Gurpreet Singh

Gurpreet Singh, Mary F. Wheeler

A space-time domain decomposition approach is presented as a natural extension of the enhanced velocity mixed finite element (EVMFE) [Wheeler et. al] for spatial domain decomposition. The proposed approach allows for different space-time discretizations on non-overlapping, subdomains by enforcing a mass continuity argument at the non-matching interface to preserve the local mass conservation property inherent to the mixed finite element methods. To this effect, we consider three different model formulations: (1) a linear single phase flow problem, (2) a non-linear slightly compressible flow and tracer transport, and (3) a non-linear slightly compressible, multiphase flow and transport. We also present a numerical solution algorithm for the proposed domain decomposition approach where a monolithic (fully coupled in space and time) system is constructed that does not require subdomain iterations. This space-time EVMFE method accurately resolves advection-diffusion transport features, in a heterogeneous medium, while circumventing non-linear solver convergence issues associated with large time-step sizes for non-linear problems. Numerical results are presented for the aforementioned, three, model formulations to demonstrate the applicability of this approach to a general class of problems in flow and transport in porous media.

Gurpreet Singh, Wingtat Leung, Mary F. Wheeler

Numerical simulations for flow and transport in subsurface porous media often prove computationally prohibitive due to property data availability at multiple spatial scales that can vary by orders of magnitude. A number of model order reduction approaches are available in the existing literature that alleviate this issue by approximating the solution at a coarse scale. We attempt to present a comparison between two such model order reduction techniques, namely: (1) adaptive numerical homogenization and (2) generalized multiscale basis functions. We rely upon a non-linear, multi-phase, black-oil model formulation, commonly encountered in the oil and gas industry, as the basis for comparing the aforementioned two approaches. An expanded mixed finite element formulation is used to separate the spatial scales between non-linear, flow and transport problems. To the author's knowledge this is the first time these approaches have been described for a practical non-linear, multiphase flow problem of interest. A numerical benchmark is setup using fine scale property information from the 10$^{th}$ SPE comparative project dataset for the purpose of comparing accuracies of these two schemes. An adaptive criterion is employed in by both the schemes for local enrichment that allows us to preserve solution accuracy compared to the fine scale benchmark problem. The numerical results indicate that both schemes are able to adequately capture the fine scale features of the model problem at hand.

Rajarshi Roy, Nasrin Imanpour, Ashhar Aziz et al.

Multimodal generative AI systems like Stable Diffusion, DALL-E, and MidJourney have fundamentally changed how synthetic images are created. These tools drive innovation but also enable the spread of misleading content, false information, and manipulated media. As generated images become harder to distinguish from photographs, detecting them has become an urgent priority. To combat this challenge, We release MS COCOAI, a novel dataset for AI generated image detection consisting of 96000 real and synthetic datapoints, built using the MS COCO dataset. To generate synthetic images, we use five generators: Stable Diffusion 3, Stable Diffusion 2.1, SDXL, DALL-E 3, and MidJourney v6. Based on the dataset, we propose two tasks: (1) classifying images as real or generated, and (2) identifying which model produced a given synthetic image. The dataset is available at https://huggingface.co/datasets/Rajarshi-Roy-research/Defactify_Image_Dataset.

Rajarshi Roy, Gurpreet Singh, Ashhar Aziz et al.

The rapid proliferation of AI-generated text has introduced significant challenges in maintaining the integrity of digital content. Advanced generative models such as GPT-4, Claude 3.5, and Llama can produce highly coherent and human-like text, making it increasingly difficult to differentiate between human-written and AI-generated content. While these models have transformative applications, their misuse has raised concerns about misinformation, biased narratives, and security threats. This paper provides a comprehensive analysis of state-of-the-art AI-generated text detection techniques and evaluates their effectiveness through the Counter Turing Test (CT2) shared tasks. Task A (Binary Classification) required participants to distinguish between human-written and AI-generated text, while Task B (Model Attribution) focused on identifying the specific language model responsible for generating a given text. The results demonstrated high performance in binary classification, with the top system achieving an F1 score of 1.0000, but significantly lower scores in model attribution, where the best system achieved 0.9531, highlighting the increased complexity of this task. The top-performing teams leveraged fine-tuned transformer models, ensemble learning, and hybrid detection approaches, with DeBERTa-based and BART-based methods demonstrating strong results. However, the lower scores in Task B underscore the challenges of distinguishing outputs from different LLMs, necessitating further research into adversarial robustness, feature extraction, and cross-domain generalization.

