Uncertainty Quantification (UQ)

Research

Atrium Health

Prostate Cancer Disparities in Charlotte Metro Area

Our analysis shows that prostate cancer patients from lower socioeconomic status (SES) backgrounds are more likely to be diagnosed with high-risk prostate cancer. Age was the strongest predictor, while SES had a greater impact than race.

A. M. Holland, H. H. Wilson, B. C. Gambill, W. R. Lorenz, M. J. Salvino, M. L. Rose, K. S. Brown, R. Tawkaliyar, G. T. Scarola, V. Patel, G. A. Terejanu, J. T. Matulay. The Influence of Disparities on Prostate Cancer at Diagnosis in the Charlotte Metropolitan Area. Annals of Surgical Oncology (2024). https://doi.org/10.1245/s10434-024-15675-1

Toyota Racing Development

Invariant NASCAR Tire Modeling

In this project, we utilize the invariance principle to scale tire models that optimize race car performance by aligning with both controlled experimental data from SOVA and track data obtained using Wheel Force Transducers (WFT). The goal is to develop models that agree with data across multiple environments.

NSF 2218841

Deep Learning for Surface Chemistry

In this project, we are using computational catalysis and deep learning to improve the analysis and understanding of surface chemistry. We will use large datasets of DFT energies and advanced neural networks to identify invariant material and surface species descriptors that can help us predict the behavior of chemical systems.

Jawad Chowdhury, Charles Fricke, Olajide Bamidele, Mubarak Bello, Wenqiang Yang, Andreas Heyden, and Gabriel Terejanu, "Invariant Molecular Representations for Heterogeneous Catalysis", Journal of Chemical Information and Modeling, 2024, 64, 2, 327–339. DOI: 10.1021/acs.jcim.3c00594
A. J. Chowdhury, W. Yang, K. E. Abdelfatah, M. Zare, A. Heyden, and G. A. Terejanu, “A multiple filter based neural network approach to the extrapolation of adsorption energies on metal surfaces for catalysis applications,” Journal of chemical theory and computation, vol. 16, iss. 2, pp. 1105-1114, 2020. doi:10.1021/acs.jctc.9b00986
https://bitbucket.org/uqlab/subnetmultifilter

ARO W911NF-22-1-0035

Causal Modeling of Affective Polarization

The objective of this project is the development of an interactive causal modeling framework to understand affective polarization. The focus is on bridging the gap between data-driven methods for discovering causal relations and expert domain knowledge to mitigate the impact of data limitations.

Jawad Chowdhury, Gabriel Terejanu. CGLearn: Consistent Gradient-Based Learning for Out-of-Distribution Generalization. In Proceedings of the 14th International Conference on Pattern Recognition Applications and Methods (ICPRAM). Porto, Portugal, 2025
Jawad Chowdhury, Gabriel Terejanu. CD-NOTEARS: Concept Driven Causal Discovery in High Dimensional Data using NOTEARS. The 22st IEEE International Conference on Machine Learning and Applications (ICMLA), Jacksonville, Florida, 2023
Rezaur Rashid, Jawad Chowdhury, Gabriel Terejanu. Causal Feature Selection: Methods and a Novel Causal Metric Evaluation Framework. The 10th IEEE International Conference on Data Science and Advanced Analytics (DSAA), Thessaloniki, Greece, 2023
Jawad Chowdhury, Rezaur Rashid, Gabriel Evaluation of Induced Expert Knowledge in Causal Structure Learning by NOTEARS. In The International Conference on Pattern Recognition Applications and Methods (ICPRAM), Lisbon, Portugal, February 2023.
Rezaur Rashid, Jawad Chowdhury, Gabriel Terejanu. From Causal Pairs to Causal Graphs. In The IEEE International Conference on Machine Learning and Applications (ICMLA), The Bahamas, December 2022.

Lowe's Innovation Fund

Modeling the "Why" in Business Operations

Businesses collect vast amounts of data, which they leverage with advanced modeling techniques to develop actions to enhance their operations. The goal is to create an AI engine that provides managers with actionable recommendations to produce a desired effect on key performance indicators.

NIFA/USDA 2017-67017-31654

Aflatoxin Prediction

The goal of this project is to develop a general predictive modeling framework for calculating mycotoxin incidence in US crop fields. Prediction and control of the most potent carcinogenic mycotoxin, aflatoxin, is a fundamental challenge for US grain industry, poultry producers, and makers of dairy products.

