Hamiltonian learning (HL), enabling precise estimation of system parameters and underlying dynamics, plays a critical role in characterizing quantum systems. However, conventional HL methods face challenges in noise robustness and resource efficiency, especially under limited measurements. In this work, we present Inverse Physics-Informed Neural Networks for Hamiltonian Learning (iPINN-HL), an approach that incorporates the Schrödinger equation as a soft constraint via a loss function penalty into the ML procedure. This formulation allows the model to integrate both observational data and known physical laws to infer Hamiltonian parameters with greater accuracy and resource efficiency. We benchmark iPINN-HL against a deep-neural-network-based quantum state tomography method [denoted as DNN-HL (Deep Neural Network for Hamiltonian Learning)] and demonstrate its effectiveness across several different scenarios, including one-dimensional spin chains, cross-resonance gate calibration, crosstalk identification, and real-time compensation to parameter drift. Our results show that iPINN-HL can approach the Heisenberg limit and exhibits robustness to noises, while outperforming DNN-HL in accuracy and resource efficiency. Therefore, iPINN-HL is a powerful and flexible framework for quantum system characterization for practical tasks.

Quantum computing faces significant challenges from decoherence and noise, which limit the practical implementation of quantum algorithms. While substantial progress has been made in improving individual qubit coherence times, the collective behavior of interconnected qubit systems remains incompletely understood. The connectivity architecture plays a crucial role in determining overall system susceptibility to environmental noise, yet systematic characterization of this relationship has been hindered by computational complexity. We develop a machine learning framework that bridges graph features with quantum device characterization to predict decoherence lifetime directly from connectivity patterns. By representing quantum architectures as connected graphs and using 14 topological features as input to supervised learning models, we achieve accurate lifetime predictions with $R^2>0.96$ for both superconducting and semiconductor platforms. Our analysis reveals fundamentally distinct decoherence mechanisms: superconducting qubits show high sensitivity to global connectivity measures (betweenness centrality ${\delta }_1=0.484$, spectral entropy ${\delta }_1=0.480$), while semiconductor quantum dots exhibit exceptional sensitivity to system scale (node count ${\delta }_2=0.919$, importance = 1.860). The complete failure of cross-platform model transfer ($R^2$ scores of −0.39 and −433.60) emphasizes the platform-specific nature of optimal connectivity design. Our approach enables rapid assessment of quantum architectures without expensive simulations, providing practical guidance for noise-optimized quantum processor design.