MParT supports the ability to serialize/archive objects when installed with the MPART_ARCHIVE cmake configuration option, powered by the cereal C++ serialization library. One example of using this to save would be to do

#include <MParT/Utilities/Serialization.h>
using namespace mpart;

void SerializeComponent(int inputDim, int maxOrder, std::string filename) {
    // Create MapOptions
    MapOptions options;
    options.basisType = BasisTypes::ProbabilistHermite;
    options.basisNorm = false;

    // Create FixedMultiIndexSet and map component
    FixedMultiIndexSet<Kokkos::HostSpace> mset (inputDim, maxOrder);
    auto comp = MapFactory::CreateComponent(mset, options);
    auto coeffs = comp->Coeffs();
    for (int i = 0; i < coeffs.extent(0); i++)
        coeffs(i) = 0.5*(i+1);

    // Serialize objects
    std::ofstream os(filename);
    cereal::BinaryOutputArchive archive(os);
    archive(options, mset, comp->Coeffs());

ConditionalMapBase<Kokkos::HostSpace> DeserializeComponent(std::string filename) {
    std::ifstream is(filename);
    cereal::BinaryInputArchive archive(is);
    MapOptions options;
    FixedMultiIndexSet<Kokkos::HostSpace> mset(1,1); // No default constructor
    Kokkos::View<double*, Kokkos::HostSpace> coeffs;
    archive(options, mset, coeffs);
    auto comp = MapFactory::CreateComponent(mset, options);
    return comp;

int main() {
    int inputDim = 5;
    int maxOrder = 3;
    std::string filename = "";
    SerializeComponent(inputDim, maxOrder, filename);
    auto comp = DeserializeComponent(filename);

In Python, you can only serialize one object per file.

import mpart as mt

def SerializeComponent(inputDim, maxOrder):
    # Create MapOptions
    options = mt.MapOptions()
    options.basisType = mt.BasisTypes.ProbabilistHermite
    options.basisNorm = False;

    # Create FixedMultiIndexSet and map component
    multis = np.array([[0],[1]])
    mset= mt.MultiIndexSet(multis)
    fixed_mset = mset.fix(True)

    component = mt.CreateComponent(fixed_mset, options)
    coeffs = component.CoeffMap()
    for i in range(len(coeffs)):
        coeffs[i] = 0.5*(i+1)

    # Serialize objects

def DeserializeComponent():
    # Deserialize the FixedMultiIndexSet
    # Note that we need to construct the object before calling Deserialize
    fixed_mset = mt.MultiIndexSet(np.array([[0]])).fix(True)

    # Deserialize the MapOptions
    options = MapOptions()

    # Deserialize the Map Coefficients and construct the component
    inputDim, outputDim, coeffs = mt.DeserializeMap("")
    component = mt.CreateComponent(fixed_mset, options)