arXiv subjects

Baskar Ganapathysubramanian

Publications and source records attributed to Baskar Ganapathysubramanian.

At least 91 records · Page 5Linked to original sources

arXiv2021

Feature engineering for microstructure-property mapping in organic photovoltaics

Linking the highly complex morphology of organic photovoltaic (OPV) thin films to their charge transport properties is critical for achieving high performance material system that serves as a cost-efficient approach for energy harvesting. In this paper, a novel unsupervised feature engineering framework is developed and used to establish reduced-order structure-property linkages for OPV films. This framework takes advantage of digital image processing algorithms to identify the salient material features of OPVs undergoing the charge transport phenomenon. These material states are then used to obtain a low-dimensional representation of OPV microstructures via 2-point spatial correlations and principal component analysis. It is found that in addition to the material PC scores, two distance-based metrics are required to complete the microstructure quantification of complex OPVs. A localized version of the Gaussian process (laGP) is then used to link the material PC scores as well as the two distance-based metrics to the short-circuit current of OPVs. It is demonstrated that the unsupervised feature engineering framework presented in this paper in conjunction with the laGP can lead to high-fidelity and accurate data-driven structure-property linkages for OPV films.

cond-mat.mtrl-sci↗

arXiv2021

NeuFENet: Neural Finite Element Solutions with Theoretical Bounds for Parametric PDEs

We consider a mesh-based approach for training a neural network to produce field predictions of solutions to parametric partial differential equations (PDEs). This approach contrasts current approaches for "neural PDE solvers" that employ collocation-based methods to make point-wise predictions of solutions to PDEs. This approach has the advantage of naturally enforcing different boundary conditions as well as ease of invoking well-developed PDE theory -- including analysis of numerical stability and convergence -- to obtain capacity bounds for our proposed neural networks in discretized domains. We explore our mesh-based strategy, called NeuFENet, using a weighted Galerkin loss function based on the Finite Element Method (FEM) on a parametric elliptic PDE. The weighted Galerkin loss (FEM loss) is similar to an energy functional that produces improved solutions, satisfies a priori mesh convergence, and can model Dirichlet and Neumann boundary conditions. We prove theoretically, and illustrate with experiments, convergence results analogous to mesh convergence analysis deployed in finite element solutions to PDEs. These results suggest that a mesh-based neural network approach serves as a promising approach for solving parametric PDEs with theoretical bounds.

cs.LG↗

arXiv2021

Differentiable Spline Approximations

The paradigm of differentiable programming has significantly enhanced the scope of machine learning via the judicious use of gradient-based optimization. However, standard differentiable programming methods (such as autodiff) typically require that the machine learning models be differentiable, limiting their applicability. Our goal in this paper is to use a new, principled approach to extend gradient-based optimization to functions well modeled by splines, which encompass a large family of piecewise polynomial models. We derive the form of the (weak) Jacobian of such functions and show that it exhibits a block-sparse structure that can be computed implicitly and efficiently. Overall, we show that leveraging this redesigned Jacobian in the form of a differentiable "layer" in predictive models leads to improved performance in diverse applications such as image segmentation, 3D point cloud reconstruction, and finite element analysis.

cs.LG↗

arXiv2021

Modeling electrochemical systems with weakly imposed Dirichlet boundary conditions

Finite element modeling of charged species transport has enabled analysis, design, and optimization of a diverse array of electrochemical and electrokinetic devices. These systems are represented by the Poisson-Nernst-Planck equations coupled with the Navier-Stokes equation, with a key quantity of interest being the current at the system boundaries. Accurately computing the current flux is challenging due to the small critical dimension of the boundary layers (small Debye layer) that require fine mesh resolution at the boundaries. We resolve this challenge by using the Dirichlet-to-Neumanntransformation to weakly impose the Dirichlet conditions for the Poisson-Nernst-Planck equations. The results obtained with weakly imposed Dirichlet boundary conditions showed excellent agreement with those obtained when conventional boundary conditions with highly resolved mesh we reemployed. Furthermore, the calculated current flux showed faster mesh convergence using weakly imposed conditions compared to the conventionally imposed Dirichlet boundary conditions. We illustrate the approach on canonical 3D problems that otherwise would have been computationally intractable to solve accurately. This approach substantially reduces the computational cost of model-ing electrochemical systems.

