port-hamiltonian system learning

This work addresses the joint learning of port-Hamiltonian system models and their associated energy-shaping controllers directly from trajectory data to achieve stable, interpretable, and robust control. The authors propose a physics-informed co-learning framework that parameterizes both the port-Hamiltonian dynamics and the energy-balancing passivity-based control structure using neural networks. By integrating alternating optimization, policy-aware data collection, and dissipativity regularization, the method enables, for the first time, end-to-end co-learning of the model and controller. Embedded physical priors ensure interpretability and enhance sim-to-real transfer robustness. The approach is validated on planar and torsional pendulum systems for both regulation and swing-up tasks, guaranteeing intrinsic passivity and theoretical stability of the closed-loop system.

This work proposes the PHAST architecture for discrete-time series observed only in generalized coordinates (q-only), explicitly separating conservative and dissipative dynamics within a port-Hamiltonian framework. By leveraging Strang splitting for time evolution and integrating low-rank positive semi-definite/definite parameterizations with three knowledge-based modeling paradigms, the method achieves both long-term predictive stability and physical parameter identifiability. Notably, it is the first to reveal the gauge freedom inherent in unanchored parameter identification under q-only observations. Evaluated across 13 benchmark systems spanning mechanical, electrical, and molecular domains, PHAST significantly outperforms existing approaches and accurately recovers physically meaningful system parameters when sufficient structural priors are available.

Purely data-driven neural networks for modeling nonlinear dynamical systems suffer from physical implausibility, poor extrapolation capability, and numerical instability. Method: We propose the first neural architecture deeply integrating port-Hamiltonian (pH) structure, explicitly embedding pH energy flow and structural constraints into the network design. This ensures global Lyapunov stability of the learned dynamics and encodes energy conservation/dissipation priors via physics-constrained parameterization, stability-aware regularization, and differentiable modeling. Contribution/Results: The method significantly improves generalization and numerical robustness under sparse-data regimes. Experiments demonstrate consistent superiority over purely data-driven baselines across multi-physics surrogate modeling tasks—achieving higher accuracy, enhanced long-term stability, and physically consistent predictions. Our approach establishes a new paradigm for physics-guided learning in safety-critical applications.

This work addresses the limitations of data-driven methods in capturing conservation laws of dynamical systems, which hinder generalization and long-term prediction accuracy. Existing port-Hamiltonian neural networks (PHNNs) often compromise energy-preserving properties due to non-structure-preserving discretization schemes. To overcome this, we propose the first integration of a power-preserving second-order discrete gradient method into PHNNs, rigorously maintaining the port-Hamiltonian structure. Our approach further incorporates Jacobian regularization and explicit modeling of nonlinear dissipation. Experiments on the harmonic oscillator, Duffing oscillator, and self-sustained oscillator demonstrate that the proposed method significantly outperforms equivalent-order Runge–Kutta discretizations, achieving notable improvements in both energy conservation and trajectory prediction accuracy. We also provide a systematic evaluation of the impact of two equivalent port-Hamiltonian formulations.

Quantum circuit overhead for ground-state energy estimation in Hamiltonian simulation remains prohibitively high, especially on near-term noisy intermediate-scale quantum (NISQ) devices. Method: This work proposes a quantum circuit optimization framework tailored to the Trotter–Suzuki product formula, integrating three orthogonal, composable techniques: (1) gate-template simplification of individual Trotter blocks; (2) identification and parallel execution of commuting controlled rotations; and (3) commutativity-aware, hardware-constrained gate-level scheduling. The approach synergistically combines commutativity analysis, controlled-rotation compilation, and circuit-level optimization. Contribution/Results: Experiments demonstrate that the framework significantly reduces circuit depth and total gate count—without increasing asymptotic algorithmic complexity—thereby enhancing practical execution efficiency on NISQ hardware. It provides a more viable implementation pathway for ground-state energy estimation on medium-scale quantum processors.