Rajarshi Roy, Nasrin Imanpour, Ashhar Aziz et al.

The rapid advancements in generative AI technologies, such as Stable Diffusion, DALL-E, and Midjourney, have significantly transformed the creation of synthetic visual content. While these models enable innovation across industries, they also pose serious challenges, including misinformation, disinformation, and biased content generation. The increasing realism of AI-generated images makes their detection a pressing concern for researchers, policymakers, and industry stakeholders. In this paper, we present the findings of the Defactify 4.0 workshop, which introduced the Counter Turing Test (CT2) for AI-Generated Image Detection. The competition consisted of two key tasks: (1) binary classification of images as either AI-generated or real and (2) identification of the specific generative model responsible for an AI-generated image. To facilitate this, we developed the MS COCOAI dataset, consisting of 50,000 synthetic images from multiple generative models alongside real-world images from the MS COCO dataset. Participants employed diverse detection strategies, including convolutional neural networks (CNNs), Vision Transformers (ViTs), frequency-based analysis, contrastive learning, and multimodal techniques. The results demonstrated that while AI-generated images can be detected with high accuracy (F1-score > 0.83), identifying the exact model used remains significantly more challenging (highest F1-score: 0.4986). These findings highlight the need for improved model fingerprinting, adversarial robustness, and real-time detection mechanisms.

Elham Peimani, Gurpreet Singh, Nisarg Mahyavanshi et al.

Retrieving semantically relevant documents in niche domains poses significant challenges for traditional TF-IDF-based systems, often resulting in low similarity scores and suboptimal retrieval performance. This paper addresses these challenges by introducing an iterative and semi-automated query refinement methodology tailored to Humber College's career services webpages. Initially, generic queries related to interview preparation yield low top-document similarities (approximately 0.2--0.3). To enhance retrieval effectiveness, we implement a two-fold approach: first, domain-aware query refinement by incorporating specialized terms such as resources-online-learning, student-online-services, and career-advising; second, the integration of structured educational descriptors like "online resume and interview improvement tools." Additionally, we automate the extraction of domain-specific keywords from top-ranked documents to suggest relevant terms for query expansion. Through experiments conducted on five baseline queries, our semi-automated iterative refinement process elevates the average top similarity score from approximately 0.18 to 0.42, marking a substantial improvement in retrieval performance. The implementation details, including reproducible code and experimental setups, are made available in our GitHub repositories \url{https://github.com/Elipei88/HumberChatbotBackend} and \url{https://github.com/Nisarg851/HumberChatbot}. We also discuss the limitations of our approach and propose future directions, including the integration of advanced neural retrieval models.

Rajarshi Roy, Nasrin Imanpour, Ashhar Aziz et al.

The rapid advancement of large language models (LLMs) has led to increasingly human-like AI-generated text, raising concerns about content authenticity, misinformation, and trustworthiness. Addressing the challenge of reliably detecting AI-generated text and attributing it to specific models requires large-scale, diverse, and well-annotated datasets. In this work, we present a comprehensive dataset comprising over 58,000 text samples that combine authentic New York Times articles with synthetic versions generated by multiple state-of-the-art LLMs including Gemma-2-9b, Mistral-7B, Qwen-2-72B, LLaMA-8B, Yi-Large, and GPT-4-o. The dataset provides original article abstracts as prompts, full human-authored narratives. We establish baseline results for two key tasks: distinguishing human-written from AI-generated text, achieving an accuracy of 58.35\%, and attributing AI texts to their generating models with an accuracy of 8.92\%. By bridging real-world journalistic content with modern generative models, the dataset aims to catalyze the development of robust detection and attribution methods, fostering trust and transparency in the era of generative AI. Our dataset is available at: https://huggingface.co/datasets/gsingh1-py/train.

