Publications

@article{nokey,

title = {Probabilistic Cardiac Digital Twins for Robust Patient-Specific Modeling},

author = {Dimitris G Giovanis, Kelly Zhang, Justin Tso, Mauro Maggioni, Ioannis G Kevrekidis, Natalia Trayanova},

url = {https://www.biorxiv.org/content/10.64898/2026.05.07.723610v1},

doi = {https://doi.org/10.64898/2026.05.07.723610},

year  = {2026},

date = {2026-05-12},

urldate = {2026-05-12},

journal = {biorxiv},

abstract = {Uncertainty quantification (UQ) in computational heart models is essential for reliable cardiac digital twins (DTs) in personalized medicine, yet remains challenging. Traditional Monte Carlo and stochastic Galerkin methods often become impractical in the high-dimensional, nonlinear state variable and parameter spaces of cardiac electrophysiology and mechanics. This article introduces a framework for learning a joint probability density over cardiac observables and model parameters, enabling the characterization of statistical dependencies across a large number of variables in patient-specific cardiac DTs. By sampling from this density and conditioning on available data, useful predictive distributions can be constructed, allowing uncertainty to be propagated through the model and quantified in terms of variability. Conditional regression can then be performed directly on this learned density, enabling systematic exploration of interdependencies among observables for both predictive inference and model design. The statistical methodology adopts a geometry-aware generative learning framework, recently introduced by the authors, that decouples the learning of data geometry from sampling. First it identifies a low-dimensional latent representation that captures the intrinsic structure of the data and its multiscale geometric features. A stochastic differential equation is then formulated directly in the low-dimensional latent space to generate samples efficiently; these are subsequently mapped back to the high-dimensional space of cardiac states and parameters through a smooth lifting operator. We demonstrate the approach on a ventricular arrhythmia prediction benchmark, where the learned joint probability density enables the construction of predictive distributions over key parameters (e.g., conductivities, fibrosis patterns) through sampling and conditioning. This enables uncertainty to be propagated and quantified through sampling and conditioning on the learned joint density, with substantially fewer model evaluations than conventional UQ methods.},

keywords = {cardiac electrophysiology, diffusion geometry, digital twins, Machine learning, uncertainty quantification},

pubstate = {forthcoming},

tppubtype = {article}

}

@article{8481477,

title = {Unsupervised Clustering and Active Learning of Hyperspectral Images With Nonlinear Diffusion},

author = {James M Murphy and Mauro Maggioni},

doi = {10.1109/TGRS.2018.2869723},

issn = {1558-0644},

year  = {2019},

date = {2019-03-01},

urldate = {2019-03-01},

journal = {IEEE Transactions on Geoscience and Remote Sensing},

volume = {57},

number = {3},

pages = {1829-1845},

keywords = {Active Learning, Clustering, diffusion geometry, hyperspectral imaging, imaging},

pubstate = {published},

tppubtype = {article}

}

@article{PathBasedSpectralClustering,

title = {Path-Based Spectral Clustering: Guarantees, Robustness to Outliers, and Fast Algorithms},

author = {Anna V Little and Mauro Maggioni and James M Murphy},

url = {http://jmlr.csail.mit.edu/papers/volume21/18-085/18-085.pdf},

year  = {2019},

date = {2019-01-01},

journal = {Journ. Mach. Learn. Res.},

volume = {21},

pages = {1-66},

keywords = {Clustering, diffusion geometry, Machine learning, Unsupervised Learning},

pubstate = {published},

tppubtype = {article}

}

@article{2639-8001_2019_3_271,

title = {Learning by active nonlinear diffusion},

author = {Mauro Maggioni and James M Murphy},

url = {http://aimsciences.org//article/id/6f8fefb2-e464-48ea-b2de-f37686725966},

doi = {10.3934/fods.2019012},

issn = {A0000-0002},

year  = {2019},

date = {2019-01-01},

journal = {Foundations of Data Science},

volume = {1},

number = {"2639-8001-2019-3-271"},

pages = {271},

keywords = {Active Learning, Clustering, diffusion geometry, Machine learning, Unsupervised Learning},

pubstate = {published},

tppubtype = {article}

}

@article{CM:ATLAS,

title = {ATLAS: A geometric approach to learning high-dimensional stochastic systems near manifolds},

author = {Miles C Crosskey and Mauro Maggioni},

url = {https://arxiv.org/abs/1404.0667

https://doi.org/10.1137/140970951},

year  = {2017},

date = {2017-01-01},

journal = {Journal of Multiscale Modeling and Simulation},

volume = {15},

number = {1},

pages = {110--156},

note = {arxiv: 1404.0667},

keywords = {diffusion geometry, Machine learning, Manifold Learning, statistics, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

