arXiv subjects

Muralikrishnan Gopalakrishnan Meena

Publications and source records attributed to Muralikrishnan Gopalakrishnan Meena.

17 recordsLinked to original sources

arXiv2026

Distributed Variational Quantum Linear Solver

The Variational Quantum Linear Solver (VQLS), a hybrid quantum-classical algorithm for solving linear systems, faces a practical scalability bottleneck: the Linear Combination of Unitaries (LCU) decomposition requires $O(L^2)$ circuit evaluations per optimizer iteration, where $L$ can grow to $4^n$ in the worst case for an $n$-qubit system. We address this computational bottleneck through two complementary strategies. First, we present a distributed VQLS (D-VQLS) framework (https://code.ornl.gov/olcf-qcfd/DVQLS.git), built on NVIDIA CUDA-Q, that enables asynchronous, scalable distribution of the $O(L^2)$ cost evaluations. Second, a fast Walsh--Hadamard transform (FWHT)-based Pauli decomposition with coefficient-amplitude pruning threshold $τ=0.01$ curbs LCU growth for the structured Toeplitz family, reducing $L$ from $O(2^n)$ to 64 for $n>6$ and compressing the circuit complexity per optimizer iteration from $O(n4^n)$ to $O(n)$. We derive the exact top-$L$ Frobenius error and connect it to worst-case solution error. For a 10-qubit tridiagonal Toeplitz system, the $L=64$ pruning yields a $256\times$ reduction---from 23 million to 90k circuits per optimizer iteration. The D-VQLS framework is validated on the NERSC Perlmutter supercomputer using multi-node, multi-GPU ideal state-vector simulations, achieving over $99.99\%$ fidelity against classical solutions on tridiagonal Toeplitz and Hele--Shaw flow benchmarks, with near-ideal strong scaling up to 24 GPUs and $95.3\%$ weak scaling efficiency at 96 GPUs processing more than 360k circuits per optimizer iteration (from larger-$L$ pruning) for the 10-qubit system. Systematic profiling identifies the optimal resource allocation for distributed quantum circuit workloads, yielding a $2.52\times$ speedup for the configurations studied.

quant-ph↗

arXiv2026

Memory-, Circuit-, and Ansatz-Efficient VQLS for CFD on Hybrid Quantum-HPC Systems

Fluid dynamics workloads are dominated by repeated solves of large, structured linear systems, motivating the search for quantum acceleration. The Variational Quantum Linear Solver (VQLS) is a leading near-term candidate, but practical deployment on hybrid quantum--high--performance computing (HPC) systems faces three persistent challenges: (i) the linear-combination-of-unitaries (LCU) encoding of the system matrix explodes in memory and runtime as the problem size grows, (ii) ansatz selection is largely empirical, with no clear link between standard circuit metrics and solver convergence, and (iii) end-to-end VQLS pipelines have rarely been exercised on production HPC hardware at non-trivial qubit counts. This work addresses these challenges through three contributions. First, we benchmark four matrix-encoding strategies---naive LCU, PennyLane-integrated, Fast Walsh--Hadamard Transform (FWHT)-based parallel Pauli decomposition, and an singular value decomposition (SVD)-based two-term LCU---and show that the FWHT approach reduces peak memory by up to $1298\times$ on an $11\times 11$ Hele--Shaw grid, while the SVD-based coherent VQLS delivers over $10{,}000\times$ per-iteration speedup over standard Pauli-based VQLS at 8 qubits. Second, we evaluate 11 ansatz families with gradient-free and gradient-based optimizers on canonical Hele--Shaw flow, and find that expressibility and entanglement metrics correlate only weakly with VQLS convergence, motivating problem-aware ansatz design. Third, we deploy the full workflow on the OLCF Frontier supercomputer and successfully simulate a 15-qubit tridiagonal Toeplitz system on a single node. Together, these results establish a practical baseline for VQLS in hybrid quantum--HPC computation fluid dynamic (CFD) workflows and identify the remaining bottlenecks for larger problems.

quant-ph↗

arXiv2026

Exploring the use of quantum computing for facilitating spatially and temporally resolved models of a biological cell

