1. Big data analysis and statistical machine learning
2. Predictive modeling and uncertainty quantification
3. Scientific computing and computational fluid dynamics
4. Stochastic multiscale modeling
My research interests include diverse topics in computational and predictive science and statistical learning both on algorithms and applications. A main current thrust is stochastic simulation (in the context of uncertainty quantification, statistical learning and beyond), and multiscale modeling of physical and biological systems (e.g., blood flow). My research goal is to develop high-order numerical algorithms to promote innovation with significant potential impact and design highly-scalable numerical solvers on petascale supercomputers to investigate new knowledge discovery and predictive modeling for critical decision making in complex physical and biological complex systems.
A crossmember is a structural component that undergoes strict X-ray inspection to ensure its quality. The optimal environmental and operational parameter settings are identified for making quality CHRYSLER crossmember castings through a novel optimization algorithm.
Y. Sun, G. Lin, Q. Han, D. Yang, C. Vian, Exploratory data analysis for achieving optimal environmental and operational parameter settings for making quality crossmember castings, Die Casting Congress & Exposition, in press, 2019.
The increase in mobile machine automation and data collection has allowed mobile equipment manufacturers to push to implement their machines with smart machine learning algorithms to assist in the condition monitoring of the system.
Advanced machine learning algorithms are employed to classify the machine functions on a Bobcat 435 mini excavator.
N.J. Keller, A. Vacca, Y. Sun, Y. Zuo, G. Lin, Classification of Machine Functions: A Case Study, the 16th Scandinavian International Conference on Fluid Power, May 22-24, 2019, Tampere, Finland.
We develop multi-fidelity model-based machine learning tools for empirical potential development for Si:H nanowires. The calculation speed using developed empirical potentials is fast compared to the first principle calculations with very good accuracy.
The complexity of distribution power grids is increasing due to widespread deployment of renewable resources and power electronic devices. We employ deep belief network with non-Gaussian uncertainties for probabilistic state estimation of distribution power system.
Y. Huang, Q. Xu, C. Hu, Y. Sun, G. Lin, Probabilistic state estimation approach for AC/MTDC Distribution system using deep belief network with non-Gaussian uncertainties, IEEE Sensors Journal, in review, 2019.
The 2014-15 Ebola outbreak in West Africa is a serious threat to global public health. To design and evaluate different control strategies for Ebola outbreak, we employ machine learning, sensitivity analysis and parameter estimation to analyze the observation dataset. The results indicate that simultaneously strengthening contact-tracing and effectiveness of isolation in hospital would be most effective control strategies.
J. Ponce, Y. Zheng, G. Lin*, Z. Feng, Assessing the effects of modeling the spectrum of clinical symptoms on the dynamics and control of Ebola, Journal theoretical biology, in press, 2019.
We develop a new machine learning approach on data-driven discovery of physical laws in implicit form from noisy datasets. This approach is effective, robust and able to quantify uncertainties by providing an error bar for each discovered candidate equations.
S. Zhang, G. Lin*, Robust data-driven discovery of governing physical laws with error bars, Proceedings of the Royal Society of London. Series A, mathematical, physical and engineering sciences, in press, 2018. 10.1098/rspa.2018.0305 https://royalsocietypublishing.org/doi/full/10.1098/rspa.2018.0305
Dr. Guang Lin’s research spans several interconnecting fields in computational and applied mathematics: numerical methods for stochastic differential equations and uncertainty quantification (UQ), modeling and simulation of complex systems, higher-order numerical methods, data assimilation, stochastic inverse problem, design and optimization under uncertainty and numerical methods for rare events.
Research Highlight Summary: (click each one with hyperlink)
1.a Stochastic Piston Problem
Fig. 1 Left: Sketch of shock paths induced by random piston motions; Right: Normalized variance of the perturbed shock paths
Motivation: This research is motivated by studying how small random piston affect the shock paths.
Methods: A second-order stochastic perturbation analysis algorithm for stochastic piston problem is developed.
