A powerful, user-friendly program for deducing patterns and extracting useful information from large data sets.

ExploreHD implements the High Dimensional Model Representations (HDMR) technique pioneered by Prof. Herschel Rabitz and collaborators at Princeton University. HDMR explains the input-output behavior of a system using a hierarchical representation involving input variables acting individually and interacting in pairs as well as triples. The mathematical formulation of HDMR enables efficient global sensitivity analysis, readily providing information about how each input variable impacts each system output.


Whether the data comes from a computer model or experimental observation, ExploreHD helps you to understand and simplify the complex relationship between the inputs and outputs of your system.  ExploreHD analyzes your data to determine the sensitivity of the system to the first, second and even third order interactions of the inputs, generating a Fully Equivalent Operational Model (FEOM) which captures the behavior of the system.

Key Features and Specifications

  • Compatible with most data formats
  • Includes both cut-HDMR and RS-HDMR algorithms
  • Provides text and graphical views of analysis results
  • Calculator utility allows prediction of system outputs at arbitrary inputs that may be specified individually or by importing a data file of several sets of inputs
  • Post-processing capabilities include exporting data from ExploreHD to CSV file format
  • Pre-processing capabilities include generating random distributions of inputs for creating input-output data sets from users systems (models or experiments).

Supported Operating Systems

  • Windows
  • Linux
  • Mac OS X


Global Sensitivity Analysis on Systems with Independent and/or Correlated Inputs, G. Li,  H. Rabitz, P. Yelvington, O. Oluwole, F. Bacon, C. Kolb, and J. Schoendorf, Journal of Physical Chemistry A,  114, (19), 6022-6032, 2010.

Other High Dimensional Model Representation (HDMR) publications

Metabolomics-driven quantitative analysis of ammonia assimilation in E. coli, J. Yuan,   C. Doucette, U. Fowler, X.-J. Feng, M. Piazza, H. Rabitz, N. Wingreen and J. Rabinowitz, Mol Syst Biol, 5, 302, 2009.

Regularized random-sampling high dimensional model representation (RS-HDMR), G. Li, H. Rabitz, J. Hu, Z. Chen and Y. Ju, J. Math. Chem. 43, 1207, 2008.

Estimation of Molecular Properties by High Dimensional Model Representation, M.Y. Hayes, B. Li, and H. Rabitz, J. Phys. Chem., 110, 264-272, 2006.

Random sampling-high dimensional model representation (RS-HDMR) and orthogonality of its different order component functions, G. Li, J. Hu, S.-W. Wang, P. Georgopoulos, J. Schoendorf, H. Rabitz, J. Phys. Chem. A, 110, 2474-2485, 2006.

High dimensional model representation of cyclic voltammograms, L. Bieniasz, H. Rabitz, Anal. Chem, 78, 1807, 2006.

Ratio control variate method for efficiently determining high dimensional model representations, G. Li, H. Rabitz, J. Comput. Chem. 27, 1112-1118, 2006.

Extraction of parameters and their error distributions from cyclic voltammograms using bootstrap re-sampling enhanced by solution maps: a computational study, L. Bieniasz, H. Rabitz, Anal. Chem., 78, 8430, 2006.

Characterizing uncertainties in human exposure modeling through the RS-HDMR Methodology, S-W Wang, P. Georgopoulos, G. Li and H. Rabitz, IJARM special issue, 5, 387-406, 2005.

Maximal use of minimal libraries through the adaptive substituent reordering algorithm, F. Liang, X. Feng, M Lowry, H. Rabitz, J. Phys. Chem. B, 109, 5842, 2005.

Optimizing genetic circuits by global sensitivity analysis, X-J Feng, R. Weiss and H. Rabitz, Biophys J, 87, 2195-2202, 2004.

Optimal Identification of Biochemical Reaction Networks,  X.-J. Feng and H. Rabitz, Biophys. J., 86, 1270-1281, 2004.

Multicut-HDMR with an application to an ionospheric model, G. Li, J. Schoendorf, T-S Ho, J. Comp. Chem., 25, 1149-1156, 2004.
Efficient Extraction of Quantum Hamiltonians Information from Optimal Laboratory Data, JM Geremia and H. Rabitz, Phys. Rev A., 70, 023804, 2004.

Closed-Loop Learning Algorithm of Bio-Networks, J. Ku, X.-J. Feng, and H. Rabitz, J. Comp. Bio., 11, 642, 2004.

