CURRENT Research

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 is being coordinated in in a collaborative project.  The current focus is on developing generalizable models with an emphasis on feature space engineering.

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

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  and conditioning for forward and inverse problems involving partial differential equations (PDEs).

AI-augmented Science

We are exploring the potential of large language models to augment and accelerate scientific reasoning and research. Effectiveness in scientific reasoning can be 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 approach: A structure-based approach that describes the state of turbulence using the morphology of coherent structures

(ii) Data-driven approach: Aided by inversion and machine learning models. 

(iii) 'Mathematical approach': Aided by the mathematics of the coarse-graining process (using projection operator-type ideas). 

Information-theoretic approaches to modeling

We are developing information theoretic methods to address issues of identifiability and generalization in data-driven modeling. Additionally, we are formulating a new class of variational approaches for inference, optimal experimental design and generative modeling.

Non-linear dynamics

We are answering fundamental questions in non-linear dynamics. e.g., a) How many time-delays are required for perfect reconstruction of periodic dynamics on an attractor using linear models? Why it is possible to accurately recover the full signal even if we only observe a partial period; b) Can we effectively guarantee the stability of non-linear dynamics in an explicit fashion, akin to asymptotic stability of linear systems?; and c)  When a non-linear dynamical system is truncated, the loss of information results in a non-local  (in time) system for the remaining variables. How does the memory kernel of the resulting system look like? Does it have self-similar characteristics? How may we use this in the modeling of complex physics?

Koopman operator theory

This work is focused on the advancement of theory and algorithms for operator-theoretic modeling and decomposition of non-linear dynamical systems, with a particular emphasis on the Koopman operator. The Koopman operator represents non-linear dynamics in the form of an infinite dimensional linear operator over the space of observables of the system state. This has broad appeal in modal analysis, reduced order modeling and control. Our work places an emphasis on the development of interpretable and robust methods for approximating the Koopman operator from a mathematically rigorous standpoint.

Deep Learning for Surrogate Modeling of unstructured physical fields

We are exploring novel ways of developing predictive models for spatio-temporal dynamics as unstructured / 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

Liquid-fueled Rocket engines 

The goal of the center is to advance the state-of-the-art in Reduced Order Models (ROMs) and enable efficient prediction of transient events leading to the onset of instabilities in liquid fueled rocket combustion systems. 

Project Website

Fusion Energy 

We are investigating efficient predictive modeling, design and control of fusion energy systems involving high temperature plasmas, multi-material mixing and radiation. 

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.

Physics-based models for Autonomous Operation of UAVs 

The goal of this work is to improve trajectory planning, on-board decision-making and autonomous operation of UAVs. This is done by (i) Development of physics-based, wind-sensitive rotor aerodynamic models reliable across a wide range of flight condition, (ii) Detailed experimental validation of the above models for small-scale rotors, (iii) Design-build-flight test of a small UAV including the integration of physics-based models in embedded controllers.

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.