Results: Lin's work on stochastic piston problem is a re-formulation, within the stochastic framework, of a classical aerodynamics benchmark problem that studies how small random piston motions affect shock paths. A second-order asymptotic analytical solution for the linearized stochastic Euler equations for the stochastic piston problem is derived. Asymptotic results of the perturbed shock paths for early and longer times are provided. This study reveals that the variance of the location of the perturbed shock paths initially grows quadratically with time and switches to linear dependence for longer times.
Why it Matters: The developed work provides insight on the effect of random piston motion on the shock paths. In addition, it will have a significant and broad impact on UQ algorithm development as it sets the foundations for the second-order stochastic asymptotic analysis for uncertainty quantification, which is useful for predictive modeling in many applications of interest to NSF, DOE, AFOSR, ONR, ARL and DARPA.
1. G. Lin, C.-H. Su and G.E. Karniadakis, The stochastic piston problem, Proceedings of the National Academy of Sciences of the United States of America, 101(45):15840-15845, 2004.
2. Z. Zhang, X. Yang, G. Lin, G. Karniadakis, Numerical solution of the Stratonovich- and Ito-Euler equations: Application to the stochastic piston problem, Journal of Computational Physics, 236: 15-27, 2013.
1.b Random Roughness Problem
Fig. 2 Left: Pressure contour for oblique shock problem with random rough surface; Right: Scaling laws for mean of the perturbed lift with respect to the correlation length and amplitude of the random roughness
Motivation: This research is motivated by studying how random surface roughness interact with the shock and affect the aerodynamics of aircraft.
Methods: A second-order stochastic perturbation analysis algorithm for random roughness problem is developed. An integrated framework by combing both the second-order stochastic perturbation methods and high-order stochastic numerical methods is used to develop to uncertainty propagation is developed. The
Results: Lin's work on random roughness problem provides the answer on how random roughness can affect the shock paths, drag and lift forces in supersonic flow. A second-order asymptotic analytical solution of the perturbed lift and drag forces as a function of the random roughness are derived for the two-dimensional random roughness problem. This study reveals that random roughness actually can enhance the lift for supersonic aircraft.
Why it Matters: The results are useful in evaluating the effects of roughness in high-speed flight but also in designing novel enhanced-lift aerodynamic surfaces using rough skin concepts. The developed work will have a significant and broad impact as it sets the foundations on combining both the second-order stochastic asymptotic analysis and high-order stochastic numerical methods to uncertainty quantification, which is useful for predictive modeling in many applications of interest to NSF, DOE, AFOSR, ONR, ARL and DARPA, such as predicting how ice on the aircraft surface will affect the dynamics of the aircraft.
1. G. Lin, C.-H. Su and G.E. Karniadakis, Random Roughness Enhances Lift in Supersonic Flow, Physical Review Letters, 99:104501, 2007.
2. G. Lin, C.-H. Su and G.E. Karniadakis, Stochastic modeling of random roughness in shock scattering problems: Theory and simulations, Comput. Methods Appl. Math. Eng., 197(43-44): 3420-3434, 2008.
3. G. Lin, X. Wan, C.-H. Su and G.E. Karniadakis, Stochastic fluid mechanics, IEEE Computing in Science and Engineering (CiSE), 9:21-29, 2007.
4. G. Lin, C.-H. Su and G.E. Karniadakis, Predicting shock dynamics in the presence of uncertainties, Journal of Computational Physics, special issue in stochastic uncertainty prediction, 217(1) 260-276, 2006.
Fig. 3 Sketch of Curse of Dimensionality: More Data are Needed as Dimension Increases
Motivation: This research is motivated by the critical challenge, so called “curse of dimensionality” issue in quantifying high-dimensional uncertainties in the complex stochastic partial differential systems.
