arXiv subjects

Devesh Upadhyay

Publications and source records attributed to Devesh Upadhyay.

24 records · Page 2Linked to original sources

arXiv2022

Towards Accurate and Robust Classification in Continuously Transitioning Industrial Sprays with Mixup

Image classification with deep neural networks has seen a surge of technological breakthroughs with promising applications in areas such as face recognition, medical imaging, and autonomous driving. In engineering problems, however, such as high-speed imaging of engine fuel injector sprays or body paint sprays, deep neural networks face a fundamental challenge related to the availability of adequate and diverse data. Typically, only thousands or sometimes even hundreds of samples are available for training. In addition, the transition between different spray classes is a continuum and requires a high level of domain expertise to label the images accurately. In this work, we used Mixup as an approach to systematically deal with the data scarcity and ambiguous class boundaries found in industrial spray applications. We show that data augmentation can mitigate the over-fitting problem of large neural networks on small data sets, to a certain level, but cannot fundamentally resolve the issue. We discuss how a convex linear interpolation of different classes naturally aligns with the continuous transition between different classes in our application. Our experiments demonstrate Mixup as a simple yet effective method to train an accurate and robust deep neural network classifier with only a few hundred samples.

cs.CV↗

arXiv2022

Virtual Rings on Highways: Traffic Control by Connected Automated Vehicles

This work gives introduction to traffic control by connected automated vehicles. The influence of vehicle control on vehicular traffic and traffic control strategies are discussed and compared. It is highlighted that vehicle-to-everything connectivity allows connected automated vehicles to access the state of the traffic behind them such that feedback can be utilized to mitigate evolving congestions. Numerical simulations demonstrate that such connectivity-based traffic control is beneficial for smoothness and energy efficiency of highway traffic. The dynamics and stability of traffic flow, under the proposed controllers, are analyzed in detail to construct stability charts that guide the selection of stabilizing control gains.

eess.SY↗

arXiv2022

BTranspose: Bottleneck Transformers for Human Pose Estimation with Self-Supervised Pre-Training

The task of 2D human pose estimation is challenging as the number of keypoints is typically large (~ 17) and this necessitates the use of robust neural network architectures and training pipelines that can capture the relevant features from the input image. These features are then aggregated to make accurate heatmap predictions from which the final keypoints of human body parts can be inferred. Many papers in literature use CNN-based architectures for the backbone, and/or combine it with a transformer, after which the features are aggregated to make the final keypoint predictions [1]. In this paper, we consider the recently proposed Bottleneck Transformers [2], which combine CNN and multi-head self attention (MHSA) layers effectively, and we integrate it with a Transformer encoder and apply it to the task of 2D human pose estimation. We consider different backbone architectures and pre-train them using the DINO self-supervised learning method [3], this pre-training is found to improve the overall prediction accuracy. We call our model BTranspose, and experiments show that on the COCO validation set, our model achieves an AP of 76.4, which is competitive with other methods such as [1] and has fewer network parameters. Furthermore, we also present the dependencies of the final predicted keypoints on both the MHSA block and the Transformer encoder layers, providing clues on the image sub-regions the network attends to at the mid and high levels.

cs.LG↗

arXiv2021

Stochastic Adversarial Koopman Model for Dynamical Systems

Dynamical systems are ubiquitous and are often modeled using a non-linear system of governing equations. Numerical solution procedures for many dynamical systems have existed for several decades, but can be slow due to high-dimensional state space of the dynamical system. Thus, deep learning-based reduced order models (ROMs) are of interest and one such family of algorithms along these lines are based on the Koopman theory. This paper extends a recently developed adversarial Koopman model (Balakrishnan \& Upadhyay, arXiv:2006.05547) to stochastic space, where the Koopman operator applies on the probability distribution of the latent encoding of an encoder. Specifically, the latent encoding of the system is modeled as a Gaussian, and is advanced in time by using an auxiliary neural network that outputs two Koopman matrices $K_μ$ and $K_σ$. Adversarial and gradient losses are used and this is found to lower the prediction errors. A reduced Koopman formulation is also undertaken where the Koopman matrices are assumed to have a tridiagonal structure, and this yields predictions comparable to the baseline model with full Koopman matrices. The efficacy of the stochastic Koopman model is demonstrated on different test problems in chaos, fluid dynamics, combustion, and reaction-diffusion models. The proposed model is also applied in a setting where the Koopman matrices are conditioned on other input parameters for generalization and this is applied to simulate the state of a Lithium-ion battery in time. The Koopman models discussed in this study are very promising for the wide range of problems considered.

cs.LG↗

arXiv2021

NeuralPDE: Automating Physics-Informed Neural Networks (PINNs) with Error Approximations

Physics-informed neural networks (PINNs) are an increasingly powerful way to solve partial differential equations, generate digital twins, and create neural surrogates of physical models. In this manuscript we detail the inner workings of NeuralPDE.jl and show how a formulation structured around numerical quadrature gives rise to new loss functions which allow for adaptivity towards bounded error tolerances. We describe the various ways one can use the tool, detailing mathematical techniques like using extended loss functions for parameter estimation and operator discovery, to help potential users adopt these PINN-based techniques into their workflow. We showcase how NeuralPDE uses a purely symbolic formulation so that all of the underlying training code is generated from an abstract formulation, and show how to make use of GPUs and solve systems of PDEs. Afterwards we give a detailed performance analysis which showcases the trade-off between training techniques on a large set of PDEs. We end by focusing on a complex multiphysics example, the Doyle-Fuller-Newman (DFN) Model, and showcase how this PDE can be formulated and solved with NeuralPDE. Together this manuscript is meant to be a detailed and approachable technical report to help potential users of the technique quickly get a sense of the real-world performance trade-offs and use cases of the PINN techniques.

cs.MS↗

arXiv2020

Deep Adversarial Koopman Model for Reaction-Diffusion systems

Reaction-diffusion systems are ubiquitous in nature and in engineering applications, and are often modeled using a non-linear system of governing equations. While robust numerical methods exist to solve them, deep learning-based reduced ordermodels (ROMs) are gaining traction as they use linearized dynamical models to advance the solution in time. One such family of algorithms is based on Koopman theory, and this paper applies this numerical simulation strategy to reaction-diffusion systems. Adversarial and gradient losses are introduced, and are found to robustify the predictions. The proposed model is extended to handle missing training data as well as recasting the problem from a control perspective. The efficacy of these developments are demonstrated for two different reaction-diffusion problems: (1) the Kuramoto-Sivashinsky equation of chaos and (2) the Turing instability using the Gray-Scott model.

cs.CE↗