arXiv subjects

Muhammad Idrees Khan

Publications and source records attributed to Muhammad Idrees Khan.

5 recordsLinked to original sources

arXiv2026

Autonomous Lindblad Realizability of Nonunitary Linear Dynamics with a Carleman Lattice Boltzmann Application

Carleman lifting converts nonlinear polynomial dynamics into finite linear systems, but the resulting truncations are generally nonunitary and need not correspond to physical quantum evolution. We prove that a finite linear endpoint admits an autonomous Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) realization on vacuum coherences if and only if it is invertible and power bounded. The construction is explicit and realizes the nonunitary map directly as open-system dynamics, with no endpoint postselection and with one encoding and one decoding over repeated timesteps. We apply the result to the complete D2Q9 multiple-relaxation-time lattice Boltzmann (LB) timestep by compiling collision and periodic streaming into a single Carleman endpoint. The resulting GKSL evolution reproduces the classical Carleman trajectory over multiple timesteps, while the remaining discrepancy from nonlinear LB dynamics is the expected Carleman truncation error. The result establishes a general criterion for autonomous open-quantum realization of finite nonunitary dynamics, with Carleman--LB dynamics as a concrete example.

physics.comp-ph↗

arXiv2026

Quadrature-Aware Complex-Linear Neural Operator for Boundary-to-Field Prediction in Resonant Acoustics

Repeated prediction of acoustic fields from spatially distributed boundary excitation is computationally expensive when each source realization requires a new wave simulation. This work introduces a quadrature-aware complex-linear boundary operator (CLBO) that maps complex normal velocity on a vibrating surface to complex pressure at receiver locations. The model couples learned source and receiver basis functions through an explicit complex surface-quadrature contraction, so the boundary excitation enters linearly by construction. This preserves complex superposition, homogeneity, and zero response to zero excitation, while representing the source through coordinates, normals, and quadrature weights rather than a fixed flattened input vector. Reference data were generated using a verified three-dimensional multiple-relaxation-time (MRT) lattice Boltzmann solver and stored in a solver-agnostic boundary-to-field format. CLBO was compared with a fixed-sensor complex DeepONet under matched case splits and optimization settings, with additional tests of structural consistency, receiver-coordinate interpolation, source discretization, source-family holdout, label efficiency, physics-informed ablations, unseen source mixtures, and computational cost. Across five training seeds, CLBO achieved a mean complex relative field error of 0.184 +/- 0.00771, compared with 0.367 +/- 0.00742 for DeepONet. Its measured source-superposition error was 1.31 x 10^-7, and its mean error on newly simulated mixed-source cases was 0.237, compared with 0.415 for DeepONet. Inference was 1.83 x 10^4 faster than the reference calculation for the reported query size. These results show that enforcing the known complex-linear boundary-to-field structure improves physical consistency and generalization under distributed acoustic excitation.

physics.flu-dyn↗

arXiv2026

Deterministic Realization of Classical Dissipation on Quantum Computers

Lattice Boltzmann (LB) on quantum devices must reconcile unitary gate evolution with the dissipative \emph{collision} step. In the multiple-relaxation-time (MRT) class, we work in the common setting of \emph{modewise diagonal} moment relaxation, $\delta m_r'=\lambda_r\,\delta m_r$ with $\lambda_r\in[-1,1]$ (overrelaxation if $\lambda_r<0$). Embedding that contraction in a unitary by block encoding or a linear combination of unitaries (LCU) typically yields subunitary success probability that decays multiplicatively across modes, sites, and time, a key bottleneck for quantum LB. \emph{For the dissipative MRT block alone} we give a \emph{block-encoding-free} construction: a signed \emph{two-rail} population encoding, then a completely positive trace-preserving (CPTP) map (per-rail amplitude damping with survival $|\lambda_r|$ and, if $\lambda_r<0$, a rail SWAP) so that, after the decode, the map agrees with classical MRT relaxation exactly (expectations of the rail number operators, common encoding--decode scale). Trace preservation gives success probability $1$ for that substage. The main result is the dissipative MRT block; construction of the equilibrium moment vector~$m^{\mathrm{eq}}=Mf^{\mathrm{eq}}$ (prescribed~$f^{\mathrm{eq}}$, host moment matrix~$M$; notation as in Section~\ref{subsec:generic-mrt}), moment transforms, streaming, and boundaries are composed with it as in a standard host pipeline and lie outside the scope of the formal theorem. Hybrid and fully coherent encodings, adaptive scales, Carleman-based context, and a one-rail no-go in the same nonnegative population framework are in the main text. Audits of the open-channel map on a long LBM collide-stream simulation and on stencil-free inputs both match the target to machine precision.

