Neural Non-Equilibrium Hamiltonian Monte Carlo for Corrected Boltzmann Sampling

Sampling from an unnormalized Boltzmann density requires proposals that move probability mass globally while retaining enough path-probability information for statistical correction. We introduce Neural Non-Equilibrium Hamiltonian Monte Carlo (NHMC), a train-then-correct learned Hamiltonian sampler. Starting from a tractable base distribution, NHMC learns stochastic Hamiltonian-style paths toward the target. Once training is complete, the learned proposal parameters are fixed; the proposal then generates complete paths and endpoint configurations, which are statistically corrected using the recorded non-equilibrium work. This dimensionless generalized work is determined by the probability ratio between the forward proposal path and a reverse reference path. During training, minimizing its mean reduces a path-space KL divergence and controls an upper bound on endpoint mismatch. During evaluation, the same quantity defines weights for self-normalized importance sampling on paths (path-SNIS), estimates normalizing constants or free-energy differences, and gives the acceptance ratio for path-space independent Metropolis-Hastings (path-IMH). The same forward-reverse laws also define a shared-bridge round-trip Metropolis kernel that acts directly on configurations and preserves the Boltzmann target. On double-well and finite-volume lattice $φ^4$ targets, the NHMC construction gives corrected estimates when path overlap is sufficient; when overlap is poor, weight degeneracy, low acceptance, and long autocorrelation expose proposal failure. We additionally report a molecular internal-coordinate feasibility study using an MD prior and learned-force path proposal.

A Review of Machine Learning for Cavitation Intensity Recognition in Complex Industrial Systems

Cavitation intensity recognition (CIR) is a critical technology for detecting and evaluating cavitation phenomena in hydraulic machinery, with significant implications for operational safety, performance optimization, and maintenance cost reduction in complex industrial systems. Despite substantial research progress, a comprehensive review that systematically traces the development trajectory and provides explicit guidance for future research is still lacking. To bridge this gap, this paper presents a thorough review and analysis of hundreds of publications on intelligent CIR across various types of mechanical equipment from 2002 to 2025, summarizing its technological evolution and offering insights for future development. The early stages are dominated by traditional machine learning approaches that relied on manually engineered features under the guidance of domain expert knowledge. The advent of deep learning has driven the development of end-to-end models capable of automatically extracting features from multi-source signals, thereby significantly improving recognition performance and robustness. Recently, physical informed diagnostic models have been proposed to embed domain knowledge into deep learning models, which can enhance interpretability and cross-condition generalization. In the future, transfer learning, multi-modal fusion, lightweight network architectures, and the deployment of industrial agents are expected to propel CIR technology into a new stage, addressing challenges in multi-source data acquisition, standardized evaluation, and industrial implementation. The paper aims to systematically outline the evolution of CIR technology and highlight the emerging trend of integrating deep learning with physical knowledge. This provides a significant reference for researchers and practitioners in the field of intelligent cavitation diagnosis in complex industrial systems.