arXiv subjects

Raghavendra Dheeraj Peddinti

Publications and source records attributed to Raghavendra Dheeraj Peddinti.

3 recordsLinked to original sources

arXiv2026

Quantum-inspired space-time PDE solver and dynamic mode decomposition

The curse of dimensionality is ubiquitous in both numerical and data-driven methods. This is particularly severe for space-time methods, which treat the combined space-time domain simultaneously. We investigate the effectiveness of a quantum-inspired approach in alleviating this curse, both for solving PDEs and making data-driven predictions. We achieve this goal by treating both spatial and temporal dimensions within a single matrix product state (MPS) encoding. First, we benchmark our MPS space-time solver for both linear and nonlinear PDEs, observing that the MPS ansatz accurately captures the underlying spatio-temporal correlations while having significantly fewer degrees of freedom. Second, we develop an MPS-DMD algorithm for accurate long-term predictions of nonlinear systems, with runtime scaling logarithmically with both spatial and temporal resolution. We also demonstrate an application where both methods can be combined for cheap and accurate prediction of long-term dynamics. This research highlights the role of tensor networks in developing effective, interpretable models that bridge the gap between numerical methods and data-driven approaches.

physics.comp-ph↗

arXiv2026

Compression, simulation, and synthesis of turbulent flows with tensor trains

Numerical simulations of turbulent fluids are paramount to real-life applications, from predicting and modeling flows to diagnostic purposes in engineering. However, they are also computationally challenging due to their intrinsically non-linear dynamics, which require a very high spatial resolution to accurately describe them. A promising idea is to represent flows on a discrete mesh using tensor trains (TTs), featuring a convenient scaling of the number of parameters with the mesh size. However, it is unclear how the compression power of TTs is affected by the complexity of the flows, as measured by the Reynolds number. In fact, no comprehensive analysis of how the TT representation affects the turbulent properties has yet been carried out. We fill this gap by analyzing TTs as an Ansatz to compress, simulate, and generate 3D snapshots with turbulent-like features. Specifically, we first investigate the effect of TT compression on key turbulence signatures, such as the energy spectrum, the PDF of velocity increments, and flatness. Second, we extend the 2D TT-solver introduced in [1] to a 3D cubic domain with periodic boundary conditions. We use it to simulate the incompressible Navier-Stokes dynamics at $Re_λ=315$ for a total of 9-10 Kolmogorov turnover times, showcasing the numerical stability of the TT-solver in fully developed turbulent regimes. Third, we develop a TT algorithm to synthesize artificial snapshots that exhibit turbulent-like features, with a logarithmic cost in the mesh size. Our analysis demonstrates the ability of the TT representation to capture the characteristic features of turbulence. This offers a powerful quantum-inspired toolkit for the computational treatment of turbulent flows.

physics.flu-dyn↗

arXiv2025

Technical report on a quantum-inspired solver for simulating compressible flows

This document presents a quantum-inspired solver for 2D Euler equations, accepted at the final phase of the Airbus-BWM Group Quantum Computing Challenge (ABQCC) 2024. We tackle the case study of Quantum Solvers for Predictive Aeroacoustic and Aerodynamic modeling tasks. We propose a tensor network based solver that scales polylogarithmically with the mesh size, in both runtime and memory. This provides a promising avenue for tackling the curse of dimensionality that plagues the direct numerical simulations in the field of computational fluid dynamics.

physics.flu-dyn↗