physics.comp-ph↗

arXiv2026

Physics-Constrained Neural Closure for Lattice Boltzmann Large-Eddy Simulation

We present a physics-constrained, data-driven subgrid-scale (SGS) stress closure for large-eddy simulation (LES) in the lattice Boltzmann method (LBM). Trained on filtered-downsampled (FD) data from LBM direct numerical simulation (DNS) of forced homogeneous isotropic turbulence (FHIT) spanning multiple filter widths, a compact neural network maps nine macroscopic derivative inputs - six strain-rate and three vorticity components - to the six independent components of the SGS stress tensor; a deviatoric projection is applied post-inference to obtain the traceless stress used in the solver. Training combines a stress data loss with physics terms for SGS energy-transfer (Pi) matching, rotational equivariance under cube rotations, and compatibility of the implied SGS forcing with the divergence-based coupling. The predicted stress is coupled to the solver through a split strategy: a dissipative, strain-aligned contribution is represented through an effective-viscosity projection, while the remaining anisotropic residual is applied through a forcing term. This construction is intended to retain both backscatter (via the effective viscosity) and non-dissipative anisotropic effects (via the residual forcing), while remaining compatible with LBM deployment. In the cases considered here, a priori results show good agreement with FD references across stress components and SGS-transfer statistics, and a posteriori rollouts improve several energetic and statistical measures relative to static and dynamic Smagorinsky baselines. A preliminary transfer test in turbulent channel flow is also reported without retraining. Finally, we demonstrate production deployment via ONNX Runtime, with throughput comparable to a dynamic Smagorinsky baseline in the tested configuration.

physics.flu-dyn↗

arXiv2025

Validating the Boltzmann approach to the Large-Eddy simulations of forced homogeneous incompressible turbulence

The simulation of turbulent flows remains a central challenge, as even our most powerful computers cannot resolve the finest scales of motion in many flows of practical interest. As a result, the effects of unresolved scales on large eddies must be modelled via closures and coarse-graining procedures. Large-eddy simulation (LES) traditionally coarse-grains Navier-Stokes equations using Smagorinsky's effective viscosity model. This has the merit of simplicity but fails to account for strong non-equilibrium effects, as they typically arise in most flows in the vicinity of solid walls, the reason being that the notion of eddy viscosity assumes scale separation between small and large eddies, an assumption that fails for high-Reynolds flows far from equilibrium. The lattice Boltzmann method (LBM) offers an alternative by coarse-graining at the kinetic level, potentially capturing non-equilibrium effects beyond reach of hydrodynamic closures. This paper addresses whether LBM-Smagorinsky LES of forced homogeneous isotropic turbulence (FHIT) exhibits kinetic behavior. We test whether the turbulent Knudsen number $K_t$, measuring scale separation, reaches order one (kinetic regime) or remains asymptotically small (hydrodynamic regime). Using reference DNS ($800^3$) and iso-Reynolds LES ($100^3$) at $Re = 2 \times 10^4$, we quantify $K_t$ via spatial maps, temporal statistics, energy spectra, and higher-order moments. Results show $K_t \sim O(10^{-3})$, strictly positive without negative excursions, with spectra and flatness following canonical LES behavior. We conclude that despite its kinetic formulation, LBM-Smagorinsky LES operates in the hydrodynamic regime, with small FHIT eddies remaining in local equilibrium with larger ones, validating Smagorinsky viscosity and confirming that LBM-LES functions as conventional hydrodynamic LES while preserving LBM efficiency and locality.

physics.flu-dyn↗