Methods: To tackle the curse of dimensionality challenge, several advanced high-order stochastic numerical algorithms have been developed:
2.a High dimensions: adaptive analysis of variance (ANOVA) algorithms - For stochastic problems with high stochastic input dimensions, an adaptive ANOVA-based gPC method based on three different adaptive criteria for solving high-dimensional stochastic PDE systems  was developed as a dimension-reduction technique to decompose of the original high-dimensional stochastic problem results into a set of low-dimensional sub-problems in stochastic space, which can be efficiently solved by the sparse-grid stochastic collocation method. This is motivated by the observation that for many real-physical systems, only a relatively small number of stochastic dimensions is important and will significantly impact the stochastic systems’ outputs. To speed up the computation, a reduced basis ANOVA method is developed in . In addition, to model high-dimensional stochastic multiscale problem, adaptive ANOVA-based data-driven stochastic methods are developed  and a variance-based mixed multiscale finite element method is proposed in . A random domain decomposition method is introduced in . To solve high-dimensional inverse problem, an adaptive ANOVA-based probabilistic collocation Kalman filter method is developed in .
2.b High dimensions: Compressive sampling algorithms - To address the “curse of dimensionality” issue, a careful model reduction can be performed through the evaluation of a gPC expansion that contains a smaller subset of significant gPC bases. Compressive sensing-based based numerical methods for selecting such smaller subset of significant gPC bases have been developed. To further improve the efficiency and accuracy of the compressive sensing-based uncertainty quantification methods, new bases for random variables are identified in [1, 2] through linear mappings such that the representation of the quantity of interest is sparser with the new basis functions associated with the new random variables.
2.c High dimensions: Bayesian model selection algorithms - Bayesian model selection-based numerical methods for selecting smaller subset of significant gPC bases have also been developed. In particular, the Bayesian model uncertainty methods  and the Bayesian mixture prior procedure  have been developed by Lin and his coworkers. In this work, a fully Bayesian stochastic procedure is employed to perform gPC basis selection and coefficient evaluation simultaneously. It recovers possible sparse structures in both stochastic and spatial domains.
2.d High dimensions: Inverse regression-based algorithms - Many high-dimensional UQ problems are intrinsically low-dimensional, because the variation of the quantity of interest is often caused by only a few latent parameters varying within a low-dimensional subspace, known as the sufficient dimension reduction subspace in the statistics literature. Motivated by this observation, two inverse regression-based UQ algorithms are developed in  for high-dimensional problems. Both algorithms use inverse regression to convert the original high-dimensional problem to a low-dimensional one, which is then efficiently solved by building a response surface for the reduced model, for example via the polynomial chaos expansion.
Results: The developed advanced high-order stochastic numerical algorithms take advantage of the special properties of the stochastic partial differential systems, such as the sparsity, or the sufficient dimension reduction subspace property, etc., which enables us to greatly reduce the high-dimensional space into a low-dimensional manifold so that we can quantify the high-dimensional uncertainties in the complex stochastic partial differential systems.
Why it Matters: The developed work will have a significant and broad impact as it sets the foundations on high-order stochastic numerical methods for high-dimensional uncertainty quantification problems, which are useful for predictive modeling in many applications of interest to NSF, DOE, AFOSR, ONR, ARL and DARPA.
1. X. Yang, H. Lei, N. Baker, G. Lin*, Enhancing sparsity of Hermite polynomial expansions by iterative rotations, Journal of Computational Physics, 307: 94-09, 2016.
2. H. Lei, X. Yang, B. Zheng, G. Lin, N. Baker, Constructing Surrogate Models of Complex Systems with Enhanced Sparsity: Quantifying the Influence of Conformational Uncertainty in Biomolecular Solvation, SIAM Multiscale Modeling and Simulation, 13(4): 1327-1353, 2016.
3. W. Li, G. Lin*, B. Li, Inverse regression-based uncertainty quantification algorithms for high-dimensional models in theory and practice, Journal of Computational Physics, 321:259-278, 2016.
4. X. Yang, M. Choi, G. Lin, G.E. Karniadakis, Adaptive ANOVA Decomposition of Incompressible and Compressible Flows, Journal of Computational Physics, 231(4): 1587–1614, 2012.
5. J. Wei, G. Lin*, L. Jiang, Y. Efendiev, Analysis of Variance-based Mixed Multiscale Finite Element Method and Applications in Stochastic Two-Phase Flows, International Journal for Uncertainty Quantification, 4(6): 455-477, 2014.
6. G. Karagiannis, B. Konomi, G. Lin*, Mixed shrinkage prior procedure for basis selection and global evaluation of gPC expansions in Bayesian framework: Applications to elliptic SPDEs, Journal of Computational Physics, 284: 528-546, 2015.