Gurpreet Singh, Soumyajit Gupta, Clint N. Dawson

Dense nets are an integral part of any classification and regression problem. Recently, these networks have found a new application as solvers for known representations in various domains. However, one crucial issue with dense nets is it's feature interpretation and lack of reproducibility over multiple training runs. In this work, we identify a basis collapse issue as a primary cause and propose a modified loss function that circumvents this problem. We also provide a few general guidelines relating the choice of activations to loss surface roughness and appropriate scaling for designing low-weight dense nets. We demonstrate through carefully chosen numerical experiments that the basis collapse issue leads to the design of massively redundant networks. Our approach results in substantially concise nets, having $100 \times$ fewer parameters, while achieving a much lower $(10\times)$ MSE loss at scale than reported in prior works. Further, we show that the width of a dense net is acutely dependent on the feature complexity. This is in contrast to the dimension dependent width choice reported in prior theoretical works. To the best of our knowledge, this is the first time these issues and contradictions have been reported and experimentally verified. With our design guidelines we render transparency in terms of a low-weight network design. We share our codes for full reproducibility available at https://github.com/smjtgupta/Dense_Net_Regress.

Ari Goodman, Gurpreet Singh, Ryan O'Shea et al.

Aircraft Ship Integrated Secure and Traverse (ASIST) is a system designed to arrest helicopters safely and efficiently on ships. Originally, a precision Helicopter Position Sensing Equipment (HPSE) tracked and monitored the position of the helicopter relative to the Rapid Securing Device (RSD). However, using the HPSE component was determined to be infeasible in the transition of the ASIST system due to the hardware installation requirements. As a result, sailors track the position of the helicopters with their eyes with no sensor or artificially intelligent decision aid. Manually tracking the helicopter takes additional time and makes recoveries more difficult, especially at high sea states. Performing recoveries without the decision aid leads to higher uncertainty and cognitive load. PETA (Pose Estimation and Tracking for ASIST) is a research effort to create a helicopter tracking system prototype without hardware installation requirements for ASIST system operators. Its overall goal is to improve situational awareness and reduce operator uncertainty with respect to the aircrafts position relative to the RSD, and consequently increase the allowable landing area. The authors produced a prototype system capable of tracking helicopters with respect to the RSD. The software included a helicopter pose estimation component, camera pose estimation component, and a user interface component. PETA demonstrated the potential for state-of-the-art computer vision algorithms Faster R-CNN and HRNet (High-Resolution Network) to be used to estimate the pose of helicopters in real-time, returning ASIST to its originally intended capability. PETA also demonstrated that traditional methods of encoder-decoders could be used to estimate the orientation of the helicopter and could be used to confirm the output from HRNet.

Ari Goodman, Gurpreet Singh, James Hing et al.

Deck tracking performed on carriers currently involves a team of sailors manually identifying aircraft and updating a digital user interface called the Ouija Board. Improvements to the deck tracking process would result in increased Sortie Generation Rates, and therefore applying automation is seen as a critical method to improve deck tracking. However, the requirements on a carrier ship do not allow for the installation of hardware-based location sensing technologies like Global Positioning System (GPS) sensors. PATRIOT (Panoramic Asset Tracking of Real-Time Information for the Ouija Tabletop) is a research effort and proposed solution to performing deck tracking with passive sensing and without the need for GPS sensors. PATRIOT is a prototype system which takes existing camera feeds, calculates aircraft poses, and updates a virtual Ouija board interface with the current status of the assets. PATRIOT would allow for faster, more accurate, and less laborious asset tracking for aircraft, people, and support equipment. PATRIOT is anticipated to benefit the warfighter by reducing cognitive workload, reducing manning requirements, collecting data to improve logistics, and enabling an automation gateway for future efforts to improve efficiency and safety. The authors have developed and tested algorithms to perform pose estimations of assets in real-time including OpenPifPaf, High-Resolution Network (HRNet), HigherHRNet (HHRNet), Faster R-CNN, and in-house developed encoder-decoder network. The software was tested with synthetic and real-world data and was able to accurately extract the pose of assets. Fusion, tracking, and real-world generality are planned to be improved to ensure a successful transition to the fleet.

Amitava Das, Suranjana Trivedy, Danush Khanna et al.