Whole-cell simulation, modeling all of a cell's functional systems over its life cycle, is an outstanding challenge in computational biology. Even the simplest living cell contains thousands of interacting proteins and metabolites (on the order of trillions of atoms) whose full functional dynamics spans roughly five orders of magnitude in space (nm to $μ$m) and nearly nineteen in time (fs to hours). Further, many of the governing physical and chemical properties remain incompletely characterized. Simulating such complex systems at fully atomistic resolution over a full cell cycle is computationally intractable on classical architectures, raising a central question: Can quantum computing offer a viable path to whole-cell simulations that integrate molecular- and systems-level complexity? This Perspective examines the potential of quantum computing across three hierarchical scales: atomistic-molecular modeling, metabolic and regulatory networks, and whole-cell spatial modeling. We present a complexity analysis comparing classical and quantum algorithms for representative biological problems, identifying regimes of substantial theoretical speedup under specified algorithmic assumptions. We highlight algorithmic developments designed to leverage both near-term exploratory and fault-tolerant quantum architectures, and discuss practical bottlenecks: data encoding overhead, system conditioning, measurement constraints, and hybrid quantum-HPC integration. Together, these results outline a roadmap for quantum-accelerated whole-cell modeling and the biological insights such multiscale frameworks may eventually enable.

quant-ph↗

arXiv2026

PAPA: Online Personalized Active Preference Alignment

Diffusion models are highly effective at modeling complex data distributions, including images and text. However, in applications like personalized recommender systems, the objective often shifts to modeling specific regions of the distribution that maximize user preferences-initially unknown but gradually uncovered through interactive feedback. This can naturally be framed as a reinforcement learning problem, where the goal is to fine-tune a diffusion model to maximize a reward function based on preferences. However, the main challenge lies in learning a parameterized reward model, which typically requires large-scale preference data-something that is often not feasible in practice. In this work, we introduce Personalized Active Preference Alignment PAPA, a novel method that bypasses the requirement for a parametrized reward model by directly optimizing the diffusion model using real-time user feedback. PAPA enables feedback-efficient preference alignment, drawing inspiration from the variational inference framework. We demonstrate PAPA's effectiveness through extensive experiments and ablation studies across diverse class-conditioned and fine-grained alignment tasks. Additionally, based on theoretical insights, we propose an enhanced fine-tuning strategy, referred to as EPAPA, that requires less computational budget and accelerates the fine-tuning process, further boosting PAPA's suitability for real-world deployment. Our code is made publicly available at https://github.com/NasikNafi/papa.

cs.LG↗

arXiv2026

Tensor network compression using fluid dynamics as a testbed: Analytical foundations in one dimension

High performance computers produce extreme-scale data sets that require sampling or compression if they are to be used to their full potential. Existing data compression techniques typically exploit features such as sparsity in the data, homogeneity in the data, or {\it a priori} knowledge of what subsets of data are of most interest. Fluid dynamics data in general do not exhibit these features and so are attractive test beds for generic compression techniques that are objective, robust, and tuneable with respect to information lost due to compression. Presented here is a method based on tensor networks, specifically matrix product states or tensor trains, that meets these requirements. The method is demonstrated for compression in one-dimension and is extensible to higher dimensionality. Lossless compression is demonstrated for random Fourier series for sufficiently high bond dimension of the tensor network, with the memory required to store the tensor network scaling directly proportional to the bond dimension. The lossy compression exhibited at lower bond dimension can be well within the relative error of many fluid simulations. The compression algorithm is tested for the time evolution of Burger's equation with excellent results. We additionally demonstrate the capability to perform computations in the compressed form through a tensor network periodic convolution that can be orders of magnitude faster than using fast Fourier transforms and the convolution theorem. In addition to being an attractive method for working with data sets generated by existing computers, the tensor network methods utilised are directly translatable to the emerging paradigm of quantum computing.

physics.comp-ph↗

arXiv2025

Scaling Hybrid Quantum-HPC Applications with the Quantum Framework

Hybrid quantum-high performance computing (Q-HPC) workflows are emerging as a key strategy for running quantum applications at scale in current noisy intermediate-scale quantum (NISQ) devices. These workflows must operate seamlessly across diverse simulators and hardware backends since no single simulator offers the best performance for every circuit type. Simulation efficiency depends strongly on circuit structure, entanglement, and depth, making a flexible and backend-agnostic execution model essential for fair benchmarking, informed platform selection, and ultimately the identification of quantum advantage opportunities. In this work, we extend the Quantum Framework (QFw), a modular and HPC-aware orchestration layer, to integrate multiple local backends (Qiskit Aer, NWQ-Sim, QTensor, and TN-QVM) and a cloud-based quantum backend (IonQ) under a unified interface. Using this integration, we execute a number of non-variational as well as variational workloads. The results highlight workload-specific backend advantages: while Qiskit Aer's matrix product state excels for large Ising models, NWQ-Sim not only leads on large-scale entanglement and Hamiltonian but also shows the benefits of concurrent subproblem execution in a distributed manner for optimization problems. These findings demonstrate that simulator-agnostic, HPC-aware orchestration is a practical path toward scalable, reproducible, and portable Q-HPC ecosystems, thereby accelerating progress toward demonstrating quantum advantage.