7. G. Karagiannis, G. Lin*, Selection of Polynomial Chaos Bases via Bayesian Model Uncertainty Methods with Applications to Sparse Approximation of PDEs with Stochastic Inputs, Journal of Computational Physics, 259: 114–134, 2014.
8. Z. Zhang, X. Hu, T.Y. Hou*, G. Lin*, P. Yan, An adaptive ANOVA-based data-driven stochastic method for elliptic PDE with random coefficients, Communications in Computational Physics, 16: 571-598, 2014.
9. Q. Liao, G. Lin*, Reduced basis ANOVA method for partial differential equation with high-dimensional random inputs, Journal of Computational Physics, 317: 148-164, 2016.
10. G. Lin*, D. M. Tartakovsky, and A. M. Tartakovsky, Uncertainty quantification via random domain decomposition and probabilistic collocation on sparse grids, Journal of Computational Physics, 229(19): 6995-7012, 2010.
11. W. Li, G. Lin*, D. Zhang, An Adaptive-ANOVA-based PCKF for High-Dimensional Nonlinear Inverse Modeling, Journal of Computational Physics, 258: 752–772, 2014.
12. G. Lin* and A. M. Tartakovsky, Numerical studies of three-dimensional stochastic Darcy's equation and stochastic advection-diffusion-dispersion equation, Journal of Scientific Computing, 43(1): 92-117, 2010.
Fig. 4 Big data challenge
Motivation: This research is motivated by studying how to quantify uncertainty for stochastic partial differential systems with big amount of data. Such data could be either generated from the stochastic partial differential systems or from observation.
Methods: In using Gaussian process for large data sets, we need to invert a large-scale covariance matrix. Scalable approaches have been developed to invert such large-scale matrix efficiently. If the covariance matrix is separable, the separable covariance function approach has been developed in , or approximate the covariance function based on a modified version of the linear model of coregionalization in [3,4]. Coregionalization approximation provides more accurate results than the separable approach. In situations where the separability assumption does not hold, a new effective method termed the full-scale approximation approach with block modulating function, with linear computational cost in time has been developed in . Model calibration based on multi-fidelity computer model mixture is developed in . These approaches enable us to obtain accurate results for Bayesian inference using linear time in big data analysis. Guang Lin received 2010 Department of Energy Advanced Scientific Computing Research Leadership Computing Challenge award in recognition of his work in analyzing big climate data using extreme-scale supercomputers.
Results: To tackling big data challenge, we developed multi-fidelity models to handle stochastic problems with big data generated by numerical models. For big data from observation, we developed advanced algorithms to approximate the covariance matrix. Numerical examples have demonstrated that the developed methods can handle stochastic partial differential systems with big data.
Why it Matters: The developed work will have a significant and broad impact as it sets the foundations on developing efficient numerical methods on handling big data in uncertainty quantification, which is useful for predictive modeling in many applications of interest to NSF, DOE, AFOSR, ONR, ARL and DARPA.
1. G. Karagiannis, G. Lin*, On the design of a predictive model of computer model mixtures and their calibration through experimental data, Technometrics, in review.
2. B. Zhang, B. Konomi, H. Sang, G. Karagiannis, G. Lin*, Full scale multi-output Gaussian process emulator with nonseparable auto-covariance functions, Journal of Computational Physics, 300: 623–642, 2015.
3. B. Konomi, G. Lin*, Low-Cost Multi-output Gaussian Process with Application to Uncertainty Quantification, International Journal for Uncertainty Quantification, 5(4): 375-392, 2015.
4. B. Konomi, G. Karagiannis, G. Lin, On the Bayesian Treed Multivariate Gaussian Process with Linear Model of Coregionalization, Journal of Statistical Planning and Inference, 157-158: 1-15, 2015.
5. Bilionis I, N. Zabaras, B Konomi, and G Lin. Multi-output separable Gaussian process: Towards an efficient, fully Bayesian paradigm for uncertainty quantification, Journal of Computational Physics, 241: 212-239, 2013.
