We are a computational modeling group. We identify and work on critical modeling challenges relevant to real-world problems from a variety of perspectives. This includes innovations in physics-based modeling, data-driven paradigms, mathematical formalisms, algorithms, numerical methods, computer science, etc.
Our applications are centered around fluid flows, but we are continually expanding our domains (such as combustion, materials, fluid structure interaction, etc.) Our work targets modeling applications at a fundamental level as well as in an integrated system-level setting.
An overarching theme in our lab involves the development and application of ``appropriate'' fidelity simulation and data-driven methods to answer a spectrum of scientific and engineering questions.
Read more about our work in these websites:
Physics-constrained, Data-enabled modeling
Our belief is that data is not an alternative for physical modeling, but when combined with—and informed by—a detailed knowledge of the physical problem and problem-specific constraints, data-driven modeling is likely to yield successful solutions. You can read more about our philosophy here. One example of our work is the development of a new paradigm that combines field inversion and machine learning to enable data-driven modeling. Our critical contribution is the idea that spatio-temporal discrepancies (which are determined by inverse modeling) can be transformed into functional forms that can be embedded into a predictive model. A bare-bones schematic can be found here . 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. These activities have directly led to the establishment of the Center for Data-driven Computational Physics . While these ideas are general, application to turbulence modeling is is being coordinated in in a collaborative project. .
Funded by NASA, DARPA, ONR and NSF/MRI (2013-present) .
Reduced Order Modeling
We are exploring techniques to reduce the dimensionality of large-scale complex systems. Specifically, we are developing techniques to
1. Develop sub-component ROMs and integrate them in a multi-fidelity setting
2. Improve the stability and robustness of ROMs of multi-scale systems,
3. Model the impact of unresolved scales on the resolved variables,
4. Accelerate the evaluation of ROMs by promoting sparse approximations.
Center of Excellence funded by AFOSR and AFRL (2017-present) .
Deep Learning for Fluid Mechanics
We are investigating the use of convolutional neural networks to augment (and under the right circumstance, to replace) detailed CFD solutions of aerodynamic flows.
Funded by General Motors (2016-present) .
This research seeks to develop a new generation of turbulence models for use in engineering predictions. This encompasses
(i) Theoretical approach: A unique approach that describes the state of turbulence using the morphology of coherent structures, and
(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).
Funded by NASA, NSF/CDESE, ONR and AFOSR (2013-present) .
Novel techniques for statistical coarse graining
We are developing mathematically-consistent models using ideas from statistical mechanics that account for the impact of unresolved physics and numerical errors on resolved variables. The novelty is that time-history (non-Markovian) effects which have long been ignored in traditional large eddy simulation approaches can be formally represented. The techniques developed in this effort have applicability in a wide range of problems.
Funded by AFOSR (2016-present) .
Adaptive control using data-based techniques
We seek to extend data-driven adaptive control to systems that are beyond the capability of traditional adaptive control algorithms due to the extreme complexity of the physics. This will be accomplished by developing, demonstrating, and validating a novel diagnostic modeling methodology that that is based on limited sensor data to uncover the essential dynamics of the system. Specificially, we combine multidisciplinary expertise in adaptive control and system identification; computational fluid dynamics and data-driven modeling; and combustion dynamics and physics-guided diagnostics. The venue for developing, demonstrating, and validating the proposed diagnostic modeling methodology is experimental control of instability in lean premixed combustion.
Funded by NSF/CMMI (2017-present) .
This research addresses the fundamental question: In the process of making computational predictions, how best can we affix “error-bars” on simulation outputs? The ultimate goal is to develop a unified framework that not only accounts for randomness and variability in the system of interest, but also to quantitatively express our deficiencies in modeling the system. We are using adjoint techniques extensively to address discretization and sampling errors and field inference and machine learning to address model form errors. Under DARPA funding, we are embedding this approach within a Design Under Uncertainty (DUU) setting. The immediate application is aerothermal/structural design of a fighter aircraft nozzle.