quant-ph↗

arXiv2025

Vortical interactions in turbulent thermoacoustic systems

This study examines the dynamics of vortical interactions and their implications for mitigating thermoacoustic instability in a turbulent combustor. The regions of intense vortical interactions are identified as vortical communities in the network space of weighted directed vortical networks constructed from two-dimensional experimental velocity data. One can expect vortical interactions in the combustor to be strongest near the moment of vortex shedding, as the shed vortices gradually weaken due to dissipation while convecting downstream. However, we show that, during the state of thermoacoustic instability, there is a non-trivial consistent phase lag of approximately 52 degrees between the shedding of the coherent structures from the backward-facing step and the time instant when the vortical interactions attain their local maximum value. We explain this phase lag by investigating the correlation between acoustic pressure fluctuations, spatio-temporal dynamics of coherent structures, and vortical interactions in the reaction field of the combustor. We also show the aperiodic variation of vortical interactions during the states of combustion noise and aperiodic epochs of intermittency. Furthermore, the spatio-temporal evolution of pairs of vortical communities with the maximum inter-community interactions provides insight into explaining the critical regions detected in the reaction field during the states of intermittency and thermoacoustic instability, also identified in previous studies. We further show that the most efficient suppression of thermoacoustic instability via air microjet injection is achieved when steady air jets are introduced to disrupt the maximum inter-community interactions present during the state of thermoacoustic instability.

physics.flu-dyn↗

arXiv2025

Pixel-Resolved Long-Context Learning for Turbulence at Exascale: Resolving Small-scale Eddies Toward the Viscous Limit

Turbulence plays a crucial role in multiphysics applications, including aerodynamics, fusion, and combustion. Accurately capturing turbulence's multiscale characteristics is essential for reliable predictions of multiphysics interactions, but remains a grand challenge even for exascale supercomputers and advanced deep learning models. The extreme-resolution data required to represent turbulence, ranging from billions to trillions of grid points, pose prohibitive computational costs for models based on architectures like vision transformers. To address this challenge, we introduce a multiscale hierarchical Turbulence Transformer that reduces sequence length from billions to a few millions and a novel RingX sequence parallelism approach that enables scalable long-context learning. We perform scaling and science runs on the Frontier supercomputer. Our approach demonstrates excellent performance up to 1.1 EFLOPS on 32,768 AMD GPUs, with a scaling efficiency of 94%. To our knowledge, this is the first AI model for turbulence that can capture small-scale eddies down to the dissipative range.

physics.flu-dyn↗

arXiv2024

Solving the Hele-Shaw flow using the Harrow-Hassidim-Lloyd algorithm on superconducting devices: A study of efficiency and challenges

The development of quantum processors capable of handling practical fluid flow problems represents a distant yet promising frontier. Recent strides in quantum algorithms, particularly linear solvers, have illuminated the path toward quantum solutions for classical fluid flow solvers. However, assessing the capability of these quantum linear systems algorithms (QLSAs) in solving ideal flow equations on real hardware is crucial for their future development in practical fluid flow applications. In this study, we examine the capability of a canonical QLSA, the Harrow-Hassidim-Lloyd (HHL) algorithm, in accurately solving the system of linear equations governing an idealized fluid flow problem, specifically the Hele-Shaw flow. Our investigation focuses on analyzing the accuracy and computational cost of the HHL solver. To gauge the stability and convergence of the solver, we conduct shots-based simulations on quantum simulators. Furthermore, we share insights gained from executing the HHL solver on superconducting quantum devices. To mitigate errors arising from qubit measurement, gate operations, and qubit decoherence inherent in quantum devices, we employ various error suppression and mitigation techniques. Our preliminary assessments serve as a foundational step towards enabling more complex quantum utility scale evaluation of using QLSA for solving fluid flow problems.