Fig. 5 Adaptive Mesh Refinement for UQ Problem with Discontinuities
Motivation: This research is motivated by studying how to quantify the uncertainty for complex stochastic partial differential systems with local feature/discontinuities/non-stationarity/low regularity.
Methods: The stochastic behavior of real-world complex systems is inevitably highly non-stationary, with local feature and discontinuities, due primarily to the relatively large number of heterogeneous sub-systems. Hence, it is a crucial to build advanced numerical methods for non-stationary systems with local feature and discontinuities. In particular, a Bayesian-treed multivariate Gaussian process model [1-3] and an adaptive WENO collocation method  have been developed to tackle such challenge, which adaptively partition the stochastic space into multiple elements. The size of each element is adaptively adjusted based on the location of local feature/discontinuities.
Results: We have developed two different efficient numerical algorithms that are able to adaptively partition the stochastic space into multiple elements. The size of each element is adaptively adjusted based on the location of local feature/discontinuities.
Why it Matters: The developed work will have a significant and broad impact as it sets the foundations on developing advanced stochastic numerical methods to uncertainty propagation for stochastic problems with local feature/discontinuities/non-stationarity/low regularity, which is useful for predictive modeling in many applications of interest to NSF, DOE, AFOSR, ONR, ARL and DARPA.
1. B. Konomi, G. Karagiannis, A. Sarkar, X. Sun, G. Lin*, Bayesian Treed Multivariate Gaussian Process with Adaptive Design: Application to a Carbon Capture Unit, Technometrics, 56(2): 145–158, 2014.
2. Konomi, B., G. Karagiannis, K. Lai, G. Lin, Bayesian treed Calibration: an application to Carbon capture with AX sorbent, Journal of American Statistical Association, ISSN: 0162-1459 (Print) 1537-274X (Online), 2016. DOI: 10.1080/01621459.2016.1190279
3. B. Konomi, G. Karagiannis, G. Lin, On the Bayesian Treed Multivariate Gaussian Process with Linear Model of Coregionalization, Journal of Statistical Planning and Inference, 157-158: 1-15, 2015.
4. W. Guo, G. Lin*, A. J. Christlieb, J. Qiu, An adaptive WENO collocation method for differential equations with random coefficients, Mathematics, 4(2), 29; doi:10.3390/math4020029, 2016.
5. G. Lin, X. Wan, C.-H. Su and G.E. Karniadakis, Stochastic fluid mechanics, IEEE Computing in Science and Engineering (CiSE), 9:21-29, 2007.
Fig. 6 Adaptive importance sampling from the posterior PDF
Motivation: A notable error source in modeling physical systems is parametric uncertainty, where the values of model parameters that characterize the system are not known exactly due to limited data or incomplete knowledge. In this situation, a data assimilation algorithm can improve modeling accuracy by quantifying and reducing such uncertainty. However, the performance of these algorithms, such as Kalman filter, will degenerate if the parametric uncertainty has non-Gaussian distribution, and fail for multimodal distribution. Quantifying the uncertainties with multimodal distribution in data assimilation is notoriously challenging and difficult. In addition, these algorithms often require a large number of repetitive model evaluations that incur significant computational resource costs, in particular for predicting complex systems, such as the global climate models.
: In response to these issues, an adaptive importance sampling algorithm is developed that alleviates the burden caused by computationally demanding models.
Two key techniques implemented in this algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed to capture the distribution of uncertain parameters and 2) a mixture of polynomial chaos (PC) expansions built as a surrogate model to alleviate the computational burden caused by forward model evaluations. These techniques afford the algorithm great flexibility to handle complex multimodal distributions and strongly nonlinear models while keeping the computational costs at a minimum level.
Results: Three test cases demonstrated that the developed algorithm can effectively capture the complex posterior parametric uncertainties for the specific problems being examined while also enhancing computational efficiency.
Why it Matters: Parametric uncertainty often arises in these models because of incomplete knowledge of the system being simulated, resulting in models that deviate from reality. The algorithm developed in this research provides an effective means to infer model parameters from any direct and/or indirect measurement data through uncertainty quantification, improving model accuracy. This algorithm has many potential applications. For example, it can be used to estimate the unknown location of an underground contaminant source and to improve the accuracy of the model that predicts how groundwater is affected by this source.