K. Abdelfatah, J. Senn, N. Glaeser, and G. Terejanu, “Prediction and Measurement Update of Fungal Toxin Geospatial Uncertainty using a Stacked Gaussian Process,” Agricultural Systems, vol. 176, p. 102662, 2019. doi:https://doi.org/10.1016/j.agsy.2019.102662
K. Abdelfatah, J. Bao, and G. Terejanu, “Geospatial uncertainty modeling using Stacked Gaussian Processes,” Environmental Modelling & Software, vol. 109, pp. 293-305, 2018. doi:https://doi.org/10.1016/j.envsoft.2018.08.022
H. Li, A. Chowdhury, G. Terejanu, A. Chanda, and S. Banerjee, “A Stacked Gaussian Process for Predicting Geographical Incidence of Aflatoxin with Quantified Uncertainties ,” in International Conference on Advances in Geographic Information Systems ACM SIGSPATIAL, Seattle, Washington, 2015.

NSF-DMREF 1534260

Machine Learning in Catalysis

Computational catalyst screening has the potential to significantly accelerate heterogeneous catalyst discovery. Machine learning models can help to reduce the large computational cost involved in computing various adsorption and transition-state energies of all possible surface states on a large number of catalyst models, and overcome the shortcomings of linear scaling relations for more complex chemistries.

https://bitbucket.org/uqlab/mladsorptionenergies
A. J. Chowdhury, W. Yang, A. Heyden, and G. A. Terejanu, "Comparative Study on the Machine Learning-Based Prediction of Adsorption Energies for Ring and Chain Species on Metal Catalyst Surfaces", The Journal of Physical Chemistry C, 2021, 125 (32), 17742-17748, DOI: 10.1021/acs.jpcc.1c05470
K. Abdelfatah, W. Yang, R. Vijay Solomon, B. Rajbanshi, A. Chowdhury, M. Zare, S. K. Kundu, A. Yonge, A. Heyden, and G. Terejanu, “Prediction of transition-state energies of hydrodeoxygenation reactions on transition-metal surfaces based on machine learning,” The journal of physical chemistry c, vol. 123, iss. 49, pp. 29804-29810, 2019. doi:10.1021/acs.jpcc.9b10507
A. J. Chowdhury, W. Yang, E. Walker, O. Mamun, A. Heyden, and G. A. Terejanu, “Prediction of Adsorption Energies for Chemical Species on Metal Catalyst Surfaces Using Machine Learning,” The Journal of Physical Chemistry C, vol. 122, iss. 49, pp. 28142-28150, 2018. doi:10.1021/acs.jpcc.8b09284

NIFA/USDA 2017-67017-31654

Uncertainty Quantification in Deep Learning

Exact Bayesian neural network methods are intractable and non-applicable for real-world applications. We propose an approximate estimation of the weights uncertainty using Ensemble Kalman Filter, which is easily scalable to a large number of weights.

Chao Chen, Lin Xiao, Yuan Huang, and Gabriel Terejanu. Approximate Bayesian Neural Network Trained with Ensemble Kalman Filter. In International Joint Conference on Neural Networks (IJCNN), Budapest, Hungary, July 2019.
Chao Chen, Xiao Lin, and Gabriel Terejanu. An Approximate Bayesian Long Short-Term Memory Algorithm for Outlier Detection. In International Conference on Pattern recognition (ICPR), Beijing, China, August 2018.

NSF-DMREF 1534260

Uncertainty Quantification in Catalysis

A comprehensive UQ framework is developed to discriminate among probabilistic models corresponding to each candidate active site. Each probabilistic model consists of a microkinetic model, a probabilistic discrepancy model to account for errors between model predictions and observations, and a prior distribution over the intermediates, transition states, as well as gas molecule corrections and model discrepancy parameters. Three hypotheses regarding the active site for the water-gas shift reaction on Pt/TiO2 catalysts are tested using the proposed UQ framework.

C. Fricke, O. Bamidele, M. Bello, J. Chowdhury, G. Terejanu, A. Heyden. Modeling the Effect of Surface Platinum-Tin Alloys on Propane Dehydrogenation on Platinum-Tin Catalysts. ACS Catalysis, 13 (16), 10627-10640, 2023
C. Fricke, B. Rajbanshi, E. A. Walker, G. Terejanu, A. Heyden. Propane Dehydrogenation on Platinum Catalysts: Identifying the Active Sites through Bayesian Analysis. ACS Catalysis, 12, 4, 2487-2498, 2022. https://doi.org/10.1021/acscatal.1c04844
E. A. Walker, D. Mitchell, G. A. Terejanu, and A. Heyden, “Identifying Active Sites of the Water–Gas Shift Reaction over Titania Supported Platinum Catalysts under Uncertainty,” ACS Catalysis, p. 3990–3998, 2018. doi:10.1021/acscatal.7b03531
E. Walker, S. C. Ammal, G. Terejanu, and A. Heyden, “Uncertainty Quantification Framework Applied to the Water-Gas Shift Reaction over Pt-Based Catalysts,” J. Phys. Chem. C, vol. 120, iss. 19, pp. 10328-10339, 2016.