physics.flu-dyn↗

arXiv2024

Integrating Quantum Computing Resources into Scientific HPC Ecosystems

Quantum Computing (QC) offers significant potential to enhance scientific discovery in fields such as quantum chemistry, optimization, and artificial intelligence. Yet QC faces challenges due to the noisy intermediate-scale quantum era's inherent external noise issues. This paper discusses the integration of QC as a computational accelerator within classical scientific high-performance computing (HPC) systems. By leveraging a broad spectrum of simulators and hardware technologies, we propose a hardware-agnostic framework for augmenting classical HPC with QC capabilities. Drawing on the HPC expertise of the Oak Ridge National Laboratory (ORNL) and the HPC lifecycle management of the Department of Energy (DOE), our approach focuses on the strategic incorporation of QC capabilities and acceleration into existing scientific HPC workflows. This includes detailed analyses, benchmarks, and code optimization driven by the needs of the DOE and ORNL missions. Our comprehensive framework integrates hardware, software, workflows, and user interfaces to foster a synergistic environment for quantum and classical computing research. This paper outlines plans to unlock new computational possibilities, driving forward scientific inquiry and innovation in a wide array of research domains.

quant-ph↗

arXiv2024

Learning the boundary-to-domain mapping using Lifting Product Fourier Neural Operators for partial differential equations

Neural operators such as the Fourier Neural Operator (FNO) have been shown to provide resolution-independent deep learning models that can learn mappings between function spaces. For example, an initial condition can be mapped to the solution of a partial differential equation (PDE) at a future time-step using a neural operator. Despite the popularity of neural operators, their use to predict solution functions over a domain given only data over the boundary (such as a spatially varying Dirichlet boundary condition) remains unexplored. In this paper, we refer to such problems as boundary-to-domain problems; they have a wide range of applications in areas such as fluid mechanics, solid mechanics, heat transfer etc. We present a novel FNO-based architecture, named Lifting Product FNO (or LP-FNO) which can map arbitrary boundary functions defined on the lower-dimensional boundary to a solution in the entire domain. Specifically, two FNOs defined on the lower-dimensional boundary are lifted into the higher dimensional domain using our proposed lifting product layer. We demonstrate the efficacy and resolution independence of the proposed LP-FNO for the 2D Poisson equation.

cs.LG↗

arXiv2024

Machine-Learned Closure of URANS for Stably Stratified Turbulence: Connecting Physical Timescales & Data Hyperparameters of Deep Time-Series Models

We develop time-series machine learning (ML) methods for closure modeling of the Unsteady Reynolds Averaged Navier Stokes (URANS) equations applied to stably stratified turbulence (SST). SST is strongly affected by fine balances between forces and becomes more anisotropic in time for decaying cases. Moreover, there is a limited understanding of the physical phenomena described by some of the terms in the URANS equations. Rather than attempting to model each term separately, it is attractive to explore the capability of machine learning to model groups of terms, i.e., to directly model the force balances. We consider decaying SST which are homogeneous and stably stratified by a uniform density gradient, enabling dimensionality reduction. We consider two time-series ML models: Long Short-Term Memory (LSTM) and Neural Ordinary Differential Equation (NODE). Both models perform accurately and are numerically stable in a posteriori tests. Furthermore, we explore the data requirements of the ML models by extracting physically relevant timescales of the complex system. We find that the ratio of the timescales of the minimum information required by the ML models to accurately capture the dynamics of the SST corresponds to the Reynolds number of the flow. The current framework provides the backbone to explore the capability of such models to capture the dynamics of higher-dimensional complex SST flows.

physics.flu-dyn↗

arXiv2020

Network broadcast analysis and control of turbulent flows

We present a network-based modal analysis technique that identifies key dynamical paths along which perturbations amplify over a time-varying base flow. This analysis is built upon the Katz centrality, which reveals the flow structures that can effectively spread perturbations over a time-evolving network of vortical interactions on the base flow. Motivated by the resolvent form of the Katz function, we take the singular value decomposition of the resulting communicability matrix, complementing the resolvent analysis for fluid flows. The right-singular vectors, referred to as the broadcast modes, give insights into the sensitive regions where introduced perturbations can be effectively spread and amplified over the entire fluid-flow network that evolves in time. We apply this analysis to a two-dimensional decaying isotropic turbulence. The broadcast mode reveals that vortex dipoles are important structures in spreading perturbations. By perturbing the flow with the principal broadcast mode, we demonstrate the utility of the insights gained from the present analysis to effectively modify the evolution of turbulent flows. The current network-inspired work presents a novel use of network analysis to guide flow control efforts, in particular for time-varying base flows.

