Faculty

Seismic Imaging; Seismic Interferometry; Earthquake Seismology

Computational methods in medical imaging, medical image processing (reconstruction/analysis), physiological signal processing, photoacoustic tomography, and diffuse optical tomography.

Computational Materials Physics, Computational algorithms for ab-initio material modeling at extreme-scale, Machine learning for materials design, High-performance computing, Computational solid mechanics, Finite-element methods, open-source code development using finite-elements for density functional theory (DFT-FE).

Engineering models for speech science; Machine learning; Text Analytics.

Development of innovative algorithms to solve optimal and nonlinear control synthesis problems, followed by applying those to challenging real-life problems is the main focus of our lab. Techniques developed in our lab so far include model predictive static programming and its various variants, single network adaptive critic, optimal dynamic inversion, generalized dynamic inversion, neuro-adaptive design etc. Application areas in aerospace include guidance and control of missiles, spacecrafts, lunar lander, aircrafts and UAVs. In bio-medicine, our focus has been computer controlled automatic drug delivery using feedback control theory and also deciphering the control activities of human brain. The feedback drug delivery philosophy has been demonstrated to work well (from in-silico experiments) to effectively cure various cancer problems. An important current research focus is to develop an adaptive and customized artificial pancreas system for Type-1 diabetic patients. Other problems of interest to our lab include path planning and guidance of ground vehicles, vibration control, temperature control, process control etc.

Developing efficient CFD algorithms for fluid flows, including central schemes, kinetic schemes and relaxation schemes; exact capturing of shocks and contact discontinuities; low numerical diffusion methods; meshless or grid-free methods; Lattice Boltzman method; non-standard finite difference methods; aerodynamic shape optimization; algorithms for turbulence simulation.

Cancer, morphogenesis, pattern formation

Tensor Decompositions, Neural Networks, Numerical Linear Algebra, Generalized Inverses of Tensors, Wavelets in Scientific Computing, High-Performance Computing.

Sirtuins in Cardiovascular diseases.

Cellular Neurophysiology, Biophysics of Neurons and Computational Neuroscience.

Neural mechanisms of learning and memory

Finite Element Analysis, High Performance Computing, Computational Fluid Dynamics, Bio-medical Applications

Structural Biology and Biocomputing, Statistical Crystallography, Algorithm development, Database analysis & maintenance, World Wide Web (WWW) based internet computin.

Groundwater hydrology, agro-hydrology, satellite hydrology using numerical methods, geospatial & geophysical methods, optimization & inverse approaches, and specifically in the following themes.

Computational finance, Monte Carlo methods for derivate pricing, Financial risk management, Real Options.

Immuno-engineering, Biomaterials, Drug Delivery

Tau pathology, Neuroinflammation, Neurodegenerative diseases

My research interest is in studying constrained and related stochastic dynamical systems with computational mathematical tools. Current work includes applications to problems of data assimilation and rough path behaviour.

Space dynamical systems (such as satellite orbit estimation) and biochemical reactions are examples of fields of application.

How does our brain enable us to pay attention selectively to some things, and to ignore others? What happens in the brain when we make important decisions? Our research focuses on understanding the neural basis of cognitive phenomena such as selective attention and decision making. To address these questions we follow a quantitative approach that combines neuroscience experiments, model-based analyses (e.g., linear/nonlinear dynamical systems, control theory, machine learning) as well as large-scale computer simulations. We directly measure or perturb brain activity with a variety of techniques, including functional neuroimaging (fMRI), diffusion imaging (dMRI), high-density electro-encephalography (EEG), and transcranial electrical and magnetic stimulation (tES/tMS). The overarching goal is to develop a unified framework that describes how cognitive phenomena emerge from neural computations by a systematic analysis of brain and behavior.

Theoretical and applied probability, statistics, branching particle systems, random geometric graphs, mathematical finance, credit-risk modelling, time-series analysis, Monte Carlo simulatio.