The rapid rise of large language models (LLMs) has unlocked many applications but also underscores the challenge of aligning them with diverse values and preferences. Direct Preference Optimization (DPO) is central to alignment but constrained by fixed divergences and limited feature transformations. We propose DPO-Kernels, which integrates kernel methods to address these issues through four key contributions: (i) Kernelized Representations with polynomial, RBF, Mahalanobis, and spectral kernels for richer transformations, plus a hybrid loss combining embedding-based and probability-based objectives; (ii) Divergence Alternatives (Jensen-Shannon, Hellinger, Renyi, Bhattacharyya, Wasserstein, and f-divergences) for greater stability; (iii) Data-Driven Selection metrics that automatically choose the best kernel-divergence pair; and (iv) a Hierarchical Mixture of Kernels for both local precision and global modeling. Evaluations on 12 datasets demonstrate state-of-the-art performance in factuality, safety, reasoning, and instruction following. Grounded in Heavy-Tailed Self-Regularization, DPO-Kernels maintains robust generalization for LLMs, offering a comprehensive resource for further alignment research.

Gurpreet Singh, Keshav Sood, P. Rajalakshmi et al.

Federated learning (FL) offers a privacy-preserving paradigm for machine learning, but its application in intrusion detection systems (IDS) within IoT networks is challenged by severe class imbalance, non-IID data, and high communication overhead.These challenges severely degrade the performance of conventional FL methods in real-world network traffic classification. To overcome these limitations, we propose Sentinel, a personalized federated IDS (pFed-IDS) framework that incorporates a dual-model architecture on each client, consisting of a personalized teacher and a lightweight shared student model. This design effectively balances deep local adaptation with efficient global model consensus while preserving client privacy by transmitting only the compact student model, thus reducing communication costs. Sentinel integrates three key mechanisms to ensure robust performance: bidirectional knowledge distillation with adaptive temperature scaling, multi-faceted feature alignment, and class-balanced loss functions. Furthermore, the server employs normalized gradient aggregation with equal client weighting to enhance fairness and mitigate client drift. Extensive experiments on the IoTID20 and 5GNIDD benchmark datasets demonstrate that Sentinel significantly outperforms state-of-the-art federated methods, establishing a new performance benchmark, especially under extreme data heterogeneity, while maintaining communication efficiency.

Vipula Rawte, Rajarshi Roy, Gurpreet Singh et al.

As Large Language Models (LLMs) continue to advance, Retrieval-Augmented Generation (RAG) has emerged as a vital technique to enhance factual accuracy by integrating external knowledge into the generation process. However, LLMs often fail to faithfully integrate retrieved evidence into their generated responses, leading to factual inconsistencies. To quantify this gap, we introduce Entity-Context Divergence (ECD), a metric that measures the extent to which retrieved information is accurately reflected in model outputs. We systematically evaluate contemporary LLMs on their ability to preserve factual consistency in retrieval-augmented settings, a capability we define as RAG-ability. Our empirical analysis reveals that RAG-ability remains low across most LLMs, highlighting significant challenges in entity retention and context fidelity. This paper introduces Radiant (Retrieval AugmenteD entIty-context AligNmenT), a novel framework that merges RAG with alignment designed to optimize the interplay between retrieved evidence and generated content. Radiant extends Direct Preference Optimization (DPO) to teach LLMs how to integrate provided additional information into subsequent generations. As a behavior correction mechanism, Radiant boosts RAG performance across varied retrieval scenarios, such as noisy web contexts, knowledge conflicts, and hallucination reduction. This enables more reliable, contextually grounded, and factually coherent content generation.

Renjith Prasad, Abhilekh Borah, Hasnat Md Abdullah et al.