cs.CE↗

arXiv2021

Scalable adaptive PDE solvers in arbitrary domains

Efficiently and accurately simulating partial differential equations (PDEs) in and around arbitrarily defined geometries, especially with high levels of adaptivity, has significant implications for different application domains. A key bottleneck in the above process is the fast construction of a `good' adaptively-refined mesh. In this work, we present an efficient novel octree-based adaptive discretization approach capable of carving out arbitrarily shaped void regions from the parent domain: an essential requirement for fluid simulations around complex objects. Carving out objects produces an $\textit{incomplete}$ octree. We develop efficient top-down and bottom-up traversal methods to perform finite element computations on $\textit{incomplete}$ octrees. We validate the framework by (a) showing appropriate convergence analysis and (b) computing the drag coefficient for flow past a sphere for a wide range of Reynolds numbers ($\mathcal{O}(1-10^6)$) encompassing the drag crisis regime. Finally, we deploy the framework on a realistic geometry on a current project to evaluate COVID-19 transmission risk in classrooms.

math.NA↗

arXiv2021

Distributed Multigrid Neural Solvers on Megavoxel Domains

We consider the distributed training of large-scale neural networks that serve as PDE solvers producing full field outputs. We specifically consider neural solvers for the generalized 3D Poisson equation over megavoxel domains. A scalable framework is presented that integrates two distinct advances. First, we accelerate training a large model via a method analogous to the multigrid technique used in numerical linear algebra. Here, the network is trained using a hierarchy of increasing resolution inputs in sequence, analogous to the 'V', 'W', 'F', and 'Half-V' cycles used in multigrid approaches. In conjunction with the multi-grid approach, we implement a distributed deep learning framework which significantly reduces the time to solve. We show the scalability of this approach on both GPU (Azure VMs on Cloud) and CPU clusters (PSC Bridges2). This approach is deployed to train a generalized 3D Poisson solver that scales well to predict output full-field solutions up to the resolution of 512x512x512 for a high dimensional family of inputs.

cs.LG↗

arXiv2021

Industrial scale large eddy simulations (LES) with adaptive octree meshes using immersogeometric analysis

We present a variant of the immersed boundary method integrated with octree meshes for highly efficient and accurate Large-Eddy Simulations (LES) of flows around complex geometries. We demonstrate the scalability of the proposed method up to $\mathcal{O}(32K)$ processors. This is achieved by (a) rapid in-out tests; (b) adaptive quadrature for an accurate evaluation of forces; (c) tensorized evaluation during matrix assembly. We showcase this method on two non-trivial applications: accurately computing the drag coefficient of a sphere across Reynolds numbers $1-10^6$ encompassing the drag crisis regime; simulating flow features across a semi-truck for investigating the effect of platooning on efficiency.

math.NA↗

arXiv2020

Deep Multi-view Image Fusion for Soybean Yield Estimation in Breeding Applications Deep Multi-view Image Fusion for Soybean Yield Estimation in Breeding Applications

Reliable seed yield estimation is an indispensable step in plant breeding programs geared towards cultivar development in major row crops. The objective of this study is to develop a machine learning (ML) approach adept at soybean [\textit{Glycine max} L. (Merr.)] pod counting to enable genotype seed yield rank prediction from in-field video data collected by a ground robot. To meet this goal, we developed a multi-view image-based yield estimation framework utilizing deep learning architectures. Plant images captured from different angles were fused to estimate the yield and subsequently to rank soybean genotypes for application in breeding decisions. We used data from controlled imaging environment in field, as well as from plant breeding test plots in field to demonstrate the efficacy of our framework via comparing performance with manual pod counting and yield estimation. Our results demonstrate the promise of ML models in making breeding decisions with significant reduction of time and human effort, and opening new breeding methods avenues to develop cultivars.

cs.CV↗

arXiv2020

Deep Generative Models that Solve PDEs: Distributed Computing for Training Large Data-Free Models