Correlation Method for Variance Reduction of Monte Carlo Integration in RS-HDMR, G. Li, H. Rabitz, S.-W. Wang, and P.G. Georgopoulos, J. Comp. Chem., 24, 277-283, 2003.

Error bounds for molecular Hamiltonians inverted from experimental data, J.M. Geremia and H. Rabitz, Phys. Rev. A, 67, 022711-1-11, 2003.

Closed-loop quantum control utilizing time domain maps, J.S. Biteen, J.M. Geremia, and H. Rabitz, Chem. Phys., 290, 35-45,2003.

Substituent Ordering and Interpolation in Molecular Library Optimization, N. Shenvi, J.M. Geremia, and H. Rabitz, J. Phys. Chem. A, 107, 2066-2074, 2003.

High Dimensional Model Representations Generated from Low Order Terms - Ip-RS-HDMR, G. Li, M. Artamonov, H. Rabitz, S.-W. Wang, P.G. Georgopoulos, and M. Demiralp, J. Comput. Chem., 24, 647-656, 2003.

Random Sampling-High Dimensional Model Representation (RS-HDMR) with Nonuniformly Distributed Variables:  Application to an Integrated Multimedia/Multipathway Exposure and Dose Model for Trichloroethylene, S.-W. Wang, P.G. Georgopoulos, G. Li, and H. Rabitz, J. Phys. Chem. A, 107, 4707-4716, 2003.

A fast and accurate model of ionospheric electron density, J. Schoendorf, H. Rabitz, and G. Li, Geophys. Res. Lett., 30, 45-1-4, 2003.

Simulating bioremediation of uranium-contaminated aquifers; uncertainty assessment of model parameters, S. Wang, P.R. Jáffe, G. Li, S.W. Wang, and H. Rabitz, Journal of Contaminant Hydrology, 64, 282-307, 2003.

Reproducing kernel Hilbert space interpolation methods as a paradigm of high dimensional model representations:  Application to multidimensional potential energy surface construction, T.-S. Ho and H. Rabitz, J. Chem. Phys., 119, 6433-6442, 2003.

Theoretical Valence Band Offsets of Semiconductor Heterojunctions, K. Shim and H. Rabitz, Appl. Phys. Lett., 80, 4543-4545, 2002.

Practical Approaches To Construct RS-HDMR Component Functions, G. Li, S.-W. Wang, and H. Rabitz, J. Phys. Chem. A, 106, 8721-8733, 2002.

Parameter equations of motion for the transition operator and the Green’s Operator, H. Cheng and H. Rabitz, and R.C. Forrey, Phys. Rev. A, 66, 022704-1-3, 2002.

Global uncertainty assessments by high dimensional model representations (HDMR), G. Li, S.-W. Wang, H. Rabitz, S. Wang, and P. Jaffé, Chem. Eng. Sci., 57, 4445-4460, 2002.

Nonlinear Kinetic Parameter Identification Through Map Inversion, N. Shenvi, J.M. Geremia, and H. Rabitz, J. Phys. Chem. A, 106, 12315-12323, 2002.

Optimal Control of Catalytic Methanol Conversion to Formaldehyde, A. Faliks, R.A. Yetter, C.A. Floudas, S. Bernasek, M. Fransson, and H. Rabitz, J. Phys. Chem. A, 105, 2099-2105, 2001.

Achieving the Laboratory Control of Quantum Dynamics Phenomena Using Nonlinear Functional Maps, J.M. Geremia, E. Weiss, and H. Rabitz, Chem. Phys., 267, 209-222, 2001.

Constructing global functional maps between molecular potentials and quantum observables, J.M. Geremia, H. Rabitz, and C. Rosenthal, J. Chem. Phys., 114, 9325-9336, 2001.

Efficient Implementation of High Dimensional Model Representations, Ö. Alis and H. Rabitz, J. Math. Chem., 29, 127-142, 2001.

Global, nonlinear algorithm for inverting quantum-mechanical observations, J.M. Geremia and H. Rabitz, Phys. Rev. A, 64, 022710-1-13, 2001.

High Dimensional Model Representations, G. Li, C. Rosenthal, and H. Rabitz, J. Phys. Chem. A, 105, 7765-7777, 2001.

The Ar-HCl potential energy surface from a global map-facilitated inversion of state-to-state rotationally resolved differential scattering cross sections and rovibrational spectral data, J.M. Geremia and H. Rabitz, J. Chem. Phys., 115, 8899-8912, 2001.