physics.flu-dyn↗

arXiv2020

Identifying vortical network connectors for turbulent flow modification

We introduce a network (graph) theoretic community-based framework to extract vortical structures that serve the role of connectors for the vortical interactions in two- and three-dimensional isotropic turbulence. The present framework represents the vortical interactions on a network, where the vortical elements are viewed as the nodes and the vortical interactions are regarded as edges weighted by induced velocity. We identify closely interacting vortical elements as vortical network communities through community detection algorithms. We show that the inter- and intra-community interactions can be used to decompose the governing equation for the evolution of network nodes. These community-based interactions are used to identify the communities which have the strongest and weakest interactions amongst them. These vortical communities are referred to as connector and peripheral communities, respectively. We demonstrate the influence of the network-based structures to modify the dynamics of a collection of discrete point vortices. Taking advantage of the strong inter-community interactions, connector community can significantly modify the collective dynamics of vortices through the application of multiple impulse perturbations. We then apply the community-based framework to extract influential structures in isotropic turbulence. The connector and peripheral communities extracted from turbulent flows resemble shear-layer and vortex-core like structures, respectively. The influence of the connector structures on the flow field and their neighboring vortical structures is analyzed by adding impulse perturbations to the connectors in direct numerical simulations. The findings are compared with the cases of perturbing the strongest vortex tube and shear-layer regions. We find that perturbing the connector structures enhances local turbulent mixing beyond what are achieved by the other cases.

physics.flu-dyn↗

arXiv2019

Randomized methods to characterize large-scale vortical flow network

We demonstrate the effective use of randomized methods for linear algebra to perform network-based analysis of complex vortical flows. Network theoretic approaches can reveal the connectivity structures among a set of vortical elements and analyze their collective dynamics. These approaches have recently been generalized to analyze high-dimensional turbulent flows, for which network computations can become prohibitively expensive. In this work, we propose efficient methods to approximate network quantities, such as the leading eigendecomposition of the adjacency matrix, using randomized methods. Specifically, we use the Nyström method to approximate the leading eigenvalues and eigenvectors, achieving significant computational savings and reduced memory requirements. The effectiveness of the proposed technique is demonstrated on two high-dimensional flow fields: two-dimensional flow past an airfoil and two-dimensional turbulence. We find that quasi-uniform column sampling outperforms uniform column sampling, while both feature the same computational complexity.

math.NA↗

arXiv2018

Network community-based model reduction for vortical flows

A network community-based reduced-order model is developed to capture key interactions amongst coherent structures in high-dimensional unsteady vortical flows. The present approach is data-inspired and founded on network-theoretic techniques to identify important vortical communities that are comprised of vortical elements that share similar dynamical behavior. The overall interaction-based physics of the high-dimensional flow field is distilled into the vortical community centroids, considerably reducing the system dimension. Taking advantage of these vortical interactions, the proposed methodology is applied to formulate reduced-order models for the inter-community dynamics of vortical flows, and predict lift and drag forces on bodies in wake flows. We demonstrate the capabilities of these models by accurately capturing the macroscopic dynamics of a collection of discrete point vortices, and the complex unsteady aerodynamic forces on a circular cylinder and an airfoil with a Gurney flap. The present formulation is found to be robust against simulated experimental noise and turbulence due to its integrating nature of the system reduction.

physics.flu-dyn↗

arXiv2017

Airfoil wake modification with Gurney flap at Low-Reynolds number

The complex wake modifications produced by a Gurney flap on symmetric NACA airfoils at low Reynolds number are investigated. Two-dimensional incompressible flows over NACA 0000 (flat plate), 0006, 0012 and 0018 airfoils at a Reynolds number of $Re = 1000$ are analyzed numerically to examine the flow modifications generated by the flaps for achieving lift enhancement. While high lift can be attained by the Gurney flap on airfoils at high angles of attack, highly unsteady nature of the aerodynamic forces are also observed. Analysis of the wake structures along with the lift spectra reveals four characteristic wake modes (steady, 2S, P and 2P), influencing the aerodynamic performance. The effects of the flap over wide range of angles of attack and flap heights are considered to identify the occurrence of these wake modes, and are encapsulated in a wake classification diagram. Companion three-dimensional simulations are also performed to examine the influence of three-dimensionality on the wake regimes. The spanwise instabilities that appear for higher angles of attack are found to suppress the emergence of the 2P mode. The use of the wake classification diagram as a guidance for Gurney flap selection at different operating conditions to achieve the required aerodynamic performance is discussed.

physics.flu-dyn↗