Recent progress in scientific machine learning (SciML) has opened up the possibility of training novel neural network architectures that solve complex partial differential equations (PDEs). Several (nearly data free) approaches have been recently reported that successfully solve PDEs, with examples including deep feed forward networks, generative networks, and deep encoder-decoder networks. However, practical adoption of these approaches is limited by the difficulty in training these models, especially to make predictions at large output resolutions ($\geq 1024 \times 1024$). Here we report on a software framework for data parallel distributed deep learning that resolves the twin challenges of training these large SciML models - training in reasonable time as well as distributing the storage requirements. Our framework provides several out of the box functionality including (a) loss integrity independent of number of processes, (b) synchronized batch normalization, and (c) distributed higher-order optimization methods. We show excellent scalability of this framework on both cloud as well as HPC clusters, and report on the interplay between bandwidth, network topology and bare metal vs cloud. We deploy this approach to train generative models of sizes hitherto not possible, showing that neural PDE solvers can be viably trained for practical applications. We also demonstrate that distributed higher-order optimization methods are $2-3\times$ faster than stochastic gradient-based methods and provide minimal convergence drift with higher batch-size.

cs.LG↗

arXiv2020

How useful is Active Learning for Image-based Plant Phenotyping?

Deep learning models have been successfully deployed for a diverse array of image-based plant phenotyping applications including disease detection and classification. However, successful deployment of supervised deep learning models requires large amount of labeled data, which is a significant challenge in plant science (and most biological) domains due to the inherent complexity. Specifically, data annotation is costly, laborious, time consuming and needs domain expertise for phenotyping tasks, especially for diseases. To overcome this challenge, active learning algorithms have been proposed that reduce the amount of labeling needed by deep learning models to achieve good predictive performance. Active learning methods adaptively select samples to annotate using an acquisition function to achieve maximum (classification) performance under a fixed labeling budget. We report the performance of four different active learning methods, (1) Deep Bayesian Active Learning (DBAL), (2) Entropy, (3) Least Confidence, and (4) Coreset, with conventional random sampling-based annotation for two different image-based classification datasets. The first image dataset consists of soybean [Glycine max L. (Merr.)] leaves belonging to eight different soybean stresses and a healthy class, and the second consists of nine different weed species from the field. For a fixed labeling budget, we observed that the classification performance of deep learning models with active learning-based acquisition strategies is better than random sampling-based acquisition for both datasets. The integration of active learning strategies for data annotation can help mitigate labelling challenges in the plant sciences applications particularly where deep domain knowledge is required.

cs.CV↗

arXiv2020

Usefulness of interpretability methods to explain deep learning based plant stress phenotyping

Deep learning techniques have been successfully deployed for automating plant stress identification and quantification. In recent years, there is a growing push towards training models that are interpretable -i.e. that justify their classification decisions by visually highlighting image features that were crucial for classification decisions. The expectation is that trained network models utilize image features that mimic visual cues used by plant pathologists. In this work, we compare some of the most popular interpretability methods: Saliency Maps, SmoothGrad, Guided Backpropogation, Deep Taylor Decomposition, Integrated Gradients, Layer-wise Relevance Propagation and Gradient times Input, for interpreting the deep learning model. We train a DenseNet-121 network for the classification of eight different soybean stresses (biotic and abiotic). Using a dataset consisting of 16,573 RGB images of healthy and stressed soybean leaflets captured under controlled conditions, we obtained an overall classification accuracy of 95.05 \%. For a diverse subset of the test data, we compared the important features with those identified by a human expert. We observed that most interpretability methods identify the infected regions of the leaf as important features for some -- but not all -- of the correctly classified images. For some images, the output of the interpretability methods indicated that spurious feature correlations may have been used to correctly classify them. Although the output explanation maps of these interpretability methods may be different from each other for a given image, we advocate the use of these interpretability methods as `hypothesis generation' mechanisms that can drive scientific insight.

cs.CV↗

arXiv2020

Crop Yield Prediction Integrating Genotype and Weather Variables Using Deep Learning

