arXiv subjects

Caglar Oskay

Publications and source records attributed to Caglar Oskay.

7 recordsLinked to original sources

arXiv2026

Variational Quantum Algorithms for Hyperelasticity: Incorporating Nonlinear Constitutive Behavior

This paper extends a recently proposed Variational Quantum Algorithm framework for nonlinear elasticity to a broader class of constitutive nonlinearities involving rational powers of the stretch. One-dimensional incompressible Ogden and Mooney-Rivlin models are employed as representative examples to demonstrate the proposed methodology. Nonlinear constitutive terms are transformed into forms compatible with the available quantum algorithmic primitives through the introduction of auxiliary variables and penalty constraints, yielding approximate solutions via a Variational Quantum Algorithm. An iterative correction strategy based on a sequence of Variational Quantum Algorithms is then introduced to improve solution accuracy. A Numerical example demonstrates the proposed approach.

quant-ph↗

arXiv2026

PHASE: Pauli Hierarchical Assembly on Subdivided Elements for Quantum-Compatible Operator Synthesis

Efficiently decomposing finite element stiffness matrices into the Pauli basis is challenging due to the exponential growth of Pauli strings with problem size. A naive Pauli expansion requires $\Theta(8^{\lceil \log_2 N \rceil})$ operations, where $N$ denotes the number of degrees of freedom, rendering direct decomposition infeasible for large systems. Existing approaches exploit algebraic sparsity or operator structure but do not incorporate the geometric organization intrinsic to finite element discretizations, and consequently exhibit poor scaling for stiffness matrices. To address this problem, we introduce PHASE, a hierarchical, geometry-aware Pauli decomposition algorithm that leverages recursive mesh partitioning to organize element contributions across multiple spatial scales. PHASE employs a hybrid strategy that combines full- and reduced-space Tensorized Pauli Decomposition with Fast Walsh-Hadamard Transform-based aggregation to assemble global Pauli coefficients efficiently. We show that this approach yields a dimension-dependent reduction in the exponential scaling exponent of Pauli assembly asymptotic complexity relative to existing methods, reducing the cost from $2^{2{\lceil \log_2 N \rceil}}$ to $2^{\gamma_d{\lceil \log_2 N \rceil}}$ with $\gamma_d < 2$ under standard mesh regularity and balanced partition assumptions. These results substantially improve the feasibility of quantum-compatible operator synthesis for large-scale finite element models.

quant-ph↗

arXiv2026

A Variational Quantum Algorithm for Nonlinear Finite Element Analysis of Hyperelastic Materials

This manuscript explores a variational quantum formulation for nonlinear elasticity problems arising from hyperelastic material models. The approach leverages the potential energy structure of hyperelasticity and employs a hybrid quantum classical framework in which the energy functional is evaluated using parameterized quantum circuits and optimized through classical routines. To enable a hybrid (classical quantum implementation), polynomial approximations of the nonlinear terms in strain energy density are introduced, yielding a representation compatible with variational quantum algorithms. The methodology is demonstrated on a special case of the NeoHookean material model in a one dimensional setting using finite element discretizations with first and second order shape functions and nonhomogeneous boundary conditions. Numerical experiments investigate the influence of the polynomial approximation order on the accuracy and efficiency of the proposed approach, illustrating its feasibility for near-term quantum devices.

quant-ph↗

arXiv2025

Variational multiscale enrichment method for dynamic response of hyperelastic materials at finite deformation

In this manuscript, we extend the variational multiscale enrichment (VME) method to model the dynamic response of hyperelastic materials undergoing large deformations. This approach enables the simulation of wave propagation under scale-inseparable conditions, including short-wavelength regimes, while accounting for material and geometric nonlinearities that lead to wave steepening or flattening. By employing an additive decomposition of the displacement field, we derive multiscale governing equations for the coarse- and fine-scale problems, which naturally incorporate micro-inertial effects. The framework allows the discretization of each unit cell with a patch of coarse-scale elements, which is essential to accurately capture wave propagation in short-wavelength regimes. An operator-split procedure is used to iteratively solve the semi-discrete equations at both scales until convergence is achieved. The coarse-scale problem is integrated explicitly, while the fine-scale problem is solved using either explicit or implicit time integration schemes, including both dissipative and non-dissipative methods. Numerical examples demonstrate that multiscale dissipative schemes effectively suppress spurious oscillations. The multiscale framework was applied to investigate how material and geometric nonlinearities, along with elastic stiffness contrast in heterogeneous microstructures, influence key wave characteristics such as dispersion, attenuation, and steepening. This multiscale computational framework provides a foundation for studying the dynamic response of architected materials.

