CURRENT RESEARCH

Science

Physics-constrained, Data-enabled modeling 

This is a long term effort and we are methodically exploring many aspects of the process including generating the data via design of experiments, developing/extending machine learning methods as well as addressing computer science aspects. While these ideas are general, application to turbulence modeling is one of the main focus areas. 

Reduced Order Modeling 

We are exploring techniques to reduce the dimensionality of large-scale complex systems. Specifically, we are developing techniques to equip ROMs with the capability to yield true predictions. Adaptive basis and adaptive sampling is the driver for this. We are also developing effective non-intrusive ROMs using Transformer architectures

Project Website

Numerical Methods

We are developing structure-preserving numerical methods for complex multi-physics computations including Extended Magneto-hydrodynamics, Plasma and Radiation transport. We also maintain a robust numerical method development pipeline for Compressible Aerodynamics.

Generative AI for physical modeling

Recent advances in generative artificial intelligence have had a significant impact on diverse domains, spanning computer vision, natural language processing, and drug discovery. Our work extends the reach of generative models into physical problem domains, particularly addressing the efficient enforcement of physical laws; conditioning for forward and inverse problems and incorporation of lower-fidelity information.

Formal Methods for Scientific Computing

We are developing theory and methods to bring formal notions of correctness into scientific computing, hence  promoting a rigorous handle over errors and uncertainties. Ultimately, the formalization of this process will allow the user to set and achieve a desired level of accuracy (or confidence) in an automated manner, opening up possibilities for the use of variable precision arithmetic. Our proofs are mechanically checked in an interactive theorem prover, and provide end-to-end guarantees. The vision is to do this end-to-end: from the problem expressed on a sheet of paper to the implementation at the C code level, and down to the executable code that computes numerical results. The mechanically-checked proofs use a variety of mathematical results ranging from convergence of functions to floating-point arithmetic and C semantics, thereby using various theories in one proof of correctness. 

AI-augmented Science

We are exploring the potential of large language models to augment and accelerate scientific reasoning and research. Effectiveness in scientific reasoning is being enhanced using new types of data organization and new algorithms and pathways.

Turbulence modeling 

This research seeks to develop a new generation of turbulence models for use in engineering predictions. This encompasses 

(i) Theoretical approaches: Foundational approaches based on rapid distortion theory and two-point closures.

(ii) Data-driven approaches: RANS models aided by inversion and machine learning models. 

(iii) Mathematical approach: Aided by the mathematics of the coarse-graining process (using statistical mechanics closures). 

Non-linear dynamics

We are pioneering a "feature-based" approach for predictive modeling of non-linear dynamics. We first identify invariant solutions (e.g. equilibria or time periodic orbits) to extract low-dimensional representations. We then bring ideas from optimal closures to extract predictive models in feature space, and use these models in the control of flows dominated by coherent structures. 

Deep Learning for Surrogate Modeling of unstructured physical fields

We are exploring novel ways of developing predictive models for spatio-temporal dynamics as unstructured / adaptive discretization fields. Examples : a) We generalize the idea of conditional parametrization -- using trainable functions of input parameters to generate the weights of a neural network, and extend them in a flexible way to encode information critical to the numerical simulations. 

Applications

Propulsion Applications

We are developing solver accelerators and reduced order models to enable efficient prediction of highly stiff, transient and chaotic events in applications relevant to rocket engines and rotating detonation engines.

Fusion Energy 

We are investigating efficient predictive modeling, design and control of fusion energy systems including inertial and magnetic confinement. 

Hypersonic aerothermodynamics

We are developing coarse-grained models to simplify the representation of energy states at the master equation level, and reduced order models at the continuum level. We are also extending our science and solvers, to unit (shock-boundary layer interactions, etc), and system level (scramjet flow path, etc) applications pertaining to high-speed aerothermodynamics. Particular interest is in near-wall modeling and heat transfer.

Automotive aerodynamics 

We are working to build a platform which can be used to rapidly study the impact of shape modifications on the aerodynamic performance and flow field.