Balaji Srinivasan

We conceptualize Distributed Learning Machines (DLMs) – a novel machine learning approach that integrates existing machine learning algorithms with traditional mesh-based numerical methods for solving forward and inverse problems in nonlinear partial differential equations (PDEs). In conventional numerical methods such as finite element method (FEM), the discretization of the computational domain is a standard technique to reduce the representation load of basis functions. Along the same lines, we propose a distributed neural network architecture that facilitates the simultaneous deployment of several localized neural networks to solve PDEs in a unified manner. The most critical requirement of the DLMs is the synchronization of the distributed neural networks. For this, we introduce a new physics-based interface regularization term to the cost function of the existing learning machines like the Physics Informed Neural Network (PINN) and the Physics Informed Extreme Learning Machine (PIELM). To evaluate the efficacy of this approach, we develop three distinct variants of DLM namely, time-marching Distributed PIELM (DPIELM), Distributed PINN (DPINN) and time-marching DPINN. We show that ideas of linearization and time-marching allow DPIELM to be able to solve nonlinear PDEs to some extent. Next, we show that DPINNs have potential advantages over existing PINNs to solve the inverse problems in heterogeneous media. Finally, we propose a rapid, time-marching version of DPINN which leverages the ideas of transfer learning to accelerate the training. Collectively, this framework leads towards the promise of hybrid Neural Network-FVM or Neural Network-FEM schemes in the future.

This work is focused on the development of a dual-layered diamond-coated tungsten carbide tool for machining titanium Ti-6Al-4V alloy. A hot-filament chemical vapor deposition technique was used to synthesize diamond films on tungsten carbide tools. A boron-doped diamond interlayer was added to a microcrystalline diamond layer in an attempt to improve the interface adhesion strength. The dual-layered diamond-coated tool was employed in machining at cutting speeds in the range of 70 to 150 m min-1 with a lower feed and a lower depth of cut of 0.5 mm rev-1 and 0.5 mm, respectively, to operate in the transition from adhesion- to diffusion-tool-wear and thereby arrive at suitable conditions for enhancing tool life. The proposed tool was then compared, on the basis of performance under real-time cutting conditions, with commercially available microcrystalline diamond, nanocrystalline diamond, titanium nitride and uncoated tungsten carbide tools. The life and surface finish of the proposed dual-layered tool and uncoated tungsten carbide were also investigated in interrupted cutting such as milling. The results of this study show a significant improvement in tool life and finish of Ti-6Al-4V parts machined with the dual-layered diamond-coated tool when compared with its uncoated counterpart. These results pave the way for the use of a low-cost tool, with respect to, polycrystalline diamond for enhancing both tool life and machining productivity in critical sectors fabricating parts out of titanium Ti-6Al-4V alloy. The application of this coating technology can also be extended to the machining of non-ferrous alloys owing to its better adhesion strength.

In this article, we study a novel adaptive mesh strategy for singularly perturbed problems (SPPs) of the parabolic convection-diffusion type that exhibit regular boundary layers. Our central insight is that the introduction of an auxiliary inequality for an entropy-like variable also serves as a remarkably effective adaptation indicator. The primary novelty of this method is that, unlike extant methods used for layer adapted meshes (in which enough mesh points exist in the layer region for well resolved numerical solution), the current method requires no a priori knowledge of the location and width of the boundary layers. Further, the current method, [(which is an extension of the methodology from Kumar and Srinivasan (Appl Math Model 39:2081–2091, 2015)] is completely independent of the perturbation parameter and results in accurate solutions for a wide range of problems. We include some preliminary error estimates and also the results of several numerical experiments including the Black–Scholes equation. The results exhibit the promise of the proposed strategy to generate efficient adaptive meshes for time dependent convection-diffusion problems.

