Research

AI/ML for Science

Deep learning at scale for scientific problems, including transformer and Vision Transformer (ViT) architectures, neural operators, diffusion models, and foundation models, trained with multi-node distributed (data-, tensor-, sequence-parallel) workflows on DOE leadership GPU systems. Applications span turbulence modeling, biomedical imaging, and physics-informed surrogate modeling.

Selected publications:

N. M. Nafi, I. Lyngaas, M. Gopalakrishnan Meena, S. de Bruyn Kops, A. Kashi, W. Brewer, and M. R. Norman, "Efficient Vision Transformer-based Surrogate for Scalable Pressure Prediction in Incompressible Turbulent Flows," ICML AI for Science Workshop, 2026
J. Yin, P. Mijanur, M. P. Laiu, M. Gopalakrishnan Meena, et al., "Pixel-Resolved Long-Context Learning for Turbulence at Exascale: Resolving Small-scale Eddies Toward the Viscous Limit," IPDPS, 2026
M. Gopalakrishnan Meena et al., "Machine-learned closure of URANS for stably stratified turbulence: connecting physical timescales & data hyperparameters of deep time-series models," Machine Learning: Science and Technology, 5 (4), 045063, 2024
I. Lyngaas, E. Calabrese, M. Gopalakrishnan Meena, and X. Wang, "Efficient Distributed Sequence Parallelism for Transformer-based Image Segmentation," Electronic Imaging / HPC for Imaging, 2024

Quantum Computing for Science

Quantum and quantum-classical hybrid algorithms for partial differential equations, with a focus on fluid dynamics. Work spans algorithm design (quantum linear solvers, tensor-network methods, quantum phase estimation), execution on real quantum hardware (IBM, IonQ, Quantinuum, IQM), and integration with HPC systems. I lead OLCF's Quantum Computing for Fluid Dynamics Working Group.

Selected publications:

M. Gopalakrishnan Meena, V. Jones, Y. Zhang, and X. Gao, "A Tensor Network-Based Quantum Algorithm for the Nonlinear 1D Burgers' Equation," AIAA SCITECH 2026, AIAA 2026-1932 (2026 AIAA Fluid Dynamics Best Paper)
C. Lu, M. Gopalakrishnan Meena, and K. C. Gottiparthi, "LuGo: an Enhanced Quantum Phase Estimation Implementation," Future Generation Computer Systems, 108270, 2025
M. Gopalakrishnan Meena et al., "Solving the Hele-Shaw flow using the Harrow-Hassidim-Lloyd algorithm on superconducting devices: A study of efficiency and challenges," Physics of Fluids, 36 (10): 101705, 2024
T. Beck et al., "Integrating Quantum Computing Resources into Scientific HPC Ecosystems," Future Generation Computer Systems, 161, 11-25, 2024

AI-Quantum Bridge

Emerging research at the intersection of AI/ML and quantum computing, exploring how modern AI methods can accelerate quantum algorithm design and how quantum representations can augment classical model architectures. Current efforts include a generative AI approach to quantum algorithm discovery (AI for QC) and augmentation of classical models with quantum circuits (QC for AI).

Network Science

Graph theory and tools from network science applied to characterize and model the behavior of complex systems in fluid dynamics and biology, including vortical interactions in turbulent and wake flows, and fungal-host metabolic interactions.

Selected publications:

M. Gopalakrishnan Meena and K. Taira, "Identifying vortical network connectors for turbulent flow modification", Journal of Fluid Mechanics, 915, A10, 2021
M. Gopalakrishnan Meena, M. J. Lane et al., "A glimpse into the fungal metabolomic abyss: Novel network analysis reveals relationships between exogenous compounds and their outputs", PNAS Nexus, Volume 2, Issue 10, 2023

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