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.

**Data Science Case Studies**

· __IMPROving The quality of ChRYSLER CROSSMEMBER CASTINGS__

**Summary:**

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.

· __Classification of Machine functions__

**Summary:**

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.

· __Multifidelity learning for material properties prediction__

**Summary:
**

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.

· __Deep learning for power system state estimation__

**Summary:
**

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.

· __design optimal control strategy
for ebola outbreak__

**Summary:**

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.

· __robust data-driven discovery of physical laws__

**Summary:
**

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. DOI: 10.1098/rspa.2018.0305 https://royalsocietypublishing.org/doi/full/10.1098/rspa.2018.0305

**Research Highlight**

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)

Second-order stochastic
asymptotic analysis

Tackling the Curse of Dimensionality
Challenge in Uncertainty Quantification

Tackling Big Data Challenge
in Data Analysis and Uncertainty Quantification of Ultra-Large Systems

Tackling Multimodal
Distribution Challenge in Large-Scale Bayesian Inverse Problems

Numerical Methods for Rare
Events

**1. ****Second-Order Stochastic Asymptotic Analysis**** **

**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.

**Reference**:

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.

**Reference**:

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.

**2.
****Tackling the Curse of
Dimensionality Challenge in Uncertainty Quantification**

**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 [4] 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 [9]. In addition, to model
high-dimensional stochastic multiscale problem, adaptive ANOVA-based
data-driven stochastic methods are developed [8] and a variance-based mixed
multiscale finite element method is proposed in [5]. A random domain
decomposition method is introduced in [10]. To solve high-dimensional inverse
problem, an adaptive ANOVA-based probabilistic collocation Kalman filter method
is developed in [11].

**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 [7] and the Bayesian mixture prior procedure [6] 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 [3]
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.

**Reference**:

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 [5], 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 [2]. Model calibration based on multi-fidelity computer model
mixture is developed in [1]. 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.

**Reference**:

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 [4] 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.

**Reference**:

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.

**5. ****Tackling Multimodal Distribution Challenge in Large-Scale
Bayesian Inverse Problems**

**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.

**Methods**: 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.

**Reference**:

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.

**6. ****Numerical Methods for Rare Events**

**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 [2]. To tackle such challenging issue,
hp-adaptive parallel minimum action methods [1] 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 [3] for failure detection.

**Results:
**The
hp-adaptive parallel minimum action method employs multi-grid technique and
hp-adaptive algorithms [1], 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.

**Reference**:

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 [1]**

**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 [1]

2.
Parallel Interactive Stochastic
Approximation Annealing for Global Optimization [2]

**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.

**Reference**:

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 [1]. 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.

**Reference**:

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
[3], 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.

**Reference**:

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.