The present study focuses on identifying the parameters from the Weather Research and Forecasting (WRF) model that strongly influence the simulation of tropical cyclones over the Bay of Bengal (BoB) region. Three global sensitivity analysis (SA) methods, namely, the Morris One-at-A-Time (MOAT), multivariate adaptive regression splines (MARS), and surrogate-based Sobol', are employed to identify the most sensitive parameters out of 24 tunable parameters corresponding to seven parameterization schemes of the WRF model. Ten tropical cyclones across different categories, such as cyclonic storms, severe cyclonic storms, and very severe cyclonic storms over BoB between 2011 and 2018, are selected in this study. The sensitivity scores of 24 parameters are evaluated for eight meteorological variables. The parameter sensitivity results are consistent across three SA methods for all the variables, and 8 out of the 24 parameters contribute 80%-90% to the overall sensitivity scores. It is found that the Sobol' method with Gaussian progress regression as a surrogate model can produce reliable sensitivity results when the available samples exceed 200. The parameters with which the model simulations have the least RMSE values when compared with the observations are considered the optimal parameters. Comparing observations and model simulations with the default and optimal parameters shows that simulations with the optimal set of parameters yield a 16.74% improvement in the 10m wind speed, 3.13% in surface air temperature, 0.73% in surface air pressure, and 9.18% in precipitation simulations compared to the default set of parameters.

Histopathology tissue analysis is considered the gold standard in cancer diagnosis and prognosis. Whole-slide imaging (WSI), i.e., the scanning and digitization of entire histology slides, are now being adopted across the world in pathology labs. Trained histopathologists can provide an accurate diagnosis of biopsy specimens based on WSI data. Given the dimensionality of WSIs and the increase in the number of potential cancer cases, analyzing these images is a time-consuming process. Automated segmentation of tumorous tissue helps in elevating the precision, speed, and reproducibility of research. In the recent past, deep learning-based techniques have provided state-of-the-art results in a wide variety of image analysis tasks, including the analysis of digitized slides. However, deep learning-based solutions pose many technical challenges, including the large size of WSI data, heterogeneity in images, and complexity of features. In this study, we propose a generalized deep learning-based framework for histopathology tissue analysis to address these challenges. Our framework is, in essence, a sequence of individual techniques in the preprocessing-training-inference pipeline which, in conjunction, improve the efficiency and the generalizability of the analysis. The combination of techniques we have introduced includes an ensemble segmentation model, division of the WSI into smaller overlapping patches while addressing class imbalances, efficient techniques for inference, and an efficient, patch-based uncertainty estimation framework. Our ensemble consists of DenseNet-121, Inception-ResNet-V2, and DeeplabV3Plus, where all the networks were trained end to end for every task. We demonstrate the efficacy and improved generalizability of our framework by evaluating it on a variety of histopathology tasks including breast cancer metastases (CAMELYON), colon cancer (DigestPath), and liver cancer (PAIP). Our proposed framework has state-of-the-art performance across all these tasks and is ranked within the top 5 currently for the challenges based on these datasets. The entire framework along with the trained models and the related documentation are made freely available at GitHub and PyPi. Our framework is expected to aid histopathologists in accurate and efficient initial diagnosis. Moreover, the estimated uncertainty maps will help clinicians to make informed decisions and further treatment planning or analysis.

Over the last several decades, the Finite Element Method (FEM) has emerged as a numerical approach method of choice for the solution of problems in solid mechanics. Part of the reason for the success of FEM is that it provides a unified framework for discretizing even complex differential equations. However, despite this overall unification, FEM still requires specific variants or corrections depending on the problem at hand. For instance, problems with skewed meshes, discontinuity, singularity, incompressible media, etc. require the analyst to modify the discretization approach in order to preserve robustness. We speculate that local-polynomial bases such as those used in FEM do not sufficiently represent local physics and more "physics-informed"approaches may be more universal. Accordingly, in this paper, we evaluate the feasibility of one such approach - the recently developed Distributed Physics Informed Neural Network (DPINN) approach - to provide a truly unified framework for addressing problems in Solid Mechanics. The DPINN approach utilizes a piecewise-neural network representation for the underlying field, rather than the piece-polynomial representation that is common in FEM. We solve a series of problems in solid mechanics using either the single or domain-distributed version of DPINN and demonstrate that the approach is able to seamlessly solve varied problems with no special treatment required for volumetric locking or capturing discontinuities. Further, we also demonstrate that the DPINN approach, due to its meshless nature, is able to avoid the curse of dimensionality. We discuss the relative merits and demerits of the DPINN approach in comparison to FEM. We expect this work to be useful to researchers looking to develop unified computational frameworks for problems in solid mechanics.

