Package: gpim
What is GPimGPim is a python package that provides an easy way to apply Gaussian processes (GP) inPyroandGpytorchto images and hyperspectral data and to perform GP-based Bayesian optimization on grid data. The intended audience are domain scientists (for example, microscopists) with a basic knowledge of how to work with numpy arrays in Python.Scientific papers where GPim was used:GP for 3D hyperspectral microscopy data:npj Comput Mater 6, 21 (2020)GP for 4D hyperspectral microscopy data:Journal of Applied Physics 128, 055101 (2020)GP and GP-based BO for Ising model:Journal of Applied Physics 128, 164304 (2020)GP-based BO for hysteresis loop engineering in ferroelectrics:Journal of Applied Physics 128, 024102 (2020)InstallationFirst installPyTorch. Then install GPim usingpipinstallgpimHow to useGP reconstructionBelow is a simple example of applying GPim to reconstructing a sparse 2D image. It can be similarly applied to 3D and 4D hyperspectral data. The missing data points in sparse data must be represented asNaNs. In the absense of missing observation GPim can be used for image and spectroscopic data cleaning/smoothing in all the dimensions simultaneously, as well as for the resolution enhancement.importgpimimportnumpyasnp# # Load datasetR=np.load('sparse_exp_data.npy')# Get full (ideal) grid indicesX_full=gpim.utils.get_full_grid(R,dense_x=1)# Get sparse grid indicesX_sparse=gpim.utils.get_sparse_grid(R)# Kernel lengthscale constraints (optional)lmin,lmax=1.,4.lscale=[[lmin,lmin],[lmax,lmax]]# Run GP reconstruction to obtain mean prediction and uncertainty for each predictied pointmean,sd,hyperparams=gpim.reconstructor(X_sparse,R,X_full,lengthscale=lscale,learning_rate=0.1,iterations=250,use_gpu=True,verbose=False).run()# Plot reconstruction resultsgpim.utils.plot_reconstructed_data2d(R,mean,cmap='jet')# Plot evolution of kernel hyperparameters during traininggpim.utils.plot_kernel_hyperparams(hyperparams)GP-based Bayesian optimizationWhen performing measurements (real or simulated), one can use the information about the expected function value and uncertainty in GP reconstruction to select the next measurement point. This is usually referred to as exploration-exploitation approach in the context of Bayesian optimization. A simple example with a "dummy" function is shown below.importgpimimportnumpyasnpnp.random.seed(42)# Create a dummy 2D functiondeftrial_func(idx):"""Takes a list of indices as input and returns function value at these indices"""deffunc(x0,y0,a,b,fwhm):returnnp.exp(-4*np.log(2)*(a*(idx[0]-x0)**2+b*(idx[1]-y0)**2)/fwhm**2)Z1=func(5,10,1,1,4.5)Z2=func(10,8,0.75,1.5,7)Z3=func(18,18,1,1.5,10)returnZ1+Z2+Z3# Create an empty observation matrixgrid_size=25Z_sparse=np.ones((grid_size,grid_size))*np.nan# Seed it with several random observationsidx=np.random.randint(0,grid_size,size=(4,2))foriinidx:Z_sparse[tuple(i)]=trial_func(i)# Get full and sparse grid indices for GPX_full=gpim.utils.get_full_grid(Z_sparse)X_sparse=gpim.utils.get_sparse_grid(Z_sparse)# Initialize Bayesian optimizer with an 'expected improvement' acquisition functionboptim=gpim.boptimizer(X_sparse,Z_sparse,X_full,trial_func,acquisition_function='ei',exploration_steps=30,use_gpu=False,verbose=1)# Run Bayesian optimizationboptim.run()# Plot exploration historygpim.utils.plot_query_points(boptim.indices_all,plot_lines=True)Running GPim notebooks in the cloudExecutable Google Colabnotebookwith the examples of applying GP to sparse spiral 2D scans in piezoresponse force microscopy (PFM), simulated 2D atomic image in electron microscopy, and hyperspectral 3D data in Band Excitation PFM.Executable Google Colabnotebookwith the example of applying "parallel" GP method to analysis of EELS data.Executable Google Colabnotebookwith the example of applying GP to 4D spectroscopic dataset for smoothing and resolution enhancement in contact Kelvin Probe Force Microscopy (cKPFM).Executable Google Colabnotebookwith a simple example of performing GP-based exploration-exploitation on a toy dataset.RequirementsIt is strongly recommended to run the codes with a GPU hardware accelerator (such as NVIDIA's P100 or V100 GPU). If you don't have a GPU on your local machine, you may rent a cloud GPU fromGoogle Cloud AI Platform. Running theexample notebooksone time from top to bottom will cost about 1 USD with a standard deep learning VM instance (one P100 GPU and 15 GB of RAM).