@article{ranade_gitushi_echekki_2023, title={Deep Learning of Joint Scalar PDFs in Turbulent Flames from Sparse Multiscalar Data}, volume={11}, ISSN={["1563-521X"]}, DOI={10.1080/00102202.2023.2283816}, abstractNote={We investigate the reconstruction of multi-dimensional joint scalar probability density functions starting with sparse multiscalar data in turbulent flames using deep operator networks (DeepONets). The formulation is based on 1) a dimensionality reduction to reduce the complexity of modeling the PDF using principal component analysis (PCA), and 2) the implementation of the deep operator neural network (or DeepONet) to construct a generalizable joint PDF of the principal components (PCs). We demonstrate the accuracy and generalizability of the DeepONet on the Sandia turbulent non-premixed flames D, E and F where the DeepONet is trained on data for flame E and is evaluated for the 3 flames. The DeepONet-based approach is able to construct multiple PDF shapes based on the PCs for all conditions. Combined with a recently proposed method for evaluating thermochemical scalar means conditioned on the PCs, the convolution of these means with the joint PDFs yields good predictions of thermochemical scalars’ unconditional means profiles in the flames.}, journal={COMBUSTION SCIENCE AND TECHNOLOGY}, author={Ranade, Rishikesh and Gitushi, Kevin M. and Echekki, Tarek}, year={2023}, month={Nov} }
 @article{taassob_ranade_echekki_2023, title={Physics-Informed Neural Networks for Turbulent Combustion: Toward Extracting More Statistics and Closure from Point Multiscalar Measurements}, volume={10}, ISSN={["1520-5029"]}, url={https://doi.org/10.1021/acs.energyfuels.3c02410}, DOI={10.1021/acs.energyfuels.3c02410}, abstractNote={We develop a physics-informed neural network (PINN) to evaluate closure terms for turbulence and chemical source terms in the Sandia turbulent nonpremixed flames. The approach relies on temperature, major species, and velocity point measurements to develop closure for the transport of momentum and the thermo-chemical state, through principal components (PCs). The PCs are derived using principal component analysis (PCA) implemented on the measured thermo-chemical scalars. With the solution for the PCs, the number of governing equations and associated closure terms is reduced relative to the solution of the measured species and temperature. The PINNs are trained on two flame conditions, the so-called Sandia flames D and F, and are validated on an additional flame, flame E. In addition to the radial and axial spatial coordinates, the Reynolds number is prescribed as an additional input parameter. A relatively shallow network attached to the PINNs is used to relate the unconditional means of the PCs to the source terms in their transport equations. The results show that PCs, species, the mixture fraction, and the axial and radial velocity components can adequately be represented with PINNs compared to experimental statistics. Moreover, PINNs are able to reconstruct closure terms associated with turbulence and scalar transport, including the averaged PCs’ chemical source terms.}, journal={ENERGY & FUELS}, author={Taassob, Arsalan and Ranade, Rishikesh and Echekki, Tarek}, year={2023}, month={Oct} }
 @article{gitushi_ranade_echekki_2022, title={Investigation of deep learning methods for efficient high-fidelity simulations in turbulent combustion}, volume={236}, ISSN={["1556-2921"]}, url={https://doi.org/10.1016/j.combustflame.2021.111814}, DOI={10.1016/j.combustflame.2021.111814}, abstractNote={Turbulent combustion modeling often faces a trade-off between the so-called flamelet-like models and PDF-like models. Flamelet-like models, are characterized by a choice of a limited set of prescribed moments, which are transported to represent the manifold of the composition space and its statistics. PDF-like approaches are designed to directly evaluate the closure terms associated with the nonlinear chemical source terms in the energy and species equations. They generate data on the fly, which can be used to accelerate the simulation of PDF-like based models. Establishing key ingredients for implementing acceleration schemes for PDF-like methods by constructing flamelet-like models on the fly can potentially result in computational saving while maintaining the ability to resolve closure terms. These ingredients are investigated in this study. They include a data-based dimensional reduction of the composition space to a low-dimensional manifold using principal component analysis (PCA). The principal components (PCs) serve as moments, which characterize the manifold; and conditional means of the thermo-chemical scalars are evaluated in terms of these PCs. A second ingredient involves adapting a novel deep learning framework, DeepONet, to construct joint PCs' PDFs as alternative methods to presumed shapes common in flamelet-like approaches. We also investigate whether the rotation of the PCs into independent components (ICs) can improve their statistical independence. The combination of these ingredients is investigated using experimental data based on the Sydney turbulent nonpremixed flames with inhomogeneous inlets. The combination of constructed PDFs and conditional mean models are able to adequately reproduce unconditional statistics of thermo-chemical scalars, and establish acceptable statistical independence between the PCs, which simplify further the modeling of the joint PCs' PDFs.