The black-box nature of deep learning models prevents them from being completely trusted in domains like biomedicine. Most explainability techniques do not capture the concept-based reasoning that human beings follow. In this work, we attempt to understand the behavior of trained models that perform image processing tasks in the medical domain by building a graphical representation of the concepts they learn. Extracting such a graphical representation of the model’s behavior on an abstract, higher conceptual level would help us to unravel the steps taken by the model for predictions. We show the application of our proposed implementation on two biomedical problems - brain tumor segmentation and fundus image classification. We provide an alternative graphical representation of the model by formulating a concept level graph as discussed above, and find active inference trails in the model. We work with radiologists and ophthalmologists to understand the obtained inference trails from a medical perspective and show that medically relevant concept trails are obtained which highlight the hierarchy of the decision-making process followed by the model. Our framework is available at https://github.com/koriavinash1/BioExp.

There has been rapid progress recently on the application of deep networks to the solution of partial differential equations, collectively labeled as Physics Informed Neural Networks (PINNs). In this paper, We develop Physics Informed Extreme Learning Machine (PIELM), a rapid version of PINNs which can be applied to stationary and time-dependent linear partial differential equations. We demonstrate that PIELM matches or exceeds the accuracy of PINNs on a range of problems. We also discuss the limitations of neural network-based approaches, including our PIELM, in the solution of PDEs on large domains and suggest an extension, a distributed version of our algorithm – DPIELM. We show that DPIELM produces excellent results comparable to conventional numerical techniques in the solution of time-dependent problems. Collectively, this work contributes towards making the use of neural networks in the solution of partial differential equations in complex domains as a competitive alternative to conventional discretization techniques.

Heat Transfer Engineering: Fundamentals and Techniques reviews the core mechanisms of heat transfer and provides modern methods to solve practical problems encountered by working practitioners, with a particular focus on developing engagement and motivation. The book reviews fundamental concepts in conduction, forced convection, free convection, boiling, condensation, heat exchangers and mass transfer succinctly and without unnecessary exposition. Throughout, copious examples drawn from current industrial practice are examined with an emphasis on problem-solving for interest and insight rather than the procedural approaches often adopted in courses. The book contains numerous important solved and unsolved problems, utilizing modern tools and computational sources wherever relevant. A subsection on common issues and recent advances is presented in each chapter, encouraging the reader to explore a greater diversity of problems.

Recently, physics informed neural networks (PINNs) have produced excellent results in solving a series of linear and nonlinear partial differential equations (PDEs) without using any prior data. However, due to slow training speed, PINNs are not directly competitive with existing numerical methods. To overcome this issue, the authors developed Physics Informed Extreme Learning Machine (PIELM), a rapid version of PINN, and tested it on a range of linear PDEs of first and second order. In this paper, we evaluate the effectiveness of PIELM on higher-order PDEs with practical engineering applications. Specifically, we demonstrate the efficacy of PIELM to the biharmonic equation. Biharmonic equations have numerous applications in solid and fluid mechanics, but they are hard to solve due to the presence of fourth-order derivative terms, especially in complicated geometries. Our numerical experiments show that PIELM is much faster than the original PINN on both regular and irregular domains. On irregular domains, it also offers an excellent alternative to traditional methods due to its meshless nature.