Alignment is crucial for text-to-image (T2I) models to ensure that generated images faithfully capture user intent while maintaining safety and fairness. Direct Preference Optimization (DPO), prominent in large language models (LLMs), is extending its influence to T2I systems. This paper introduces DPO-Kernels for T2I models, a novel extension enhancing alignment across three dimensions: (i) Hybrid Loss, integrating embedding-based objectives with traditional probability-based loss for improved optimization; (ii) Kernelized Representations, employing Radial Basis Function (RBF), Polynomial, and Wavelet kernels for richer feature transformations and better separation between safe and unsafe inputs; and (iii) Divergence Selection, expanding beyond DPO's default Kullback-Leibler (KL) regularizer by incorporating Wasserstein and R'enyi divergences for enhanced stability and robustness. We introduce DETONATE, the first large-scale benchmark of its kind, comprising approximately 100K curated image pairs categorized as chosen and rejected. DETONATE encapsulates three axes of social bias and discrimination: Race, Gender, and Disability. Prompts are sourced from hate speech datasets, with images generated by leading T2I models including Stable Diffusion 3.5 Large, Stable Diffusion XL, and Midjourney. Additionally, we propose the Alignment Quality Index (AQI), a novel geometric measure quantifying latent-space separability of safe/unsafe image activations, revealing hidden vulnerabilities. Empirically, we demonstrate that DPO-Kernels maintain strong generalization bounds via Heavy-Tailed Self-Regularization (HT-SR). DETONATE and complete code are publicly released.

Abhilekh Borah, Chhavi Sharma, Danush Khanna et al.

Alignment is no longer a luxury, it is a necessity. As large language models (LLMs) enter high-stakes domains like education, healthcare, governance, and law, their behavior must reliably reflect human-aligned values and safety constraints. Yet current evaluations rely heavily on behavioral proxies such as refusal rates, G-Eval scores, and toxicity classifiers, all of which have critical blind spots. Aligned models are often vulnerable to jailbreaking, stochasticity of generation, and alignment faking. To address this issue, we introduce the Alignment Quality Index (AQI). This novel geometric and prompt-invariant metric empirically assesses LLM alignment by analyzing the separation of safe and unsafe activations in latent space. By combining measures such as the Davies-Bouldin Score (DBS), Dunn Index (DI), Xie-Beni Index (XBI), and Calinski-Harabasz Index (CHI) across various formulations, AQI captures clustering quality to detect hidden misalignments and jailbreak risks, even when outputs appear compliant. AQI also serves as an early warning signal for alignment faking, offering a robust, decoding invariant tool for behavior agnostic safety auditing. Additionally, we propose the LITMUS dataset to facilitate robust evaluation under these challenging conditions. Empirical tests on LITMUS across different models trained under DPO, GRPO, and RLHF conditions demonstrate AQI's correlation with external judges and ability to reveal vulnerabilities missed by refusal metrics. We make our implementation publicly available to foster future research in this area.

Amitava Das, Yaswanth Narsupalli, Gurpreet Singh et al.

Precise alignment in Text-to-Image (T2I) systems is crucial to ensure that generated visuals not only accurately encapsulate user intents but also conform to stringent ethical and aesthetic benchmarks. Incidents like the Google Gemini fiasco, where misaligned outputs triggered significant public backlash, underscore the critical need for robust alignment mechanisms. In contrast, Large Language Models (LLMs) have achieved notable success in alignment. Building on these advancements, researchers are eager to apply similar alignment techniques, such as Direct Preference Optimization (DPO), to T2I systems to enhance image generation fidelity and reliability. We present YinYangAlign, an advanced benchmarking framework that systematically quantifies the alignment fidelity of T2I systems, addressing six fundamental and inherently contradictory design objectives. Each pair represents fundamental tensions in image generation, such as balancing adherence to user prompts with creative modifications or maintaining diversity alongside visual coherence. YinYangAlign includes detailed axiom datasets featuring human prompts, aligned (chosen) responses, misaligned (rejected) AI-generated outputs, and explanations of the underlying contradictions.

Soumyajit Gupta, Gurpreet Singh, Raghu Bollapragada et al.

Multi-objective optimization (MOO) problems require balancing competing objectives, often under constraints. The Pareto optimal solution set defines all possible optimal trade-offs over such objectives. In this work, we present a novel method for Pareto-front learning: inducing the full Pareto manifold at train-time so users can pick any desired optimal trade-off point at run-time. Our key insight is to exploit Fritz-John Conditions for a novel guided double gradient descent strategy. Evaluation on synthetic benchmark problems allows us to vary MOO problem difficulty in controlled fashion and measure accuracy vs. known analytic solutions. We further test scalability and generalization in learning optimal neural model parameterizations for Multi-Task Learning (MTL) on image classification. Results show consistent improvement in accuracy and efficiency over prior MTL methods as well as techniques from operations research.