}, journal={COMBUSTION AND FLAME}, publisher={Elsevier BV}, author={Gitushi, Kevin M. and Ranade, Rishikesh and Echekki, Tarek}, year={2022}, month={Feb} }
 @article{rade_balu_herron_pathak_ranade_sarkar_krishnamurthy_2021, title={Algorithmically-consistent deep learning frameworks for structural topology optimization}, url={https://doi.org/10.1016/j.engappai.2021.104483}, DOI={10.1016/j.engappai.2021.104483}, abstractNote={Topology optimization has emerged as a popular approach to refine a component's design and increase its performance. However, current state-of-the-art topology optimization frameworks are compute-intensive, mainly due to multiple finite element analysis iterations required to evaluate the component's performance during the optimization process. Recently, machine learning (ML)-based topology optimization methods have been explored by researchers to alleviate this issue. However, previous ML approaches have mainly been demonstrated on simple two-dimensional applications with low-resolution geometry. Further, current methods are based on a single ML model for end-to-end prediction, which requires a large dataset for training. These challenges make it non-trivial to extend current approaches to higher resolutions. In this paper, we develop deep learning-based frameworks consistent with traditional topology optimization algorithms for 3D topology optimization with a reasonably fine (high) resolution. We achieve this by training multiple networks, each learning a different step of the overall topology optimization methodology, making the framework more consistent with the topology optimization algorithm. We demonstrate the application of our framework on both 2D and 3D geometries. The results show that our approach predicts the final optimized design better (5.76x reduction in total compliance MSE in 2D; 2.03x reduction in total compliance MSE in 3D) than current ML-based topology optimization methods.}, journal={Engineering Applications of Artificial Intelligence}, author={Rade, Jaydeep and Balu, Aditya and Herron, Ethan and Pathak, Jay and Ranade, Rishikesh and Sarkar, Soumik and Krishnamurthy, Adarsh}, year={2021}, month={Nov} }
 @article{ranade_li_li_echekki_2021, title={An Efficient Machine-Learning Approach for PDF Tabulation in Turbulent Combustion Closure}, volume={193}, url={https://doi.org/10.1080/00102202.2019.1686702}, DOI={10.1080/00102202.2019.1686702}, abstractNote={ABSTRACT Probability density function (PDF) based turbulent combustion modeling is limited by the need to store multi-dimensional PDF tables that can take up large amounts of memory. A significant saving in storage can be achieved by using various machine-learning techniques that represent the thermo-chemical quantities of a PDF table using mathematical functions. These functions can be computationally more expensive than the existing interpolation methods used for thermo-chemical quantities. More importantly, the training time can amount to a considerable portion of the simulation time. In this work, we address these issues by introducing an adaptive training algorithm that relies on multi-layer perception (MLP) neural networks for regression and self-organizing maps (SOMs) for clustering data to tabulate using different networks. The algorithm is designed to address both the multi-dimensionality of the PDF table as well as the computational efficiency of the proposed algorithm. SOM clustering divides the PDF table into several parts based on similarities in data. Each cluster of data is trained using an MLP algorithm on simple network architectures to generate ‘local’ functions for thermo-chemical quantities. The algorithm is validated for the so-called DLR-A turbulent jet diffusion flame using both RANS and LES simulations and the results of the PDF tabulation are compared to the standard linear interpolation method. The comparison yields a very good agreement between the two tabulation techniques and establishes the MLP-SOM approach as a viable method for PDF tabulation.}, number={7}, journal={Combustion Science and Technology}, publisher={Informa UK Limited}, author={Ranade, Rishikesh and Li, Genong and Li, Shaoping and Echekki, Tarek}, year={2021}, month={May}, pages={1258–1277} }
