arXiv subjects

Ziv Chen

Publications and source records attributed to Ziv Chen.

5 recordsLinked to original sources

arXiv2026

Hybrid Quantum-Classical PINNs for Scientific Computing: A Multi-GPU Open-Source Framework

We present QPINNACLE, an open-source computational framework for physics-informed neural networks (PINNs) that integrates modern training strategies, multi-GPU acceleration, and hybrid quantum-classical architectures within a unified modular workflow. The framework enables systematic evaluation of PINN performance across benchmark problems including 1D hyperbolic conservation laws, incompressible flows, and electromagnetic wave propagation. It supports a range of architectural and training enhancements, including Fourier feature embeddings, random weight factorization, strict boundary condition enforcement, adaptive loss balancing, curriculum training, and second-order optimization strategies, with extensibility to additional methods. We provide a comprehensive benchmark study quantifying the impact of these methods on convergence, accuracy, and computational cost, and analyze distributed data parallel scaling in terms of runtime and memory efficiency. In addition, we extend the framework to hybrid quantum-classical PINNs and derive a formal estimate for circuit-evaluation complexity under parameter-shift differentiation. Results highlight the sensitivity of PINNs to architectural and training choices, confirm their high computational cost relative to classical solvers, and identify regimes where hybrid quantum models offer improved parameter efficiency. QPINNACLE provides a foundation for benchmarking physics-informed learning methods and guiding future developments through quantitative assessment of their trade-offs.

cs.LG↗

arXiv2025

Spectral Bottleneck in Sinusoidal Representation Networks: Noise is All You Need

This work identifies and attempts to address a fundamental limitation of implicit neural representations with sinusoidal activation. The fitting error of SIRENs is highly sensitive to the target frequency content and to the choice of initialization. In extreme cases, this sensitivity leads to a spectral bottleneck that can result in a zero-valued output. This phenomenon is characterized by analyzing the evolution of activation spectra and the empirical neural tangent kernel (NTK) during the training process. An unfavorable distribution of energy across frequency modes was noted to give rise to this failure mode. Furthermore, the effect of Gaussian perturbations applied to the baseline uniformly initialized weights is examined, showing how these perturbations influence activation spectra and the NTK eigenbasis of SIREN. Overall, initialization emerges as a central factor governing the evolution of SIRENs, indicating the need for adaptive, target-aware strategies as the target length increases and fine-scale detail becomes essential. The proposed weight initialization scheme (WINNER) represents a simple ad hoc step in this direction and demonstrates that fitting accuracy can be significantly improved by modifying the spectral profile of network activations through a target-aware initialization. The approach achieves state-of-the-art performance on audio fitting tasks and yields notable improvements in image fitting tasks.

eess.AS↗

arXiv2025

Quantum Singular Value Transformation for Solving the Time-Dependent Maxwell's Equations

This work presents a quantum algorithm for solving linear systems of equations of the form $\mathbf{A}{\frac{\mathbf{\partial f}}{\mathbf{\partial x}}} = \mathbf{B}\mathbf{f}$, based on the Quantum Singular Value Transformation (QSVT). The algorithm uses block-encoding of $A$ and applies an 21st-degree polynomial approximation to the inverse function $f(x) = 1/x$, enabling relatively shallow quantum circuits implemented on 9 qubits, including two ancilla qubits, corresponding to a grid size of 128 points. Phase angles for the QSVT circuit were optimized classically using the Adagrad gradient-based method over 100 iterations to minimize the solution cost. This approach was simulated in PennyLane and applied to solve a 1D benchmark case of Maxwell's equations in free space, with a Gaussian pulse as the initial condition, where the quantum-computed solution showed high fidelity of more than 99.9% when compared to the normalized classical solution. Results demonstrate the potential of QSVT-based linear solvers on simulators with full quantum state access. However, practical hardware implementations face challenges because accessing the complete quantum state is infeasible. This limitation restricts applicability to cases where only $O({poly}(n))$ observables are needed. These findings highlight both the promise and current limitations of using quantum algorithms, such as QSVT, to solve linear systems of equations, and they point to the need for the development of measurement-efficient algorithms for near-term quantum devices.

quant-ph↗

arXiv2025

Quantum Physics-Informed Neural Networks for Maxwell's Equations: Circuit Design, "Black Hole" Barren Plateaus Mitigation, and GPU Acceleration

Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving partial differential equations (PDEs) by embedding the governing physics into the loss function associated with a deep neural network. In this work, a Quantum PINNs (QPINN) framework is proposed to solve two-dimensional (2D) time-dependent Maxwell's equations. Our approach utilizes a parametrized quantum circuit in conjunction with the classical neural network architecture and enforces physical laws, including a global energy conservation principle, during training. A quantum simulation library, TorQ, was developed to efficiently compute circuit outputs and derivatives by leveraging GPU acceleration based on PyTorch, enabling end-to-end training of the QPINN. The method was evaluated on two 2D electromagnetic wave propagation problems: one in free space (vacuum) and the other has an added dielectric medium. Multiple quantum circuit ans\"atze, input scales, and an added loss term were compared in a thorough ablation study. Furthermore, recent techniques to enhance PINN convergence, including random Fourier feature embeddings and adaptive time weighting, have been incorporated. Our results demonstrate that the QPINN achieves accuracy comparable to, and even greater than, the classical PINN baseline, while using a significantly smaller number of trainable parameters. This study also shows that adding an energy conservation term to the loss stabilizes training and improves the physical fidelity of the solution in the lossless free-space case. This added term helps mitigate a new kind of barren plateau (BP) related phenomenon - ``black hole'' (BH) loss landscape for the quantum experiments in that scenario. By optimizing the quantum-circuit ansatz and embedding energy-conservation constraints, our QPINN achieves up to a 19% higher accuracy on 2D Maxwell benchmark problems compared to a classical PINN.

quant-ph↗

arXiv2025

PINNs for Solving Unsteady Maxwell's Equations: Convergence Issues and Comparative Assessment with Compact Schemes

Physics-Informed Neural Networks (PINNs) have recently emerged as a promising alternative for solving partial differential equations, offering a mesh-free framework that incorporates physical laws directly into the learning process. In this study, we explore the application of PINNs for solving unsteady Maxwell's equations and compare their performance with two established numerical methods: the Finite-Difference Time-Domain (FDTD) method and a compact Pade scheme with filtering. Three benchmark problems are considered, ranging from 1D free-space wave propagation to 2D Gaussian pulses in periodic and dielectric media. We assess the effectiveness of convergence-enhancing strategies for PINNs, including random Fourier features, spatio-temporal periodicity, and temporal causality training. An ablation study highlights that architectural choices must align with the underlying physics. Additionally, we employ a Neural Tangent Kernel framework to examine the spatio-temporal convergence behavior of PINNs. Results show that convergence rates correlate with error over time but not in space, revealing a limitation in how training dynamics allocate learning effort. Overall, this study demonstrates that PINNs, when properly configured, can match or surpass traditional solvers in accuracy and flexibility, though challenges remain in addressing spatial inhomogeneity and adapting training to localized complexity.

physics.comp-ph↗