Digital twin of Look-up libraries

Hypersonic flows are of great interest in a wide range of aerospace applications and are a critical component of many technological advances. Accurate simulations of these flows in thermodynamic (non)-equilibrium (accounting for high temperature effects) rely on detailed thermochemical gas models. While accurately capturing the underlying aerothermochemistry, these models dramatically increase the cost of such calculations. In our group, we present a novel model-agnostic machine-learning technique to extract a reduced thermochemical model of a gas mixture from a library. A first simulation gathers all relevant thermodynamic states and the corresponding gas properties via a given model. The states are embedded in a low-dimensional space and clustered to identify regions with different levels of thermochemical (non)-equilibrium. Then, a surrogate surface from the reduced cluster-space to the output space is generated using radial-basis-function networks. The method is validated and benchmarked on simulations of a hypersonic flat-plate boundary layer and shock-wave boundary layer interaction (shown in the figure below) with finite-rate chemistry. The gas properties of the reactive air mixture are initially modeled using the open-source Mutation++ library. Substituting Mutation++ with the light-weight, machine-learned alternative improves the performance of the solver by up to 70% while maintaining overall accuracy in both cases.

Data-driven dynamic identification

With advances in computing power, larger and more accurate simulations are being performed, capable of capturing detailed interactions of various physical phenomena present in the flow. One of the main products of such expensive calculations is the resulting data, which is also increasing in size, opening the door to data-driven analysis, such as system identification and machine learning techniques.

In many regimes, the dynamics of physical systems, usually described by complex partial differential equations, are governed by only a few nonlinear terms, allowing the production of simpler models capable of predicting the main features of the underlying system. The determination of these structures inherent in such physical systems can be accomplished through the use of data-driven models and system identification.

In our group we explore a data-driven dynamics identification procedure realized by coupling sparse linear regression with network partitioning used for clustering purposes.

EDNN - AI-aided aolution of PDE’s

Machine-learning (ML) holds significant promise in revolutionizing a wide range of applications, in particular in the domain of multi-scale and multi-physics problems. Success in realizing the promise of ML is predicated on the availability of training data, which are often obtained from scientific computations. Conventional approaches to solving the equations of physics require difficult and specialized software development, grid generation and adaptation, and the use of specialized data and software pipelines that differ from those adopted in ML. A disruptive new approach that was recently proposed Zaki et al. is Evolutional Deep Neural Networks (EDNN, pronounced “Eden”) which leverages the software and hardware infrastructure used in ML to replace conventional computational methods, and to tackle their shortcomings. EDNN is unique because it does not rely on training to express known solutions, but rather the network parameters evolve using the governing physical laws such that the network can predict the evolution of the physical system. In our group, we are furhutr
developping the EDNN framework to solve high-dimensional partial differential equations, used to model a vast range of phenomena in economics, finance, operational research, and multi-phase fluid dynamics, where population balance equations govern phenomena as diverse as aerosol transmission of airborne pathogens or mixing enhancement in energy conversion devices. The simulation of such flows is an open issue of particular interest. We will demonstrate the ease of software development using automatic differentiation tools and the capacity of EDNN to eliminate the curse of dimensionality and the tyranny of moment closure. Success stands to disrupt and transform the decades-old computational approach to solving nonlinear differential equations and to remove the barriers to generation of training data required for ML.