 @article{ranade_hill_pathak_2021, title={DiscretizationNet: A machine-learning based solver for Navier–Stokes equations using finite volume discretization}, volume={378}, url={https://doi.org/10.1016/j.cma.2021.113722}, DOI={10.1016/j.cma.2021.113722}, abstractNote={Over the last few decades, existing Partial Differential Equation (PDE) solvers have demonstrated a tremendous success in solving complex, non-linear PDEs. Although accurate, these PDE solvers are computationally costly. With the advances in Machine Learning (ML) technologies, there has been a significant increase in the research of using ML to solve PDEs. The goal of this work is to develop an ML-based PDE solver, that couples’ important characteristics of existing PDE solvers with ML technologies. The two solver characteristics that have been adopted in this work are: (1) the use of discretization-based schemes to approximate spatio-temporal partial derivatives and (2) the use of iterative algorithms to solve linearized PDEs in their discrete form. In the presence of highly non-linear, coupled PDE solutions, these strategies can be very important in achieving good accuracy, better stability and faster convergence. Our ML-solver, DiscretizationNet, employs a generative CNN-based encoder–decoder model with PDE variables as both input and output features. During training, the discretization schemes are implemented inside the computational graph to enable faster GPU computation of PDE residuals, which are used to update network weights that result into converged solutions. A novel iterative capability is implemented during the network training to improve the stability and convergence of the ML-solver. The ML-Solver is demonstrated to solve the steady, incompressible Navier–Stokes equations in 3-D for several cases such as, lid-driven cavity, flow past a cylinder and conjugate heat transfer.}, journal={Computer Methods in Applied Mechanics and Engineering}, publisher={Elsevier BV}, author={Ranade, Rishikesh and Hill, Chris and Pathak, Jay}, year={2021}, month={May}, pages={113722} }
 @article{ranade_echekki_masri_2021, title={Experiment-Based Modeling of Turbulent Flames with Inhomogeneous Inlets}, volume={11}, ISSN={["1573-1987"]}, url={https://doi.org/10.1007/s10494-021-00304-8}, DOI={10.1007/s10494-021-00304-8}, journal={FLOW TURBULENCE AND COMBUSTION}, author={Ranade, Rishikesh and Echekki, Tarek and Masri, Assaad R.}, year={2021}, month={Nov} }
 @article{discretizationnet: a machine-learning based solver for navier-stokes equations using finite volume discretization_2020, year={2020}, month={May} }
 @article{ranade_echekki_2019, title={A Framework for Data-Based Turbulent Combustion Closure: A Priori Validation}, volume={206}, url={https://doi.org/10.1016/j.combustflame.2019.05.028}, DOI={10.1016/j.combustflame.2019.05.028}, abstractNote={Experimental multi-scalar measurements in laboratory flames have provided important databases for the validation of turbulent combustion closure models. In this work, we present a framework for data-based closure in turbulent combustion and establish an a priori validation of this framework. The approach is based on the construction of joint probability density functions (PDFs) and conditional statistics using experimental data based on the parameterization of the composition space using principal component analysis (PCA). The PCA on the data identifies key parameters, principal components (PCs), on which joint scalar PDFs and conditional scalar means can be constructed. To enable a generic implementation for the construction of joint scalar PDFs, we use the multi-dimensional kernel density estimation (KDE) approach. An a priori validation of the PCA-KDE approach is carried out using the Sandia piloted jet turbulent flames D, E and F. The analysis of the results suggests that a few PCs are adequate to reproduce the statistics, resulting in a low-dimensional representation of the joint scalars PDFs and the scalars' conditional means. A reconstruction of the scalars' means and RMS statistics are in agreement of the corresponding statistics extracted directly from the experimental data. We also propose one strategy to recover missing species and construct conditional means for the reaction rates based on a variation of the pairwise-mixing stirred reactor (PMSR) model. The model is demonstrated using numerical simulations based on the one-dimensional turbulence (ODT) model for the same flames.}, journal={Combustion and Flame}, publisher={Elsevier BV}, author={Ranade, Rishikesh and Echekki, Tarek}, year={2019}, month={May}, pages={490–505} }
