Physics-constrained, Data-enabled modeling
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 general 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. 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. 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
1. Improve the stability and robustness of ROMs of multi-scale systems,
2. Equip ROMs with the capability to yield TRUE predictions. Adaptive basis and adaptive sampling is the driver for this
3. Develop sub-component ROMs and integrate them in a multi-fidelity setting
4. Model the impact of unresolved scales on the resolved variables,
5. Accelerate the evaluation of ROMs by promoting sparse approximations.
6. Develop effective non-intrusive ROMs.
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).
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.
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.
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. Inspired by discretized numerical methods, choices of the parameters include physical quantities and mesh topology features. The functional relation between the modeled features and the parameters are built into the network architecture; b) A deep learning surrogate model for discretization-independent, continuous representation of PDE solutions, which can be used for prediction over domains with complex, variable geometries and mesh topologies. This technique leverages implicit neural representations to develop a non-linear mapping between problem parameters and spatial coordinates to state predictions by combining evaluations of a case-wise parameter network and a point-wise spatial network in a linear output layer.
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.
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.
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
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 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.
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.
Cooling Pack Design for Electrified Vehicles
We are developing Machine-learning-based ROMs of the front-end engine airflow with the goal of incorporation in system-level design.