Gurpreet Singh, Soumyajit Gupta

SVD serves as an exploratory tool in identifying the dominant features in the form of top rank-r singular factors corresponding to the largest singular values. For Big Data applications it is well known that Singular Value Decomposition (SVD) is restrictive due to main memory requirements. However, a number of applications such as community detection, clustering, or bottleneck identification in large scale graph data-sets rely upon identifying the lowest singular values and the singular corresponding vectors. For example, the lowest singular values of a graph Laplacian reveal the number of isolated clusters (zero singular values) or bottlenecks (lowest non-zero singular values) for undirected, acyclic graphs. A naive approach here would be to perform a full SVD however, this quickly becomes infeasible for practical big data applications due to the enormous memory requirements. Furthermore, for such applications only a few lowest singular factors are desired making a full decomposition computationally exorbitant. In this work, we trivially extend the previously proposed Range-Net to \textbf{Tail-Net} for a memory and compute efficient extraction of lowest singular factors of a given big dataset and a specified rank-r. We present a number of numerical experiments on both synthetic and practical data-sets for verification and bench-marking using conventional SVD as the baseline.

Gurpreet Singh, Soumyajit Gupta, Clint Dawson

Hyperspectral unmixing involves separating a pixel as a weighted combination of its constituent endmembers and corresponding fractional abundances, with the current state of the art results achieved by neural models on benchmark datasets. However, these networks are severely over-parameterized and consequently, the invariant endmember spectra extracted as decoder weights have a high variance over multiple runs. These approaches perform substantial post-processing while requiring an exact specification of the number of endmembers and specialized initialization of weights from other algorithms like VCA. We show for the first time that a two-layer autoencoder (SCA), with $2FK$ parameters ($F$ features, $K$ endmembers), achieves error metrics that are scales apart ($10^{-5})$ from previously reported values $(10^{-2})$. SCA converges to this low error solution starting from a random initialization of weights. We also show that SCA, based upon a bi-orthogonal representation, performs a self-correction when the number of endmembers are over-specified. Numerical experiments on Samson, Jasper, and Urban datasets demonstrate that SCA outperforms previously reported error metrics for all the cases while being robust to noise and outliers.

Gurpreet Singh, Soumyajit Gupta, Matthew Lease et al.

Classification, recommendation, and ranking problems often involve competing goals with additional constraints (e.g., to satisfy fairness or diversity criteria). Such optimization problems are quite challenging, often involving non-convex functions along with considerations of user preferences in balancing trade-offs. Pareto solutions represent optimal frontiers for jointly optimizing multiple competing objectives. A major obstacle for frequently used linear-scalarization strategies is that the resulting optimization problem might not always converge to a global optimum. Furthermore, such methods only return one solution point per run. A Pareto solution set is a subset of all such global optima over multiple runs for different trade-off choices. Therefore, a Pareto front can only be guaranteed with multiple runs of the linear-scalarization problem, where all runs converge to their respective global optima. Consequently, extracting a Pareto front for practical problems is computationally intractable with substantial computational overheads, limited scalability, and reduced accuracy. We propose a robust, low cost, two-stage, hybrid neural Pareto optimization approach that is accurate and scales (compute space and time) with data dimensions, as well as number of functions and constraints. The first stage (neural network) efficiently extracts a weak Pareto front, using Fritz-John conditions as the discriminator, with no assumptions of convexity on the objectives or constraints. The second stage (efficient Pareto filter) extracts the strong Pareto optimal subset given the weak front from stage 1. Fritz-John conditions provide us with theoretical bounds on approximation error between the true and network extracted weak Pareto front. Numerical experiments demonstrates the accuracy and efficiency on a canonical set of benchmark problems and a fairness optimization task from prior works.

Gurpreet Singh, Soumyajit Gupta, Matthew Lease et al.