NSF-RII 1632824

Stacked Gaussian Processes

A network of independently trained Gaussian processes (StackedGP) is introduced to integrate different datasets through model composition, enhance predictions of quantities of interest through a cascade of intermediate predictions, and to propagate uncertainties through emulated dynamical systems driven by uncertain forcing variables.

https://bitbucket.org/uqlab/stackedgp
K. Abdelfatah, J. Bao, and G. Terejanu, “Geospatial uncertainty modeling using Stacked Gaussian Processes,” Environmental Modelling & Software, vol. 109, pp. 293-305, 2018. doi:https://doi.org/10.1016/j.envsoft.2018.08.022
H. Li, A, Chowdhury, G. Terejanu, A. Chanda, S. Banerjee, "A stacked Gaussian process for predicting geographical incidence of aflatoxin with quantified uncertainties", ACM SIGSPATIAL, 2015, https://doi.org/10.1145/2820783.2820849

NIFA/USDA 2017-67017-31654

Fast Approximate Bayesian Inference

Real-time nonlinear Bayesian filtering algorithms are overwhelmed by data volume, velocity and increasing complexity of computational models. We propose a novel ensemble based nonlinear Bayesian filtering approach which only requires a small number of simulations and can be applied to high-dimensional systems in the presence of intractable likelihood functions.

X. Lin and G. Terejanu, “EnLLVM: Ensemble based Nonlinear Bayesian Filtering using Linear Latent Variable Models,” in International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Brighton, UK, 2019.
Asif J. Chowdhury, Gabriel Terejanu, "Approximate Sampling using an Accelerated Metropolis-Hastings based on Bayesian Optimization and Gaussian Processes", 2019, arXiv:1910.09347

NSF-IUSE 1504728

Scientific-based Learning Assessment

The goal is to develop a computational assessment framework that easily integrates into an instructor’s routine efforts to track student knowledge, suggest remedial interventions, and guide future examinations. The rationale is that individual student knowledge is a hypothesis/model that needs to be tested using the scientific method.

https://bitbucket.org/uqlab/scilaf
S. Madarshahian, C. Chen, J. Caicedo, C. Pierce, and G. Terejanu, “Using Multiple Choice Responses to Assess Uncertainty in Student Understanding of Vector Concepts,” in ASEE Annual Conference and Exposition, Columbus OH, 2017.
G. Terejanu, J. Caicedo, and C. Pierce, “SciLAF: Scientific-based Learning Assessment Framework for Student Knowledge Tracking,” in Envisioning the Future of Undergraduate STEM Education: Research and Practice, Washington DC, 2016.
C. Chen, S. Madarshahian, J. Caicedo, C. Pierce, and G. Terejanu, “Bayesian network models for student knowledge tracking in large classes,” in ASEE Annual Conference and Exposition, New Orleans LA, 2016.

NNSA DE-FC52-08NA28615

Experimental Design and Sensor Placement

Instead of estimating mutual information in high-dimensions, we map the limited number of samples onto a lower dimensional space while capturing dependencies between the QoIs and observables. We then estimate a lower bound of the original mutual information in this low dimensional space, which becomes our new dependence measure between QoIs and observables.

X. Lin, A. Chowdhury, X. Wang, and G. Terejanu, “Approximate Computational Approaches for Bayesian Sensor Placement in High Dimensions,” Information Fusion, vol. 46, pp. 193-205, 2019.
G. Terejanu, R. R. Upadhyay, and K. Miki, “Bayesian Experimental Design for the Active Nitridation of Graphite by Atomic Nitrogen,” Experimental Thermal and Fluid Science, vol. 36, pp. 178-193, 2012.
G. Terejanu, “Active Data Collection for Inadequate Models,” in Information Fusion (Fusion), 2015 18th International Conference on, 2015, pp. 421-427.
C. Bryant and G. Terejanu, “An Information-Theoretic Approach to Optimally Calibrate Approximate Models,” in The 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Nashville, Tennessee, 9-12 January, 2012.
G. Terejanu, C. Bryant, R. Morrison, and S. Prudhomme, “Two Phase Optimal Experimental Design Process for Predictive Model Assessment,” in 14th AIAA Non-Deterministic Approaches Conference, Special Session on Uncertainty Quantification in V&V, Honolulu, Hawaii, 23-26 April, 2012.