High dimensional model representations generated from low dimensional data samples.  I. mp-Cut-HDMR, G. Li, S.-W. Wang, C. Rosenthal, and H. Rabitz, J. Math. Chem., 30, 1-30, 2001.

Computationally Efficient Atmospheric Chemical Kinetic Modeling by Means of High Dimensional Model Representation (HDMR), S.W. Wang, P.G. Georgopoulos, G. Li, and H. Rabitz, in ICLSSC 2001, LNCS 2179, S. Margenov, J. Wasniewski, and P. Yalamov, eds., Springer-Verlag, Berlin, pp. 326-333, 2001 .

Quantum Optimal Quantum Control Field Design Using Logarithmic Maps, J.S. Biteen, J.M. Geremia, and H. Rabitz, Chem. Phys. Lett., 348, 440-446, 2001.

Properties of lattice matched ZnMgSeTe quaternary alloys grown on ZnTe substrates, J.H. Chang, M.W. Cho, H. Makino, T. Yao, K. Shim, H. Rabitz, and T. Yao, Journal of Crystal Growth, 214/215, 373-377, 2000.

Energy band gap of the alloy Zn1-xMgxSeyTe1-y lattice matched to ZnTe, InAs and InP, K. Shim, H. Rabitz, J.H. Chang, and T. Yao, Journal of Crystal Growth, 214/215, 350-354, 2000 .

Optical properties of ZnMgSeTe quaternary alloys grown on ZnTe substrates by molecular-beam epitaxy, J.H. Chang, H.M. Wang, M.W. Cho, H. Makino, H. Hanada, T. Yao, K. Shim, and H. Rabitz, J. Vac. Sci. Technol. B,18, 1530-1533, 2000.

Material Properties Obtained by Using the Correlated Function Expansion for the Quaternary Alloy GaxIn1-xPyAs1-y, K. Shim and H. Rabitz, J. Korean Physical Society, 2000, 37, 124-128, 2000.

Radiation transport simulation by means of a fully equivalent operational model, J. Shorter, P. Ip, and H. Rabitz, Geophys. Res. Lett., 27, 3485-3488, 2000.

Managing the Tyranny of Parameters in Mathematical Modelling of Physical Systems, H. Rabitz and O. Alis, in Sensitivity Analysis, A. Saltelli, K. Chan, and M. Scott, eds., p. 199-223, John Wiley & Sons, Chichester, 2000.

The band gap and lattice constant of GaxIn1-xAsySb1-y, K. Shim, H. Rabitz, and P. Dutta, J. Appl. Phys., 88, 7157-7161, 2000.

Efficient input-output model representations, H. Rabitz, Ö.F. Alis, J. Shorter, and K. Shim, Computer Phys. Comm., 117, 11-20, 1999.

Electronic and Structural Properties of Pentanary Alloys GaxIn1-xPySbzAs1-y-z, K. Shim and H. Rabitz, J. Appl. Phys., 85, 7705-7715, 1999.

Composition Dependent Band Gap Variations of GaxIn1-xPySbzAs1-y-z Lattice Matched to Different Substrates, K. Shim and H. Rabitz, J. Korean Physical Society, 34, S28-S31, 1999.

An Efficient Chemical Kinetics Solver Using High Dimensional Model Representation, J.A. Shorter, P.C. Ip, and H. Rabitz, J. Phys. Chem. A, 103, 7192-7198, 1999.

General Foundations of High Dimensional Model Representations, H. Rabitz and Ö. Alis, J. Math. Chem., 25, 197-233, 1999.

Multicomponent semiconductor material discovery guided by a generalized correlated function expansion, H. Rabitz and K. Shim, J. Chem. Phys., 111, 10640-10651, 1999.

Fully Equivalent Operational Models for Atmospheric Chemical Kinetics within Global Chemistry-Transport Models, S.W. Wang, H. Levy II, G. Li, and H. Rabitz, J. Geophys. Res., 104, 30, 417-30, 426, 1999.

Universal Tight Binding Calculation for the Electronic Structure of the Quaternary Alloy In1-xGaxAs1-yPy, K. Shim and H. Rabitz, Phys. Rev. B, 58, 12874-12881, 1998.

Independent and correlated conposition behavior of material properties: Application to energy band gaps for the GaaIn1-aPbAs1-b and GaaIn1-aPbSbgAs1-b-g alloys, K. Shim and H. Rabitz, Phys. Rev. B, 58, 1940-1946, 1998.

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