arXiv subjects

Sharmila Karumuri

Publications and source records attributed to Sharmila Karumuri.

6 recordsLinked to original sources

arXiv2025

Active Learning Discovery of High Temperature Oxidation Resistant Refractory Complex Concentrated Alloys

Refractory complex concentrated alloys (RCCAs) are of significant interest for advanced high-temperature applications, owing to their broad compositional range and potential for attractive mechanical properties and oxidation resistance. However, their compositional complexity poses significant challenges to conventional alloy discovery methodologies. In this study, an active learning framework is introduced that integrates Gaussian process regression with Bayesian global optimization to accelerate identification of oxidation-resistant RCCAs. Focusing on aluminum-containing quaternary systems, alloy and oxide descriptors were used to predict oxidation performance at 1000$^\circ$C. Beginning with a dataset of 81 experimentally validated RCCAs, this framework was used to iteratively select alloy batches (five alloys per batch) with optimization based on a balance between exploration and exploitation to minimize associated experimental costs. After six iterations, two alloys were identified (nominal Al$_{30}$Mo$_5$Ti$_{15}$Cr$_{50}$ and Al$_{40}$Mo$_5$Ti$_{30}$Cr$_{25}$) that exhibited specific mass gains less than 1 mg/cm$^2$ at 1000$^\circ$C in air. Both of these alloys formed adherent external $α$-Al$_2$O$_3$ scales and exhibited parabolic oxidation kinetics consistent with diffusion-limited scale growth. Furthermore, our multiobjective analysis demonstrates that these alloys simultaneously achieve high specific hardness ($>0.12$ HV$_{0.5}$m$^3$/kg) and thermal expansion compatibility with thermal barrier coating systems, positioning them as promising bond coat candidates. This work underscores the efficacy of active learning in traversing complex compositional landscapes, and offers a scalable strategy for the development of advanced materials suitable for extreme environments.

cond-mat.mtrl-sci↗

arXiv2025

Physics-Informed Latent Neural Operator for Real-time Predictions of time-dependent parametric PDEs

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied to systems with high-dimensional input-output mappings arising from large numbers of spatial and temporal collocation points, these models often require heavily overparameterized networks, leading to long training times. Latent DeepONet addresses some of these challenges by introducing a two-step approach: first learning a reduced latent space using a separate model, followed by operator learning within this latent space. While efficient, this method is inherently data-driven and lacks mechanisms for incorporating physical laws, limiting its robustness and generalizability in data-scarce settings. In this work, we propose PI-Latent-NO, a physics-informed latent neural operator framework that integrates governing physics directly into the learning process. Our architecture features two coupled DeepONets trained end-to-end: a Latent-DeepONet that learns a low-dimensional representation of the solution, and a Reconstruction-DeepONet that maps this latent representation back to the physical space. By embedding PDE constraints into the training via automatic differentiation, our method eliminates the need for labeled training data and ensures physics-consistent predictions. The proposed framework is both memory and compute-efficient, exhibiting near-constant scaling with problem size and demonstrating significant speedups over traditional physics-informed operator models. We validate our approach on a range of parametric PDEs, showcasing its accuracy, scalability, and suitability for real-time prediction in complex physical systems.

cs.LG↗

arXiv2025

Efficient Training of Deep Neural Operator Networks via Randomized Sampling

Neural operators (NOs) employ deep neural networks to learn mappings between infinite-dimensional function spaces. Deep operator network (DeepONet), a popular NO architecture, has demonstrated success in the real-time prediction of complex dynamics across various scientific and engineering applications. In this work, we introduce a random sampling technique to be adopted during the training of DeepONet, aimed at improving the generalization ability of the model, while significantly reducing the computational time. The proposed approach targets the trunk network of the DeepONet model that outputs the basis functions corresponding to the spatiotemporal locations of the bounded domain on which the physical system is defined. While constructing the loss function, DeepONet training traditionally considers a uniform grid of spatiotemporal points at which all the output functions are evaluated for each iteration. This approach leads to a larger batch size, resulting in poor generalization and increased memory demands, due to the limitations of the stochastic gradient descent (SGD) optimizer. The proposed random sampling over the inputs of the trunk net mitigates these challenges, improving generalization and reducing memory requirements during training, resulting in significant computational gains. We validate our hypothesis through three benchmark examples, demonstrating substantial reductions in training time while achieving comparable or lower overall test errors relative to the traditional training approach. Our results indicate that incorporating randomization in the trunk network inputs during training enhances the efficiency and robustness of DeepONet, offering a promising avenue for improving the framework's performance in modeling complex physical systems.

