arXiv subjects

Eunsik Choi

Publications and source records attributed to Eunsik Choi.

3 recordsLinked to original sources

arXiv2026

Quantum Homotopy Perturbation Method to Solve Nonlinear Partial Differential Equations

Solving nonlinear partial differential equations (PDEs) is important in various scientific and engineering applications. Recently, quantum computing was introduced as an alternative computational paradigm for solving nonlinear PDEs. In this paper, a new method called the quantum homotopy perturbation method (QHPM) is proposed to improve the scalability of solving nonlinear PDEs through two aspects. First, the dimension of the Hilbert space remains the same after the nonlinear PDE is linearized through the homotopy perturbation. Second, the solutions are obtained with a variational quantum simulation framework, where the number of qubits is decreased with functional encoding and the depth of parametrized circuits is reduced. The additional contribution of this paper is the introduction of new criteria for selecting the homotopy series truncation order and circuit depth for cost-effective QHPM. The proposed approach is demonstrated with several examples, including the vorticity transport equation and the reduced magnetohydrodynamics equations.

quant-ph↗

arXiv2026

Lindbladian Homotopy Analysis Method to Solve Nonlinear Partial Differential Equations

Quantum scientific computing is to solve engineering and science problems such as simulation and optimization on quantum computers. Solving ordinary and partial differential equations (PDEs) is essential in simulations. However, existing quantum approaches to solve nonlinear PDEs suffer from the issues of curse of dimensionality and convergence during the linearization process. In this paper, a Lindbladian homotopy analysis method (LHAM) is proposed as a quantum differential equation solver to simulate non-unitary and nonlinear dynamics. The original nonlinear problem is first converted to a recursive sequence of linear PDEs with the homotopy analysis method and reformulated as a higher-dimensional lower block triangular linear homogeneous autonomous system. The solution is then embedded in the density matrix and obtained through the Lindbladian dynamics simulation. Compared to other methods such as Carleman linearization and the Koopman-von Neumann approach where the dimension of Hilbert space increases polynomially with the inverse of truncation error, the Hilbert space dimension in LHAM increases only logarithmically. LHAM is demonstrated with nonlinear PDEs including Burgers' equation and reduced magnetohydrodynamics equations.

math.NA↗

arXiv2026

Muscle Synergy Priors Enhance Biomechanical Fidelity in Predictive Musculoskeletal Locomotion Simulation

Human locomotion emerges from high-dimensional neuromuscular control, making predictive musculoskeletal simulation challenging. We present a physiology-informed reinforcement-learning framework that constrains control using muscle synergies. We extracted a low-dimensional synergy basis from inverse musculoskeletal analyses of a small set of overground walking trials and used it as the action space for a muscle-driven three-dimensional model trained across variable speeds, slopes and uneven terrain. The resulting controller generated stable gait from 0.7-1.8 m/s and on $\pm$ 6$^{\circ}$ grades and reproduced condition-dependent modulation of joint angles, joint moments and ground reaction forces. Compared with an unconstrained controller, synergy-constrained control reduced non-physiological knee kinematics and kept knee moment profiles within the experimental envelope. Across conditions, simulated vertical ground reaction forces correlated strongly with human measurements, and muscle-activation timing largely fell within inter-subject variability. These results show that embedding neurophysiological structure into reinforcement learning can improve biomechanical fidelity and generalization in predictive human locomotion simulation with limited experimental data.

cs.LG↗