This repository contains the accompanying software for the paper "Inference of dynamic systems from noisy and sparse data via manifold-constrained Gaussian processes" by Shihao Yang, Samuel W.K. Wong, and S. C. Kou.
User interfaces are available in R, MATLAB, and Python.
A comprehensive shell script build.sh is provided, which by default prepares all three interfaces. Edit build.sh to specify the location of your R libraries, and remove the compilation blocks for any of R, MATLAB, Python that either will not be used or is unavailable on your system. Then execute build.sh to install dependencies and compile the library.
The pre-compiled binary for C++, R, and Python is also available as a Docker image on Docker Hub: https://hub.docker.com/repository/docker/shihaoyangphd/magi
Inference is performed via the unified function MagiSolver which can be called from R, MATLAB, Python. A description of its basic syntax is as follows, where D is the number of components in the dynamic system, and |I| is the number of discretization points for computation.
MagiSolver(
yFull, # |I|-by-D data matrix of observations Y, with unobserved entries set to NA
model, # ODE model specification (see examples)
tvecFull, # length |I| vector of time points
sigmaExogenous, # (optional) length D vector of starting values of Gaussian noise SD sigma,
recommended value: supply if known, else leave blank
phiExogenous, # (optional) 2-by-D matrix of GP hyperparameters phi
recommended value: supply if known, else leave blank
xInitExogenous, # (optional) |I|-by-D matrix of starting values for X_I
recommended value: linearly interpolate between observed points of Y
thetaInitExogenous, # (optional) starting value of theta
recommended value: leave blank
muExogenous, # (optional) starting GP mean curve
recommended value: leave blank
dotmuExogenous, # (optional) starting GP derivative of mean curve
recommended value: leave blank
priorTemperatureLevel, # tempering factor on GP prior
recommended value: D|I| / (number of observed data values in Y)
priorTemperatureDeriv, # tempering factor on GP derivative
recommended value: D|I| / (number of observed data values in Y)
priorTemperatureObs, # tempering factor on observations
recommended value: 1
kernel, # currently supported GP kernel is "generalMatern"
nstepsHmc, # number of leapfrog steps per HMC iteration
burninRatioHmc, # proportion of HMC iterations to treat as burn-in
niterHmc, # number of HMC iterations to run
stepSizeFactorHmc, # initial step size for HMC sampler
nEpoch, # currently supported value is 1
bandSize, # band size for band matrix approximation
useFrequencyBasedPrior, # recommended value: TRUE
useBand, # recommended value: TRUE
useMean, # recommended value: TRUE
useScalerSigma, # set to FALSE each component has its own noise level sigma, else TRUE
useFixedSigma, # set to TRUE if sigma known (must supply sigmaExogenous)
verbose) # set to TRUE to print out additional diagnostic information
See the README in the corresponding subfolders: rmagi (for R), pymagi (for Python), matlabmagi (for Matlab).
There, we provide specific examples of how to set up and call MagiSolver in each software environment, and how to supply your own ODE systems and data to the method.
For a full discussion of our method and examples, please see our paper "Inference of dynamic systems from noisy and sparse data via manifold-constrained Gaussian processes", PNAS 118 (15), e2020397118 (https://doi.org/10.1073/pnas.2020397118).