cs.CE↗

arXiv2025

Mixed Precision Photonic Computing with 3D Electronic-Photonic Integrated Circuits

We propose advancing photonic in-memory computing through three-dimensional photonic-electronic integrated circuits using phase-change materials (PCM) and AlGaAs-CMOS technology. These circuits offer high precision (greater than 12 bits), scalability (greater than 1024 by 1024), and massive parallelism (greater than 1 million operations) across the wavelength, spatial, and temporal domains at ultra-low power (less than 1 watt per PetaOPS). Monolithically integrated hybrid PCM-AlGaAs memory resonators handle coarse-precision iterations (greater than 5-bit most significant bit precision) through reversible PCM phase transitions. Electro-optic memristive tuning enables fine-precision updates (greater than 8-bit least significant bit precision), resulting in over 12-bit precision for in-memory computing. The use of low-loss PCM (less than 0.01 dB per cm) and electro-optical tuning yields memristive optical resonators with high Q-factors (greater than 1 million), low insertion loss, and low tuning power. A W by W photonic tensor core composed of PCM-AlGaAs memresonators performs general matrix multiplication (GEMM) across W wavelengths from optical frequency combs, with minimal crosstalk and loss. Hierarchical scaling in the wavelength domain (K) and spatial domain (L) enables this system to address high-dimensional (N) scientific partial differential equation (PDE) problems in a single constant-time operation, compared to the conventional quadratic-time (N squared) computational complexity.

physics.optics↗

arXiv2024

An Implementation of the Finite Element Method in Hybrid Classical/Quantum Computers

This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the classical FEM procedure to perform the unitary decomposition of the stiffness matrix and employs generator functions to design explicit quantum circuits corresponding to the unitaries. Q-FEM keeps the structure of the finite element discretization intact allowing for the use of variable element lengths and material coefficients in FEM discretization. The proposed method is tested on a steady-state heat equation discretized using linear and quadratic shape functions. Numerical verification studies are performed on the IBM QISKIT simulator and it is demonstrated that Q-FEM is effective in converging to the correct solution for a variety of problems and model discretizations, including with different element lengths, variable coefficients, and different boundary conditions. The formalism developed herein is general and can be extended to problems with higher dimensions. However, numerical examples also demonstrate that the number of parameters for the variational ansatz scale exponentially with the number of qubits, and increases the odds of convergence. Moreover, the deterioration of system conditioning with problem size results in barren plateaus and convergence difficulties.

quant-ph↗

arXiv2021

Multiscale Reduced-Order Modeling of a Titanium Skin Panel Subjected to Thermo-Mechanical Loading

This manuscript presents the formulation, implementation, calibration and application of a multiscale reduced-order model to simulate a titanium panel structure subjected to thermo-mechanical loading associated with high-speed flight. The formulation is based on the eigenstrain-based reduced-order homogenization model (EHM) and further considers thermal strain as well as temperature dependent material properties and evolution laws. The material microstructure (i.e., at the scale of a polycrystalline representative volume element (RVE)) and underlying microstructural mechanisms are directly incorporated and fully coupled with a structural analysis, allowing concurrently probing the response at the structural scale and the material microscale. The proposed approach was fully calibrated using a series of uniaxial tension tests of Ti-6242S at a wide range of temperatures and two different strain rates. The calibrated model is then adopted to study the response of a generic aircraft skin panel subjected to thermo-mechanical loading associated with high-speed flight. The analysis focuses on demonstrating the capability of the model to predict not only the structural scale response, but simultaneously the microscale response, and further studies the effects of temperature and texture on the response.

cs.CE↗