Funded by DARPA (2015-present) .
Efficient numerical schemes for the vorticity transport equations
With a view towards computing high Reynolds number vortex dominated flows such as those in the wakes of helicopters and ships, we are developing techniques to solving fluid flow equations in vorticity-velocity form. This technique presents inherent advantages over solving the conventional Navier—Stokes equations because coherent structures can be compactly described in terms of Vorticity variables. Toward this end, we are developing sharp gradient-capturing numerical schemes such coherent structures can be resolved using a relatively small number of mesh points over the length scales.
Funded by Continuum Dynamics, Inc. and Navy (2016-present) .
Physics-inspired learning and learning the structure of physics
We are looking to develop novel machine learning algorithms that are capable of learning and enforcing physics principles and constraints. A number of critical tasks can be enacted from data alone: (i) the discovery of first principles models, (ii) the identification of physical constraints and conservation laws, and (iii) improved models using known physics and enforcing known constraints.
Funded by DARPA (2018-present) .
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. The key outcomes are the following:
1. ROMs of variable/adaptive fidelity derived from an organized hierarchy of higher fidelity simulations.
2. Integration of ROMs into a multi-fidelity model that can predict the stability characteristics of a full-scale LRE containing multiple injector elements.
3. Given a nominal engine configuration, end use is a methodology that designers can use to: a) Efficiently characterize combustion dynamics in O(days) on small cluster; b) Explore effect of parametric changes on QoIs
4. Innovations to the science of reduced modeling of complex systems
5. Engagement with AFRL researchers and exchange of knowledge, tools and data.
Center of excellence funded by AFOSR and AFRL (2017-present) .
Gas Turbine Combustors
We are investigating efficient modeling and control of thermoacoustic instabilities in gas turbine combustors. The experimental configuration is being built at UM and reduced order techniques and control formalisms are being developed.
Funded by NSF (2017-present) .
This project seeks to advance a more complete and quantitative understanding of the physics of battery materials. It will enable battery design for performance (specific capacity, specific power density, charge/discharge rates etc.), thermal management, prevention of mechanical degradation, and closed-loop control, guided by computational modeling. This project will combine new ideas of machine learning with the development of advanced computational methods to enhance the ability of the computational materials physicist to predict battery properties with quantitative accuracy. The machine learning programs will link the simulation codes at the various scales using large data sets from lower scale calculations to inform the models at each scale.
Funded by Toyota (2017-present) .
Unmanned Air Vehicles (UAVs)
We are developing techniques to a) characterize realistic operating environments of UAVs and b) develop an accurate flight dynamic model with the goal of planning optimal trajectories.
Funded by NASA and NSF-IUCRC (2016-present) .
Helicopter-ship board dynamics interface
We are developing surrogate and reduced order techniques to efficiently simulate the operation of helicopters in the airwakes of ships.
Funded by Navy (2016-present) .
We are working to build a platform which can be used to rapidly study the impact of shape modifications on the aerodynamic performance and flowfield.
Funded by General Motors (2016-present) .
High-speed air vehicles
We are extending our science and solvers, to unit (shock-boundary layer interactions, etc), and system level (scramjet flow path, etc) applications pertaining to high-speed aircraft. A currently funded effort is aimed at robust design (optimization under uncertainty) of aircraft nozzles.
Funded by DARPA (2015-present) .
Personal aircraft, powered by batteries have the potential to re-invigorate aviation. We are using our suite of computational tools to analyze and design distributed propulsion systems. Specifically, we are studying efficient propeller designs for improved performance and noise as well as optimal wing designs to beneficially utilize the propeller wake.
Funded by FXB Fellowship (2017-present) .
We are exploring the performance limits and design of unconventional concepts in wind energy. These include vertical axis wind turbine farms, shrouded wind turbines, etc.
Funded by DOE (2011-2013) and NDSEG Fellowship (2012-2015) .