@article{WCM:HSIandMovies,

title = {High Dimensional Data Modeling Techniques for Detection of Chemical Plumes and Anomalies in Hyperspectral Images and Movies},

author = {Yang Wang and Guangliang Chen and Mauro Maggioni},

url = {https://arxiv.org/abs/1509.07497

},

doi = {10.1109/JSTARS.2016.2539968},

year  = {2016},

date = {2016-05-16},

urldate = {2016-05-16},

journal = {IEEE Journal of selected topics in applied Earth observations and remote sensing},

volume = {9},

number = {9},

pages = {4316--4324},

keywords = {Active Learning, Clustering, diffusion geometry, hyperspectral imaging, imaging},

pubstate = {published},

tppubtype = {article}

}

@article{ZRMC:PolymerReversal,

title = {Polymer reversal rate calculated via locally scaled diffusion map},

author = {W Zheng and M A Rohrdanz and Mauro Maggioni and Cecilia Clementi},

year  = {2011},

date = {2011-01-01},

journal = {J. Chem. Phys.},

number = {134},

pages = {144108},

keywords = {diffusion geometry, Machine learning, Manifold Learning, molecular dynamics, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

@article{RZMC:ReactionCoordinatesLocalScaling,

title = {Determination of reaction coordinates via locally scaled diffusion map},

author = {M A Rohrdanz and W Zheng and Mauro Maggioni and Cecilia Clementi},

year  = {2011},

date = {2011-01-01},

journal = {J. Chem. Phys.},

number = {134},

pages = {124116},

keywords = {diffusion geometry, Machine learning, Manifold Learning, molecular dynamics, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

@article{jms:UniformizationEigenfunctions2,

title = {Universal local manifold parametrizations via heat kernels and eigenfunctions of the Laplacian},

author = {Peter W Jones and Mauro Maggioni and Raanan Schul},

year  = {2010},

date = {2010-01-01},

journal = {Ann. Acad. Scient. Fen.},

volume = {35},

pages = {1--44},

note = {http://arxiv.org/abs/0709.1975},

keywords = {diffusion geometry, heat kernels, Laplacian eigenfunctions, Manifold Learning, multiscale analysis, random walks, spectral graph theory},

pubstate = {published},

tppubtype = {article}

}

@article{SMC:GeneralFrameworkAdaptiveRegularization,

title = {Regularization on Graphs with Function-adapted Diffusion Processes},

author = {Arthur D Szlam and Mauro Maggioni and Ronald R Coifman},

url = {https://jmlr.csail.mit.edu/papers/volume9/szlam08a/szlam08a.pdf},

year  = {2008},

date = {2008-08-01},

urldate = {2008-08-01},

journal = {Jour. Mach. Learn. Res.},

number = {9},

pages = {1711--1739},

note = {(YALE/DCS/TR1365, Yale Univ, July 2006)},

keywords = {diffusion geometry, Machine learning, Manifold Learning, random walks, semisupervised learning, spectral graph theory},

pubstate = {published},

tppubtype = {article}

}

@article{MM:DiffusionPolynomialFrames,

title = {Diffusion polynomial frames on metric measure spaces},

author = {Mauro Maggioni and Hrushikesh Mhaskar},

year  = {2008},

date = {2008-05-01},

journal = {ACHA},

volume = {3},

pages = {329--353},

keywords = {approximation theory, diffusion geometry, heat kernels, Laplacian eigenfunctions, multiscale analysis},

pubstate = {published},

tppubtype = {article}

}

@article{jms:UniformizationEigenfunctions,

title = {Manifold parametrizations by eigenfunctions of the Laplacian and heat kernels},

author = {Peter W Jones and Mauro Maggioni and Raanan Schul},

year  = {2008},

date = {2008-02-01},

journal = {Proc. Nat. Acad. Sci.},

volume = {105},

number = {6},

pages = {1803--1808},

keywords = {diffusion geometry, heat kernels, Laplacian eigenfunctions, Manifold Learning, multiscale analysis, random walks, spectral graph theory},

pubstate = {published},

tppubtype = {article}

}

@article{CKLMN:DiffusionMapsReductionCoordinates,

title = {Diffusion Maps, reduction coordinates and low dimensional representation of stochastic systems},

author = {Ronald R Coifman and Ioannis G Kevrekidis and Stephane Lafon and Mauro Maggioni and Boaz Nadler},

year  = {2008},

date = {2008-01-01},

journal = {SIAM J.M.M.S.},

volume = {7},

number = {2},

pages = {842--864},

keywords = {diffusion geometry, dynamical systems, Laplacian eigenfunctions, Machine learning, model reduction, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