NNSA DE-FC52-08NA28615

Model Validation

The proposed internal discrepancy representation is based on the fact that physics-based models are constructed using a set of highly reliable conservative laws (mass, momentum, energy). This formulation exploits the source of the model error to develop reliable calibration and predictive validation methodologies. This approach removes the constraints associated with the external discrepancy approach: (1) its stochastic solution satisfies physical constraints, (2) it reduces inference bias and under-estimation of uncertainty, and (3) it provides reliable extrapolated predictions for the QoI.

https://bitbucket.org/uqlab/predictiveselectioncoupledmodels
T. A. Oliver, G. Terejanu, C. S. Simmons, and R. D. Moser, “Validating Predictions of Unobserved Quantities,” Computer Methods in Applied Mechanics and Engineering, vol. 283, pp. 1310-1335, 2015. doi:10.1016/j.cma.2014.08.023
R. E. Morrison, C. M. Bryant, G. Terejanu, S. Prudhomme, and K. Miki, “Data partition methodology for validation of predictive models,” Computers & Mathematics with Applications, vol. 66, iss. 10, p. 2114–2125, 2013.
G. Terejanu, “From Model Calibration and Validation to Reliable Extrapolations,” in IMAC-XXXIV Conference and Exposition on Structural Dynamics, Orlando, Florida, 2016.
G. Terejanu, “Predictive Validation of Dispersion Models Using a Data Partitioning Methodology,” in IMAC-XXXII Conference and Exposition on Structural Dynamics, Orlando, Florida, 2015, pp. 151-156.
R. Morrison, C. Bryant, G. Terejanu, K. Miki, and S. Prudhomme, “Optimal Data Split Methodology for Model Validation,” in Proceedings of the World Congress on Engineering and Computer Science 2011 Vol II, WCECS 2011, 2011, pp. 1038-1043.
G. Terejanu, T. Oliver, and C. Simmons, “Application of Predictive Model Selection to Coupled Models,” in Proceedings of the World Congress on Engineering and Computer Science 2011 Vol II, WCECS 2011, 2011, pp. 927-932.

NFS-CMMI 0908403
ONR HM1582-08-1-0012

Adaptive Gaussian Mixture Models

The basic idea of this approach is to approximate the state probability density function (pdf) by a weighted average of sufficient number of distinct local Gaussian density functions. We propose two approaches to update the weights for accurate propagation of the state pdf.

https://bitbucket.org/uqlab/adaptivegaussiansumfilter
G. Terejanu, P. Singla, T. Singh, and P. D. Scott, “Adaptive Gaussian Sum Filter for Nonlinear Bayesian Estimation,” Automatic Control, IEEE Transactions on, vol. 56, iss. 9, pp. 2151-2156, 2011. doi:10.1109/TAC.2011.2141550
G. Terejanu, P. Singla, T. Singh, and P. D. Scott, “Uncertainty Propagation for Nonlinear Dynamical Systems using Gaussian Mixture Models,” Journal of Guidance, Control, and Dynamics, vol. 31, iss. 6, pp. 1622-1633, 2008.
J. George, G. Terejanu, and P. Singla, “Spacecraft Attitude Estimation Using Adaptive Gaussian Sum Filter,” Journal of the Astronautical Sciences, Special Issue: Markley Symposium, vol. 57, iss. 1, pp. 31-45, 2009.
G. Terejanu, P. Singla, T. Singh, and P. D. Scott, “Uncertainty Propagation for Nonlinear Dynamical Systems using Gaussian Mixture Models,” in AIAA Guidance, Navigation and Control Conference and Exhibit, Honolulu, Hawaii, 2008.
G. Terejanu, P. Singla, T. Singh, and P. D. Scott, “A Novel Gaussian Sum Filter Method for Accurate Solution to Nonlinear Filtering Problem,” in 11th International Conference on Information Fusion, Cologne, Germany, 2008.

DTRA W911NF-06-C-0162

Data Assimilation for CBRN

CBRN = Chemical, Biological, Radiological and Nuclear. The objective is the systematic study and elucidation of the basic physico-mathematical principles underlying data assimilation in the chem-bio context, that is, the blending of chem-bio dispersion forecasts with uncertain sensor data.

G. Terejanu, P. Singla, T. Singh, and P. D. Scott, “A Decision-Centric Framework for Density Forecasting,” Journal of Advances in Information Fusion, vol. 5, iss. 2, pp. 73-87, 2010.
G. Terejanu, P. Singla, T. Singh, and P. D. Scott, “Decision Based Uncertainty Propagation Using Adaptive Gaussian Mixtures,” in 12th International Conference on Information Fusion, Seattle, Washington, 2009.
G. Terejanu, Y. Cheng, T. Singh, and P. D. Scott, “Comparison of SCIPUFF Plume Prediction with Particle Filter Assimilated Prediction for Dipole 26 Data,” in Chemical and Biological Defense Physical Science and Technology Conference, New Orleans, 2008.
G. Terejanu, T. Singh, and P. D. Scott, “Unscented Kalman Filter/Smoother for a CBRN Puff-Based Dispersion Model,” in 11th International Conference on Information Fusion, Quebec City, Canada, 2007.

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