardMom1D(address; u=6.0)

HubbardMom1D(BoseFS{10,10}(0, 0, 0, 0, 10, 0, 0, 0, 0, 0); u=6.0, t=1.0)

Next, we construct the starting vector. We use a PDVec, which is automatically MPI distributed if MPI is available. We set the vector's stochastic style to IsDynamicSemistochastic, which improves statistics and reduces the sign problem.

dvec = PDVec(address => 1.0; style=IsDynamicSemistochastic())

1-element PDVec: style = IsDynamicSemistochastic{Float64,ThresholdCompression,DynamicSemistochastic}()
  fs"|0 0 0 0 10 0 0 0 0 0⟩" => 1.0

We set a reporting strategy. We will use ReportToFile, which writes the reports directly to a file. This is useful for reducing memory use in long-running jobs, as we don't need to keep the results in memory. Setting save_if=is_mpi_root() will ensure only the root MPI rank will write to the file. The chunk_size parameter determines how often the data is saved to the file. Progress messages are suppressed with io=devnull.

r_strat = ReportToFile(filename="result.arrow", save_if=is_mpi_root(), reporting_interval = 1, chunk_size=1000, io=devnull)

ReportToFile{Symbol}("result.arrow", 1, 1000, true, false, Base.DevNull(), :zstd, nothing)

Now, we can set other parameters as usual. We will perform the computation with 10_000 walkers. We will also compute the projected energy.

s_strat = DoubleLogUpdate(targetwalkers=10_000)
post_step = ProjectedEnergy(hamiltonian, dvec)

ProjectedEnergy{HubbardMom1D{Float64, 10, BoseFS{10, 10, BitString{19, 1, UInt32}}, 6.0, 1.0}, Rimu.DictVectors.FrozenPDVec{BoseFS{10, 10, BitString{19, 1, UInt32}}, Float64, 1}, Rimu.DictVectors.FrozenPDVec{BoseFS{10, 10, BitString{19, 1, UInt32}}, Float64, 1}}(:vproj, :hproj, HubbardMom1D(BoseFS{10,10}(0, 0, 0, 0, 10, 0, 0, 0, 0, 0); u=6.0, t=1.0), Rimu.DictVectors.FrozenPDVec{BoseFS{10, 10, BitString{19, 1, UInt32}}, Float64, 1}((Pair{BoseFS{10, 10, BitString{19, 1, UInt32}}, Float64}[fs"|0 0 0 0 10 0 0 0 0 0⟩" => 1.0],)), Rimu.DictVectors.FrozenPDVec{BoseFS{10, 10, BitString{19, 1, UInt32}}, Float64, 1}((Pair{BoseFS{10, 10, BitString{19, 1, UInt32}}, Float64}[fs"|1 0 0 0 8 0 0 0 1 0⟩" => 5.692099788303083, fs"|0 0 0 0 8 0 0 0 0 2⟩" => 4.024922359499621, fs"|0 0 0 0 10 0 0 0 0 0⟩" => 7.0, fs"|0 0 1 0 8 0 1 0 0 0⟩" => 5.692099788303083, fs"|0 0 0 1 8 1 0 0 0 0⟩" => 5.692099788303083, fs"|0 1 0 0 8 0 0 1 0 0⟩" => 5.692099788303083],)))

The @mpi_root macro performs an action on the root rank only, which is useful for printing.

@mpi_root println("Running FCIQMC with ", mpi_size(), " rank(s).")

Running FCIQMC with 1 rank(s).

Finally, we can run the computation.

lomc!(hamiltonian, dvec; r_strat, s_strat, post_step, dτ=1e-4, laststep=10_000);

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