 @article{ranade_echekki_2019, title={A framework for data-based turbulent combustion closure: A posteriori validation}, volume={210}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85071963353&partnerID=MN8TOARS}, DOI={10.1016/j.combustflame.2019.08.039}, abstractNote={In this work, we demonstrate a framework for developing closure models in turbulent combustion using experimental multi-scalar measurements. The framework is based on the construction of conditional means and joint scalar PDFs from experimental data based on the parameterization of the composition space using principal component analysis (PCA). The resulting principal components (PCs) act as both conditioning variables and transported variables. Their chemical source terms are constructed starting from instantaneous temperature and species measurements using a variant of the pairwise mixing stirred reactor (PMSR) approach. A multi-dimensional kernel density estimation (KDE) approach is used to construct the joint PDFs in PC space. Convolutions of these joint PDFs with conditional means are used to determine the unconditional means for the closure terms: the mean PCs chemical source terms and the density. These means are parameterized in terms of the mean PCs using artificial neural networks (ANN). The framework is demonstrated a posteriori using the data from the Sandia piloted turbulent jet flames D, E and F by performing RANS calculations. The radial profiles of mean and RMS of temperature and measured species mass fractions agree well with the experimental means for these flames.}, journal={Combustion and Flame}, author={Ranade, R. and Echekki, T.}, year={2019}, pages={279–291} }
 @article{ranade_alqahtani_farooq_echekki_2019, title={An ANN based hybrid chemistry framework for complex fuels}, volume={241}, ISSN={["1873-7153"]}, url={https://doi.org/10.1016/j.fuel.2018.12.082}, DOI={10.1016/j.fuel.2018.12.082}, abstractNote={The oxidation chemistry of complex hydrocarbons involves large mechanisms with hundreds or thousands of chemical species and reactions. For practical applications and computational ease, it is desirable to reduce their chemistry. To this end, high-temperature fuel oxidation for large carbon number fuels may be described as comprising two steps, fuel pyrolysis and small species oxidation. Such an approach has recently been adopted as 'hybrid chemistry' or HyChem to handle high-temperature chemistry of jet fuels by utilizing time-series measurements of pyrolysis products. In the approach proposed here, a shallow Artificial Neural Network (ANN) is used to fit temporal profiles of fuel fragments to directly extract chemical reaction rate information. This information is then correlated with the species concentrations to build an ANN-based model for the fragments' chemistry during the pyrolysis stage. Finally, this model is combined with a C0-C4 chemical mechanism to model high-temperature fuel oxidation. This new hybrid chemistry approach is demonstrated using homogeneous chemistry calculations of n-dodecane (n-C12H26) oxidation. The experimental uncertainty is simulated by introducing realistic noise in the data. The comparison shows a good agreement between the proposed ANN hybrid chemistry approach and detailed chemistry results.}, journal={FUEL}, publisher={Elsevier BV}, author={Ranade, Rishikesh and Alqahtani, Sultan and Farooq, Aamir and Echekki, Tarek}, year={2019}, month={Apr}, pages={625–636} }
 @article{ranade_alqahtani_farooq_echekki_2019, title={An extended hybrid chemistry framework for complex hydrocarbon fuels}, volume={251}, ISSN={["1873-7153"]}, url={https://doi.org/10.1016/j.fuel.2019.04.053}, DOI={10.1016/j.fuel.2019.04.053}, abstractNote={An extended hybrid chemistry approach for complex hydrocarbons is developed to capture high-temperature fuel chemistry beyond the pyrolysis stage. The model may be constructed based on time-resolved measurements of oxidation species beyond the pyrolysis stage. The species' temporal profiles are reconstructed through an artificial neural network (ANN) regression to directly extract their chemical reaction rate information. The ANN regression is combined with a foundational C0-C2 chemical mechanism to model high-temperature fuel oxidation. This new approach is demonstrated for published experimental data sets of 3 fuels: n-heptane, n-dodecane and n-hexadecane. Further, a perturbed numerical data set for n-dodecane, generated using a detailed mechanism, is used to validate this approach with homogeneous chemistry calculations. The results demonstrate the performance and feasibility of the proposed approach.}, journal={FUEL}, publisher={Elsevier BV}, author={Ranade, Rishikesh and Alqahtani, Sultan and Farooq, Aamir and Echekki, Tarek}, year={2019}, month={Sep}, pages={276–284} }