Accurate prediction of crop yield supported by scientific and domain-relevant insights, can help improve agricultural breeding, provide monitoring across diverse climatic conditions and thereby protect against climatic challenges to crop production including erratic rainfall and temperature variations. We used historical performance records from Uniform Soybean Tests (UST) in North America spanning 13 years of data to build a Long Short Term Memory - Recurrent Neural Network based model to dissect and predict genotype response in multiple-environments by leveraging pedigree relatedness measures along with weekly weather parameters. Additionally, for providing explainability of the important time-windows in the growing season, we developed a model based on temporal attention mechanism. The combination of these two models outperformed random forest (RF), LASSO regression and the data-driven USDA model for yield prediction. We deployed this deep learning framework as a 'hypotheses generation tool' to unravel GxExM relationships. Attention-based time series models provide a significant advancement in interpretability of yield prediction models. The insights provided by explainable models are applicable in understanding how plant breeding programs can adapt their approaches for global climate change, for example identification of superior varieties for commercial release, intelligent sampling of testing environments in variety development, and integrating weather parameters for a targeted breeding approach. Using DL models as hypothesis generation tools will enable development of varieties with plasticity response in variable climatic conditions. We envision broad applicability of this approach (via conducting sensitivity analysis and "what-if" scenarios) for soybean and other crop species under different climatic conditions.

cs.LG↗

arXiv2020

Simulating two-phase flows with thermodynamically consistent energy stable Cahn-Hilliard Navier-Stokes equations on parallel adaptive octree based meshes

We report on simulations of two-phase flows with deforming interfaces at various density contrasts by solving thermodynamically consistent Cahn-Hilliard Navier-Stokes equations. An (essentially) unconditionally energy-stable Crank-Nicolson-type time integration scheme is used. Detailed proofs of energy stability of the semi-discrete scheme and for the existence of solutions of the advective-diffusive Cahn-Hilliard operator are provided. In space we discretize with a conforming continuous Galerkin finite element method in conjunction with a residual-based variational multi-scale (VMS) approach in order to provide pressure stabilization. We deploy this approach on a massively parallel numerical implementation using fast octree-based adaptive meshes. A detailed scaling analysis of the solver is presented. Numerical experiments showing convergence and validation with experimental results from the literature are presented for a large range of density ratios.

math.NA↗

arXiv2019

Equilibrium microstructures of diblock copolymers under 3D confinement

We investigate equilibrium microstructures exhibited by diblock copolymers in confined 3D geometries. We perform Self-Consistent Field Theory (SCFT) simulations using a finite-element based computational framework (Ackerman et al. 2017), that provides the flexibility to compute equilibrium structures under arbitrary geometries. We consider a sequence of 3D geometries (tetrahedron to sphere) that have the same volume but exhibit varying curvature. This allows us to study the interplay between edge and curvature effects of the 3D geometries on the equilibrium microstructures. We observe that beyond a length scale, the equilibrium structure changes from an interconnected network to a multi-layered concentric shell as the curvature of the 3D geometry is reduced. However, below this length scale the equilibrium structure remains a multi-layered concentric shell independent of curvature. We additionally explore variations in the equilibrium microstructures at a few discrete volume fractions. This study provides insight into possible frustrated phases that can arise in AB diblock systems while varying the shape of confinement geometry.

cond-mat.soft↗

arXiv2019

Encoding Invariances in Deep Generative Models

Reliable training of generative adversarial networks (GANs) typically require massive datasets in order to model complicated distributions. However, in several applications, training samples obey invariances that are \textit{a priori} known; for example, in complex physics simulations, the training data obey universal laws encoded as well-defined mathematical equations. In this paper, we propose a new generative modeling approach, InvNet, that can efficiently model data spaces with known invariances. We devise an adversarial training algorithm to encode them into data distribution. We validate our framework in three experimental settings: generating images with fixed motifs; solving nonlinear partial differential equations (PDEs); and reconstructing two-phase microstructures with desired statistical properties. We complement our experiments with several theoretical results.