cs.LG↗

arXiv2024

Learning to solve Bayesian inverse problems: An amortized variational inference approach using Gaussian and Flow guides

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies epistemic uncertainty. Since analytical posteriors are not typically available, one resorts to Markov chain Monte Carlo sampling or approximate variational inference. However, inference needs to be rerun from scratch for each new set of data. This drawback limits the applicability of the Bayesian formulation to real-time settings, e.g., health monitoring of engineered systems, and medical diagnosis. The objective of this paper is to develop a methodology that enables real-time inference by learning the Bayesian inverse map, i.e., the map from data to posteriors. Our approach is as follows. We parameterize the posterior distribution as a function of data. This work outlines two distinct approaches to do this. The first method involves parameterizing the posterior using an amortized full-rank Gaussian guide, implemented through neural networks. The second method utilizes a Conditional Normalizing Flow guide, employing conditional invertible neural networks for cases where the target posterior is arbitrarily complex. In both approaches, we learn the network parameters by amortized variational inference which involves maximizing the expectation of evidence lower bound over all possible datasets compatible with the model. We demonstrate our approach by solving a set of benchmark problems from science and engineering. Our results show that the posterior estimates of our approach are in agreement with the corresponding ground truth obtained by Markov chain Monte Carlo. Once trained, our approach provides the posterior distribution for a given observation just at the cost of a forward pass of the neural network.

stat.ML↗

arXiv2023

Mass uptake during oxidation of metallic alloys: literature data collection, analysis, and FAIR sharing

The area-normalized change of mass ($Δ$m/A) with time during the oxidation of metallic alloys is commonly used to assess oxidation resistance. Analyses of such data can also aid in evaluating underlying oxidation mechanisms. We performed an exhaustive literature search and digitized normalized mass change vs. time data for 407 alloys. To maximize the impact of these and future mass uptake data, we developed and published an open, online, computational workflow that fits the data to various models of oxidation kinetics, uses Bayesian statistics for model selection, and makes the raw data and model parameters available via a queryable database. The tool, Refractory Oxidation Database (https://nanohub.org/tools/refoxdb/), uses nanoHUB's Sim2Ls to make the workflow and data (including metadata) findable, accessible, interoperable, and reusable (FAIR). We find that the models selected by the original authors do not match the most likely one according to the Bayesian information criterion (BIC) in 71% of the cases. Further, in 56% of the cases, the published model was not even in the top 3 models according to the BIC. These numbers were obtained assuming an experimental noise of 2.5% of the mass gain range, a smaller noise leads to more discrepancies. The RefOxDB tool is open access and researchers can add their own raw data (those to be included in future publications, as well as negative results) for analysis and to share their work with the community. Such consistent and systematic analysis of open, community generated data can significantly accelerate the development of machine-learning models for oxidation behavior and assist in the understanding and improvement of oxidation resistance.

cond-mat.mtrl-sci↗

arXiv2019

Simulator-free Solution of High-Dimensional Stochastic Elliptic Partial Differential Equations using Deep Neural Networks

Stochastic partial differential equations (SPDEs) are ubiquitous in engineering and computational sciences. The stochasticity arises as a consequence of uncertainty in input parameters, constitutive relations, initial/boundary conditions, etc. Because of these functional uncertainties, the stochastic parameter space is often high-dimensional, requiring hundreds, or even thousands, of parameters to describe it. This poses an insurmountable challenge to response surface modeling since the number of forward model evaluations needed to construct an accurate surrogate grows exponentially with the dimension of the uncertain parameter space; a phenomenon referred to as the \textit{curse of dimensionality}. State-of-the-art methods for high-dimensional uncertainty propagation seek to alleviate the curse of dimensionality by performing dimensionality reduction in the uncertain parameter space. However, one still needs to perform forward model evaluations that potentially carry a very high computational burden. We propose a novel methodology for high-dimensional uncertainty propagation of elliptic SPDEs which lifts the requirement for a deterministic forward solver. Our approach is as follows. We parameterize the solution of the elliptic SPDE using a deep residual network (ResNet). In a departure from the traditional squared residual (SR) based loss function for training the ResNet, we introduce a novel physics-informed loss function derived from variational principles. Specifically, our loss function is the expectation of the energy functional of the PDE over the stochastic variables. We demonstrate our solver-free approach through various examples where the elliptic SPDE is subjected to different types of high-dimensional input uncertainties. Also, we solve high-dimensional uncertainty propagation and inverse problems.

physics.data-an↗