1. Li W and G Lin. 2015. “An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions.” Journal of Computational Physics 294:173-190. DOI:10.1016/j.jcp.2015.03.047.
2. W. Li, D. Zhang, G. Lin, A surrogate-based adaptive sampling approach for history matching and uncertainty quantification, SPE Reservoir Simulation Symposium, SPE 173298, Houston, Texas, Feb. 23-25, USA, 2015.
Fig. 7 Sketch of a transition pathway of rare event
Motivation: Dynamical systems are often subject to random perturbations or noise. Even when the noise amplitude is very small, it has a profound influence on the dynamics on the appropriate time-scale. When the noise is small, which is the case of interest here, the classic methods, such as Monte Carlo or direct simulation of Langevin equations, become prohibitively expensive, due to the presence of two disparate time-scales: the time-scale of the deterministic dynamics and the time-scale between the rare events caused by the noise.
Methods: An asymptotic analysis and efficient rare event simulation for stochastic Korteweg-de Vries equation has been developed in . To tackle such challenging issue, hp-adaptive parallel minimum action methods  have been developed to study the transition behavior induced by small noise and the structure of the phase space for nonlinear dynamical systems. In addition, a efficient Bayesian experimental design method is developed in  for failure detection.
Results: The hp-adaptive parallel minimum action method employs multi-grid technique and hp-adaptive algorithms , which further improve the efficiency of MAM by replacing the global reparametrization with hp-adaptivity and parallel implementation.
Why it Matters: Rare events play a critical role in nature. In fact, phenomena like nucleation events during phase transitions, chemical reactions, conformation changes of biomolecules, bitable behaviors in genetic switches, or regime changes in climate are just a few examples of rare events among many others. The developed work will have a significant and broad impact as it sets the foundations on developing efficient adaptive algorithms for rare events, which is useful for predictive modeling of rare events in many applications of interest to NSF, DOE, AFOSR, ONR, ARL and DARPA.
1. X. Wan, G. Lin, Hybrid parallel computing of minimum action method, Parallel Computing, 39: 638-651, 2013.
2. G. Xu, G. Lin*, J. Liu, Rare Event Simulation for Stochastic Korteweg-de Vries Equation, SIAM/ASA Journal on Uncertainty Quantification, 2 (1): 698-716, 2014.
3. H. Wang, G. Lin, J. Li, Gaussian process surrogates for failure detection: a Bayesian experimental design approach, Journal of Computational Physics, 313: 247-259, 2016.
Fig. 8 Regional climate model parameter estimation using Simulated Stochastic Approximation Annealing algorithm 
Motivation: This research is motivated by studying how to efficiently solve large-scale stochastic inverse problem or parameter estimation problem with computational expensive model. In practice, most often the computational expensive model is given as a black box and we don’t know the mathematical models inside.
Methods: We treat such large-scale inverse problem or parameter estimation problem as a global optimization problem. Two advanced numerical methods have been developed as follows:
1. Simulated Stochastic Approximation Annealing for Global Optimization with a Square-Root Cooling Schedule published at the prestigious journal: Journal of the American Statistical Association 
2. Parallel Interactive Stochastic Approximation Annealing for Global Optimization 
Results: The convergence of the two advanced global optimization algorithms has been demonstrated through benchmark examples. In addition, we have employed the two developed algorithms to improve both the regional [3,5] and global [4,6] climate model predictivity by tuning the uncertain parameters inside the convection scheme using the available satellite datasets. This study reveals that we can not only tune the uncertain parameters to improve the capability in predicting the precipitation, but also correct the non-physical phenomena, e.g., double ITCZ in global climate modeling, that bothers climate modelers for long time. Guang Lin received Ronald L. Brodzinski Award for Early Career Exception Achievement from Department of Energy Pacific Northwest National Laboratory in 2012 in recognition of his work on developing advanced optimization algorithms to calibrate complex global and regional climate models.