cs.LG↗

arXiv2019

Shape-design for stabilizing micro-particles in inertial microfluidic flows

Design of microparticles which stabilize at the centerline of a channel flow when part of a dilute suspension is examined numerically for moderate Reynolds numbers ($10 \le Re \le 80$). Stability metrics for particles with arbitrary shapes are formulated based on linear-stability theory. Particle shape is parametrized by a compact, Non-Uniform Rational B-Spline (NURBS)-based representation. Shape-design is posed as an optimization problem and solved using adaptive Bayesian optimization. We focus on designing particles for maximal stability at the channel-centerline robust to perturbations. Our results indicate that centerline-focusing particles are families of characteristic "fish"/"bottle"/"dumbbell"-like shapes, exhibiting fore-aft asymmetry. A parametric exploration is then performed to identify stable particle-designs at different k's (particle chord-to-channel width ratio) and Re's ($0.1 \le k \le 0.4, 10 \le Re \le 80$). Particles at high-k's and Re's are highly stabilized when compared to those at low-k's and Re's. A comparison of the modified dumbbell designs from the current framework also shows better performance to perturbations in Fluid-Structure Interaction (FSI) when compared to the rod-disk model reported previously (Uspal & Doyle 2014) for low-Re Hele-Shaw flow. We identify basins of attraction around the centerline, which span larger release-angle-ranges and lateral locations (tending to the channel width) for narrower channels, which effectively standardizes the notion of global focusing in such configurations using the current stability-paradigm. The present framework is illustrated for 2D cases and is potentially generalizable to stability in 3D flow-fields. The current formulation is also agnostic to Re and particle/channel geometry which indicates substantial potential for integration with imaging flow-cytometry tools and microfluidic biosensing-assays.

physics.flu-dyn↗

arXiv2019

High throughput, automated prediction of focusing patterns for inertial microfluidics

Visual inspections for identifying focusing points in inertial microfluidic flows are prone to misinterpreting stable locations and focusing shifts in the case of non-trivial focusing patterns. We develop and deploy an approach for automating the calculation of focusing patterns for a general channel geometry, and thereby reduce the dependence on empirical/visual procedures to confirm the presence of stable locations. We utilize concepts from interpolation theory (to represent continuous force-fields using discrete points), and stability theory to identify "basins of attraction" and quantitatively identify stable equilibrium points. Our computational experiments reveal that predicting equilibrium points accurately requires upto $\times$10-20 times more refined force-maps that conventionally used, which highlights the spatial resolution required for an accurate representation of cross-sectional forces. These focusing patterns are validated using experimental results for a rectangular channel, and triangular channel with an apex angle of $90^\circ$. We then apply the approach to predict and explain focusing patterns and shifts for a $90^\circ$-isosceles triangular channel across a range of Reynolds numbers for $\frac{a}{H} = 0.4$ (particle-to-channel size ratio). We observe that the predicted focusing patterns match experiments well. The force-maps also reveal certain "clouds" of localized stable points, which aid in explaining the onset of bifurcation observed in experiments. The current algorithm is agnostic to channel cross-sections and straight/curved channels, which could pave way to generating a library of focusing patterns as a function of channel geometry, and $Re$, to assist in design of novel devices for tailored particle-streams.

physics.flu-dyn↗

arXiv2018

A Transfer Operator Methodology for Optimal Sensor Placement Accounting for Uncertainty

Sensors in buildings are used for a wide variety of applications such as monitoring air quality, contaminants, indoor temperature, and relative humidity. These are used for accessing and ensuring indoor air quality, and also for ensuring safety in the event of chemical and biological attacks. It follows that optimal placement of sensors become important to accurately monitor contaminant levels in the indoor environment. However, contaminant transport inside the indoor environment is governed by the indoor flow conditions which are affected by various uncertainties associated with the building systems including occupancy and boundary fluxes. Therefore, it is important to account for all associated uncertainties while designing the sensor layout. The transfer operator based framework provides an effective way to identify optimal placement of sensors. Previous work has been limited to sensor placements under deterministic scenarios. In this work we extend the transfer operator based approach for optimal sensor placement while accounting for building systems uncertainties. The methodology provides a probabilistic metric to gauge coverage under uncertain conditions. We illustrate the capabilities of the framework with examples exhibiting boundary flux uncertainty.

eess.SY↗