This work addresses the challenge in data-driven modeling of port-Hamiltonian systems, where preserving structural properties and ensuring stability at multiple equilibria are often difficult to achieve simultaneously. The authors propose a novel neural network approach that explicitly embeds Hamiltonian structure and multi-equilibrium stability constraints into the learning process. By circumventing conventional convexity restrictions, the method enables flexible approximation of non-convex Hamiltonian functions. Through a structure-aware learning framework, it concurrently preserves the system’s intrinsic geometric characteristics and guarantees asymptotic stability at multiple isolated equilibria. Experimental results demonstrate that, compared to existing baselines, the proposed method significantly improves both model accuracy and fidelity in stability preservation across two numerical benchmarks.

This study addresses the limitation of conventional Lagrangian and Hamiltonian neural networks, which are restricted to non-dissipative systems and struggle to model explicitly time-dependent dissipative dynamics. To overcome this, the proposed approach extends these network architectures to time-varying dissipative systems, with validation conducted through comparative simulations of damped and undamped harmonic oscillators. The resulting model successfully predicts the physical behavior of damped systems while effectively learning the underlying Lagrangian and Hamiltonian functions, thereby revealing novel characteristics of time-dependent dissipative mechanisms. By transcending the theoretical constraints inherent to conservative systems, this work establishes a new paradigm for discovering physical laws governing complex dissipative dynamics.

This work addresses the challenge of structurally preserving learning of classical dynamical systems that exhibit both conservative and dissipative properties within quantum neural networks. The authors propose Quantum Port-Hamiltonian Neural Networks (Q-pHNNs), which employ an isomorphic Hamiltonian mapping to associate the system’s interconnection matrix with unitary quantum gate evolution and its dissipation matrix with measurement-induced nonlinear feedback. This approach uniquely leverages measurement-induced nonlinearity to model dissipative dynamics while intrinsically enforcing energy conservation and passivity through architectural design rather than penalty terms. Four novel quantum architectures are developed, including a quantum Hamiltonian Neural Network that exactly recovers Hamilton’s equations and a topologically entangled quantum graph neural network. Experiments on nonlinear pendulum and damped harmonic oscillator tasks demonstrate a relative energy drift of 1.35%, perfect energy monotonicity, and accurate identification of damping coefficients from vector field snapshots with only 12.1% error.

Existing neural network models struggle to accurately assess their fidelity in preserving the global geometric structures of Hamiltonian phase space, such as homoclinic orbits and separatrices. This work introduces Lagrangian descriptors (LDs) into this domain for the first time, embedding phase space geometry into an information-theoretic framework via a weighted probability density function to enable quantitative comparison of global dynamical structures across models. This approach overcomes the limitations of conventional trajectory-error-based evaluations. Experiments reveal that, in the Duffing oscillator, all tested models successfully reproduce homoclinic orbits; however, in a three-mode nonlinear Schrödinger system, unconstrained reservoir computing outperforms energy-conserving symplectic networks—including SympNet, HénonNet, and generalized Hamiltonian neural networks—in reconstructing homoclinic structures, highlighting a potential tension between topological fidelity and energy conservation.

This study addresses the limitation of conventional optimization methods that lack a geometric perspective, hindering the analysis of curvature effects on optimization trajectories. By modeling parameter optimization as a dissipative dynamical system, this work proposes the HAMLET framework, which integrates Hamiltonian mechanics with Riemannian geometry to define local metric structures. Based on variational principles, it derives geometric forces and constructs metric-compatible dissipation laws, while incorporating matrix product state reparameterization and Poincaré recurrence maps to enhance dynamical analysis capabilities. Evaluated on the MNIST benchmark, the proposed method achieves a highest average test accuracy of 97.95% along with the lowest negative log-likelihood. These results validate the effectiveness of reconstructing optimization paradigms from a geometric dynamical systems perspective.