Why it Matters: The developed work will have a significant and broad impact as it sets the foundations on advanced computational stochastic methods to large-scale inverse problem or parameter estimation problem with computational expensive model, which is useful for improving the model predictivity in many critical applications of interest to NSF, DOE, AFOSR, ONR, ARL and DARPA.
1. F. Liang, Y. Cheng, and G Lin, Simulated Stochastic Approximation Annealing for Global Optimization with a Square-Root Cooling Schedule, Journal of the American Statistical Association, 109(506): 847-863, 2014.
2. G. Karagiannis, B. Konomi, F. Liang, G. Lin, Parallel Interactive Stochastic Approximation Annealing for Global Optimization, Journal of Computational and Graphical Statics, 1-19, doi:10.1007/s11222-016-9663-0, 2016.
3. H. Yan, Y. Qian, G. Lin, L.R. Leung, B. Yang, Q. Fu, Parametric Sensitivity and Calibration for the Kain-Fritsch Convective Parameterization Scheme in the WRF Model, Climate Research, 59: 135-147, 2014.
4. C. Zhao, X. Liu, Y. Qian, J. Yoon, Z. Hou, G. Lin, S. McFarlane, H. Wang, B. Yang, P.-L. Ma, H. Yan, J. Bao, A Sensitivity Study of Radiative Fluxes at the Top of Atmosphere to Cloud-Microphysics and Aerosol Parameters in the Community Atmosphere Model CAM5, Atmos. Chem. Phys., 13: 10969-10987, 2013
5. B. Yang, Y. Qian, G. Lin, R. Leung, Y. Zhang, Some issues in uncertainty quantification and parameter tuning: a case study of convective parameterization scheme in the WRF regional climate model, Atmospheric Chemistry and Physics, 12(5): 2409-2427, 2012.
6. B. Yang, Y Qian, G Lin, LYR Leung, PJ Rasch, GJ Zhang, SA McFarlane, C Zhao, Y Zhang, H Wang, M Wang, and X Liu, Uncertainty Quantification and Parameter Tuning in the CAM5 Zhang-McFarlane Convection Scheme and Physical Impact of Improved Convection on the Global Circulation and Climate, Journal of Geophysical Research. D. (Atmospheres), 118: 395-415, 2013.
Fig. 9 Sketch of stochastic network problem
Motivation: Dynamical network systems, such as social network, cyber-network, epidemic disease network and power grid, are critical to our daily life. Such network systems are often subject to random noise. Such noise plays critical rule in changing the topology, the dynamics, and the stability of the dynamical network systems. When the size of the network increases, it is a great challenge to quantify the uncertainties in complex ultra-large network systems.
Methods: To tackle such challenging issue, advanced dimension reduction methods have been developed to perform dimension reduction on the dynamical network systems in . Rigorous uncertainty quantification algorithms have been employed to endow ultra-large dynamical stochastic network simulations with a composite error bar [2-10]. Guang Lin received 2016 NSF faculty early career development award in recognition of his work on uncertainty quantification and big data analysis in smart grid and other complex stochastic network systems.
Results: The numerical examples have demonstrated that the developed methods are able to effectively reduce the size of the stochastic network systems and quantify the uncertainties in the stochastic network systems. In particular, we have demonstrated the developed methods on the next generation smart grid.
Why it Matters: Noise plays a critical role in dynamical network systems, such as social network, power grids and epidemic disease network. The developed work will have a significant and broad impact as it sets the foundations on developing efficient adaptive algorithms for predictive modeling of stochastic network in many applications of interest to NSF, DOE, AFOSR, ONR, ARL and DARPA.
1. S. Wang, S. Lu, N. Zhou, G. Lin, M. Elizondo, M.A. Pai, Dynamic-feature Extraction, Attribution and Reconstruction (DEAR) Method for Power System Model Reduction, IEEE Transactions on Power Systems, 99: 1-11, 2014.
2. G. Lin*, M. Elizondo, S. Lu, X. Wan, Uncertainty Quantification in Dynamic Simulations of Large-scale Power System Models using the High-Order Probabilistic Collocation Method on Sparse Grids, International Journal for Uncertainty Quantification, 4(3): 185-204, 2014.
