rom: Decoder

A key assumption of projection-based ROMs is to approximate the full-order model (FOM) state, , as:

where is the reduced state (or generalized coordinates), and is the decoder (or mapping).

Custom Decoder

A custom decoder in pressio4py implements the general mapping above.

This allows one to use an arbitrary function to map the ROM state to the FOM state.

class CustomMapper:
  def __init__(self, fomSize, romSize):
    # attention: the jacobian of the mapping must be column-major oder
    # so that pressio can view it without deep copying it, this enables
    # to keep only one jacobian object around and to call the update
    # method below correctly
    self.jacobian_ = np.zeros((fomSize,romSize), order='F')

  def jacobian(self): return self.jacobian_

  def applyMapping(self, romState, fomState):
    #fomState[:] = whatever is needed
    pass

  def updateJacobian(self, romState):
    # update the self.jacobian_[:,:]
    pass

# create the mapper
myMapper = CustomMapper(10,3)
# to create a custom decoder, one can do
customDecoder = rom.Decoder(myMapper, "MyMapper")

Requirements

rom_state_type : rank-1 numpy.array
fom_state_type : rank-1 numpy.array
jacobian_type : rank-2 numpy.array

Note: there is no explicit constraint on what the mapping is, it can be anything.

As long as the decoder (or mapper) class implements the concept, it is admissible.

Linear Decoder

A linear decoder is a mapping of the form:

where is the Jacobian matrix (for the time being, assume it constant).

Example usage

# create the matrix
# attention: phi must be column-major for these reasons:
#
# 1. pressio4py uses blas (wherever possible) to operate on numpy arrays,
#    so a column-major layout implies seamless compatiblity with blas
#
# 2. when using column-major layout, pressio4py references the
#    matrix phi without doing a deep copy, which saves memory
#    since a single jacobian matrix is alive.
#
phi = np.ones((10,3), order='F')

# to create the linear decoder, you simply do
linearDecoder = rom.Decoder(phi)

# linearDecoder exposes a method to evaluate the mapping
fomState, romState = np.zeros(10), np.ones(3)
linearDecoder.applyMapping(romState, fomState)
print(fomState)

Requirements

rom_state_type : rank-1 numpy.array
fom_state_type : rank-1 numpy.array
jacobian_type : rank-2 numpy.array