@article{CM:MsDataDiffWavelets,

title = {Multiscale Data Analysis with Diffusion Wavelets},

author = {Ronald R Coifman and Mauro Maggioni},

year  = {2007},

date = {2007-04-01},

journal = {Proc. SIAM Bioinf. Workshop, Minneapolis},

keywords = {diffusion geometry, diffusion wavelets, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

@article{smmm:jmrl1,

title = {Proto-value Functions: A Spectral Framework for Solving Markov Decision Processes},

author = {Sridhar Mahadevan and Mauro Maggioni},

year  = {2007},

date = {2007-01-01},

journal = {JMLR},

volume = {8},

pages = {2169--2231},

keywords = {diffusion geometry, Laplacian eigenfunctions, Machine learning, Manifold Learning, random walks, reinforcement learning, representation learning, spectral graph theory},

pubstate = {published},

tppubtype = {article}

}

@article{CMDiffusionWavelets,

title = {Diffusion Wavelets},

author = {Ronald R Coifman and Mauro Maggioni},

year  = {2006},

date = {2006-07-01},

journal = {Appl. Comp. Harm. Anal.},

volume = {21},

number = {1},

pages = {53--94},

note = {(Tech. Rep. YALE/DCS/TR-1303, Yale Univ., Sep. 2004)},

keywords = {diffusion geometry, diffusion wavelets, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

@article{DiffusionWaveletPackets,

title = {Diffusion Wavelet Packets},

author = {James Jr. C Bremer and Ronald R Coifman and Mauro Maggioni and Arthur D Szlam},

year  = {2006},

date = {2006-07-01},

journal = {Appl. Comp. Harm. Anal.},

volume = {21},

number = {1},

pages = {95--112},

note = {(Tech. Rep. YALE/DCS/TR-1304, 2004)},

keywords = {diffusion geometry, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

@article{CMZK:CONB,

title = {Geometric diffusions for the analysis of data from sensor networks},

author = {Ronald R Coifman and Mauro Maggioni and Steven W Zucker and Ioannis G Kevrekidis},

year  = {2005},

date = {2005-10-01},

journal = {Curr Opin Neurobiol},

volume = {15},

number = {5},

pages = {576--84},

keywords = {diffusion geometry, Laplacian eigenfunctions, Machine learning, Manifold Learning, random walks, spectral graph theory, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

@article{DiffusionPNAS,

title = {Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps},

author = {Ronald R Coifman and Stephane Lafon and Ann B Lee and Mauro Maggioni and B Nadler and Frederick Warner and Steven W Zucker},

year  = {2005},

date = {2005-01-01},

journal = {Proceedings of the National Academy of Sciences of the United States of America},

volume = {102},

number = {21},

pages = {7426-7431},

keywords = {diffusion geometry, Machine learning, Manifold Learning, random walks, spectral graph theory, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

@article{DiffusionPNAS2,

title = {Geometric diffusions as a tool for harmonic analysis and structure definition of data: Multiscale methods},

author = {Ronald R Coifman and S Lafon and A B Lee and Mauro Maggioni and B Nadler and Frederick Warner and Steven W Zucker},

year  = {2005},

date = {2005-01-01},

journal = {Proceedings of the National Academy of Sciences of the United States of America},

volume = {102},

number = {21},

pages = {7432--7438},

keywords = {diffusion geometry, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

@article{AuditoryDisplay,

title = {Auditory display of hyperspectral colon tissue images using vocal synthesis models},

author = {Ryan J Cassidy and Jim Berger and Mauro Maggioni and Ronald R Coifman},

year  = {2004},

date = {2004-01-01},

urldate = {2004-01-01},

journal = {Proc. 2004 Intern. Con. Auditory Display},

keywords = {Clustering, diffusion geometry, hyperspectral imaging, imaging, Machine learning},

pubstate = {published},

tppubtype = {article}

}

@article{MMIEEEPath,

title = {Algorithms from Signal and Data Processing Applied to Hyperspectral Analysis: Application to Discriminating Normal and Malignant Microarray Colon Tissue Sections},

author = {Mauro Maggioni and F J Warner and Gus L Davis and Ronald R Coifman and Frank B Geshwind and Andreas C Coppi and R A DeVerse},

year  = {2004},

date = {2004-01-01},

urldate = {2004-01-01},

journal = {submitted},

keywords = {Clustering, diffusion geometry, hyperspectral imaging, imaging, Machine learning, Unsupervised Learning},

pubstate = {published},

tppubtype = {article}

}