Active Research Topics:
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Scientific Machine Learning (SciML)
This is an emerging area that brings together the fields of Machine Learning and Scientific Computation. SciML introduces scientific model constraints in Machine Learning algorithms, allowing the extrapolation and prediction of the behavior of complex systems in an interpetable and verifiable way. Our research goals concern improved training of physically-informed neural networks and probabilistic models for forward and inverse modeling and its applications in science and engineering problems. We collaborate with Simo Särkkä’s group at Aalto University, Finland, on Bayesian filtering and Gaussian process approaches to SciML. We are coordinating the recently established Texas A&M Institute of Data Science (TAMIDS) SciML Lab. For more information: https://sciml.tamids.tamu.edu/.
Active Funding: NSF Award CCF-2225507; Texas A&M Institute of Data Science (TAMIDS).
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Statistical Signal Processing
This research concerns the development of optimal estimation and control tools for stochastic nonlinear dynamical systems. The main applications of this work are modeling of gene regulatory networks and epidemic spread of viral diseases, in particular, Covid-19. One of the main tools used in this work is the partially-observed Boolean dynamical system (POBDS) model and its optimal state estimator, the Boolean Kalman Filter and Smoother. Joint estimation of state and parameters is accomplished using maximum-likelihood, swarm optimization, and Bayesian approaches. State-feedback, point-based, and reinforcement-learning control algorithms are developed for optimal intervention.
Past Funding: NSF Awards CCF-1320884, CCF-1718924.
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Classification and Error Estimation
The research goals here concern the solution of significant computational and statistical problems in classifier design and classification error estimation based on small samples in high-dimensional spaces, with application in the classification of genomic, proteomic, immunomic, and metagenomic signals Some of the milestones of this research include the introduction of the Bolstered Error Estimator, the detailed distributional study of error estimation methods in small-sample settings and separate sampling schemes, and the development of Bayesian classification algorithms for transcriptomic, proteomic, and metagenomic data.
Past Funding: NSF Award CCF-0845407 (CAREER); Texas A&M Engineering Interdisciplinary Seed Grants for Strategic Initiatives.
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Active Collaborative Applications
Our active collaborative work has five main active components:
(1) Application of SciML in Radiative Transfer for Supernova Explosions. Collaborators: Lifan Wang (TAMU Physics and Astronomy) and David Jeffery (UNLV).
(2) Application of SciML in Subsurface Flows. Collaborator: Eduardo Gildin (TAMU Petroleum Engineering)
(3) Application of SciML in Plasma Physics and Fusion Science. Collaborators: David Hatch (Fusion Institute, UT-Austin) and Aaro Järvinen (VTT, Finland).
(4) Modeling of Infectious Disease Epidemics. Collaborator: Martial Ndeffo Mbah (TAMU College of Veterinary Medicine).
(5) Microstructure Informatics. Collaborator: Raymundo Arroyave (TAMU Materials Science and Engineering).Past Funding: NSF Awards CCF-2225507, CCF-1718924; Data-Enabled Discovery and Design of Energy Materials (D3EM) training program.