3. D. Meng, N. Zhou, S. Lu, G. Lin, An Expectation-Maximization Method for Calibrating Synchronous Machine Models, 2013 IEEE PES General meeting, July 21-25, 2013, Vancouver, BC, Canada.
4. Elizondo MA, S Lu, G Lin, and S Wang, Dynamic Response of Large Wind Power Plant Affected by Diverse Conditions at Individual Turbines, In IEEE Power and Energy Society General meeting, July 27-31, 2014, National Harbor, MD, USA.
5. J.B. Coble, G. Lin, B. Shumaker, P. Ramuhalli, Approaches to Quantify Uncertainty in Online Sensor Calibration Monitoring, 2013 American Nuclear Society Winter Meeting and Technology Expo., 2013.
6. TA Ferryman, DJ Haglin, M Vlachopoulou, J Yin, C Shen, N Zhou, G Lin, FK Tuffner, and J Tong. Net Interchange Schedule Forecasting of Electric Power Exchange for RTO/ISOs, 2012 IEEE PES General meeting, July 22-26, 2012, San Diego, CA.
7. D Meng, N Zhou, S Lu, and G Lin. Estimate the Electromechanical States Using Particle Filtering and Smoothing, 2012 IEEE PES General meeting, July 22-26, 2012, San Diego, CA.
8. S Wang, S Lu, G Lin, and N Zhou. Measurement-based Coherency Identification and Aggregation for Power Systems, 2012 IEEE PES General meeting, July 22-26, 2012, San Diego, CA.
9. G. Lin, N. Zhou, T. Ferryman, and F. Tuffner, Uncertainty Quantification in State Estimation using the Probabilistic Collocation Method, Power Systems Conference and Exposition, March 20th, 2011, Phoenix, AZ.
10. T. Ferryman, F. Tuffner, N. Zhou, and G. Lin, Initial Study on the Predictability of Real Power on the Grid based on PMU Data, Power Systems Conference and Exposition, March 20th, 2011, Phoenix, AZ.
Fig. 10 Sketch of 3D red blood cell modeling in a blood vessel
Motivation: According to a World Health Organization report, malaria, a disease related to red blood cells remains a global threat. Hence modeling red blood cells and their related disease are critical to our life.
Methods: Lin and his collaborators have developed advanced numerical methods in modeling red blood cell deformation and interaction in flow. In particular, to model red blood cell (RBC) deformation and multiple-cell interactions in flow, the lattice Boltzmann method and the distributed Lagrange multiplier/fictitious domain method [1,2] is extended to employ the mesoscopic network model for simulations of RBCs in flow.
In , a hybrid model is developed representing the cellular structure consists of a continuum representation of the lipid bilayer, from which the bending force is calculated through energetic variational approach, a discrete cytoskeleton model utilizing the worm-like chain to represent network filament, and area/volume constraints. Guang Lin received 2015 Mathematical Biosciences Institute Early Career Award from Mathematical Biosciences Institute in recognition his work on modeling complex biological flow systems.
Results: The numerical examples have demonstrated that the developed methods are able to effectively model the dynamics of red blood cell in flow.
Why it Matters: Modeling red blood cells and their related disease are critical to our life. The developed work can be employed to model complex biological systems in many applications of interest to NSF, NIH and DARPA.
1. X. Shi, G. Lin*, J. Zhou, D. Fedosov, A Lattice Boltzmann Fictitious Domain Method for Modeling Red Blood Cell Deformation and Multiple-Cell Hydrodynamic Interaction in Flow, International Journal for Numerical Methods in fluids, 72 (8): 895-911, 2013.
2. X. Shi, G. Lin*, Modeling the Sedimentation of Red Blood Cells in Flow under Strong External Magnetic Body Force using a Lattice Boltzmann Fictitious Domain Method, Numer. Math. Theor. Meth. Appl. 72014: 512-523, 2014.
3. W. Hao, Z. Xu, C. Liu, G. Lin, A Fictitious Domain Method with a Hybrid Cell Model for Simulating Motion of Cells in Fluid Flow, Journal of Computational Physics, 280: 345-362, 2015.