arXiv subjects

Rishikesh Ranade

Publications and source records attributed to Rishikesh Ranade.

27 records · Page 2Linked to original sources

arXiv2021

A composable autoencoder-based iterative algorithm for accelerating numerical simulations

Numerical simulations for engineering applications solve partial differential equations (PDE) to model various physical processes. Traditional PDE solvers are very accurate but computationally costly. On the other hand, Machine Learning (ML) methods offer a significant computational speedup but face challenges with accuracy and generalization to different PDE conditions, such as geometry, boundary conditions, initial conditions and PDE source terms. In this work, we propose a novel ML-based approach, CoAE-MLSim (Composable AutoEncoder Machine Learning Simulation), which is an unsupervised, lower-dimensional, local method, that is motivated from key ideas used in commercial PDE solvers. This allows our approach to learn better with relatively fewer samples of PDE solutions. The proposed ML-approach is compared against commercial solvers for better benchmarks as well as latest ML-approaches for solving PDEs. It is tested for a variety of complex engineering cases to demonstrate its computational speed, accuracy, scalability, and generalization across different PDE conditions. The results show that our approach captures physics accurately across all metrics of comparison (including measures such as results on section cuts and lines).

cs.LG↗

arXiv2021

Geometry encoding for numerical simulations

We present a notion of geometry encoding suitable for machine learning-based numerical simulation. In particular, we delineate how this notion of encoding is different than other encoding algorithms commonly used in other disciplines such as computer vision and computer graphics. We also present a model comprised of multiple neural networks including a processor, a compressor and an evaluator.These parts each satisfy a particular requirement of our encoding. We compare our encoding model with the analogous models in the literature

cs.LG↗

arXiv2021

A Latent space solver for PDE generalization

In this work we propose a hybrid solver to solve partial differential equation (PDE)s in the latent space. The solver uses an iterative inferencing strategy combined with solution initialization to improve generalization of PDE solutions. The solver is tested on an engineering case and the results show that it can generalize well to several PDE conditions.

cs.LG↗

arXiv2021

Generalized Joint Probability Density Function Formulation inTurbulent Combustion using DeepONet

Joint probability density function (PDF)-based models in turbulent combustion provide direct closure for turbulence-chemistry interactions. The joint PDFs capture the turbulent flame dynamics at different spatial locations and hence it is crucial to represent them accurately. The jointPDFs are parameterized on the unconditional means of thermo-chemical state variables, which can be high dimensional. Thus, accurate construction of joint PDFs at various spatial locations may require an exorbitant amount of data. In a previous work, we introduced a framework that alleviated data requirements by constructing joint PDFs in a lower dimensional space using principal component analysis (PCA) in conjunction with Kernel Density Estimation (KDE). However, constructing the principal component (PC) joint PDFs is still computationally expensive as they are required to be calculated at each spatial location in the turbulent flame. In this work, we propose the concept of a generalized joint PDF model using the Deep Operator Network (DeepONet). The DeepONet is a machine learning model that is parameterized on the unconditional means of PCs at a given spatial location and discrete PC coordinates and predicts the joint probability density value for the corresponding PC coordinate. We demonstrate the accuracy and generalizability of the DeepONet on the Sandia flames, D, E and F. The DeepONet is trained based on the PC joint PDFs observed inflame E and yields excellent predictions of joint PDFs shapes at different spatial locations of flamesD and F, which are not seen during training

physics.flu-dyn↗

arXiv2021

ActivationNet: Representation learning to predict contact quality of interacting 3-D surfaces in engineering designs

Engineering simulations for analysis of structural and fluid systems require information of contacts between various 3-D surfaces of the geometry to accurately model the physics between them. In machine learning applications, 3-D surfaces are most suitably represented with point clouds or meshes and learning representations of interacting geometries form point-based representations is challenging. The objective of this work is to introduce a machine learning algorithm, ActivationNet, that can learn from point clouds or meshes of interacting 3-D surfaces and predict the quality of contact between these surfaces. The ActivationNet generates activation states from point-based representation of surfaces using a multi-dimensional binning approach. The activation states are further used to contact quality between surfaces using deep neural networks. The performance of our model is demonstrated using several experiments, including tests on interacting surfaces extracted from engineering geometries. In all the experiments presented in this paper, the contact quality predictions of ActivationNet agree well with the expectations.

cs.LG↗

arXiv2020

An Efficient Machine-Learning Approach for PDF Tabulation in Turbulent Combustion Closure

Probability density function (PDF) based turbulent combustion modelling 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.

cs.CE↗

arXiv2020

DiscretizationNet: A Machine-Learning based solver for Navier-Stokes Equations using Finite Volume Discretization

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.

physics.comp-ph↗

arXiv2019

A Framework for Data-Based Turbulent Combustion Closure: A Posteriori Validation

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 composition space using principal component analysis (PCA). The resulting principal components (PCs) act as both conditioning variables and transport 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.

physics.flu-dyn↗

arXiv2019

A Framework for Data-Based Turbulent Combustion Closure: A Priori Validation

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 with 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.

physics.flu-dyn↗