In a Big Data setting computing the dominant SVD factors is restrictive due to the main memory requirements. Recently introduced streaming Randomized SVD schemes work under the restrictive assumption that the singular value spectrum of the data has exponential decay. This is seldom true for any practical data. Although these methods are claimed to be applicable to scientific computations due to associated tail-energy error bounds, the approximation errors in the singular vectors and values are high when the aforementioned assumption does not hold. Furthermore from a practical perspective, oversampling can still be memory intensive or worse can exceed the feature dimension of the data. To address these issues, we present Range-Net as an alternative to randomized SVD that satisfies the tail-energy lower bound given by Eckart-Young-Mirsky (EYM) theorem. Range-Net is a deterministic two-stage neural optimization approach with random initialization, where the main memory requirement depends explicitly on the feature dimension and desired rank, independent of the sample dimension. The data samples are read in a streaming setting with the network minimization problem converging to the desired rank-r approximation. Range-Net is fully interpretable where all the network outputs and weights have a specific meaning. We provide theoretical guarantees that Range-Net extracted SVD factors satisfy EYM tail-energy lower bound at machine precision. Our numerical experiments on real data at various scales confirms this bound. A comparison against the state of the art streaming Randomized SVD shows that Range-Net accuracy is better by six orders of magnitude while being memory efficient.

Gurpreet Singh, Soumyajit Gupta, Matthew Lease

Constrained Optimization solution algorithms are restricted to point based solutions. In practice, single or multiple objectives must be satisfied, wherein both the objective function and constraints can be non-convex resulting in multiple optimal solutions. Real world scenarios include intersecting surfaces as Implicit Functions, Hyperspectral Unmixing and Pareto Optimal fronts. Local or global convexification is a common workaround when faced with non-convex forms. However, such an approach is often restricted to a strict class of functions, deviation from which results in sub-optimal solution to the original problem. We present neural solutions for extracting optimal sets as approximate manifolds, where unmodified, non-convex objectives and constraints are defined as modeler guided, domain-informed $L_2$ loss function. This promotes interpretability since modelers can confirm the results against known analytical forms in their specific domains. We present synthetic and realistic cases to validate our approach and compare against known solvers for bench-marking in terms of accuracy and computational efficiency.

Gurpreet Singh, Soumyajit Gupta, Matt Lease et al.

Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully convolutional architecture that captures the invariant structure of the domain to reconstruct the observable system. The proposed architecture is significantly low-weight compared to other networks for such problems. Our intent is to learn coupled dynamic processes interpreted as deviations from true kernels representing isolated processes for model-adaptivity. Experimental analysis shows that our architecture is robust and transparent in capturing process kernels and system anomalies. We also show that high weights representation is not only redundant but also impacts network interpretability. Our design is guided by domain knowledge, with isolated process representations serving as ground truths for verification. These allow us to identify redundant kernels and their manifestations in activation maps to guide better designs that are both interpretable and explainable unlike traditional deep-nets.

Gurpreet Singh, Mary F. Wheeler

We present an adaptive space-time mesh refinement approach based a domain decomposition approach (Singh and Wheeler, 2018) that allows different time-step sizes and mesh refinements in different subdomains. Our numerical experiments indicate that non-linear solvers fail to converge, to the desired tolerance, due to large non-linear residuals in a smaller subdomain. We exploit this feature to identify subdomains where smaller time-step sizes are necessary while using large time-step sizes in the rest of the reservoir domain. The three key components of our approach are: (1) a space-time, enhanced velocity, domain decomposition approach that allows different mesh refinements and time-step sizes in different subdomains while preserving local mass conservation, (2) a residual based error estimator to identify or mark regions (or subdomains) that pose non-linear convergence issues, and (3) a fully coupled monolithic solver is also presented that solves the coarse and fine subdomain problems, both in space and time, simultaneously. This solution scheme is fully implicit and is therefore unconditionally stable. The proposed space-time domain decomposition approach, with smaller time-step sizes in a subdomain and large time-step sizes everywhere else, circumvents the non-linear convergence issue without adding computational costs. Additionally, a space-time monolithic solver renders a massively parallel, time concurrent framework for solving flow and transport problems in subsurface porous media. Since the proposed approach is similar to the widely used finite difference scheme, it can be easily integrated in any existing legacy reservoir simulator.

Harjinder Kaur, Gurpreet Singh, Jaspreet Minhas

Intrusion detection is so much popular since the last two decades where intrusion is attempted to break into or misuse the system. It is mainly of two types based on the intrusions, first is Misuse or signature based detection and the other is Anomaly detection. In this paper Machine learning based methods which are one of the types of Anomaly detection techniques is discussed.