arXiv subjects

Moxian Qian

Publications and source records attributed to Moxian Qian.

5 recordsLinked to original sources

arXiv2026

Operator-Guided Model Reduction for Generative Sampling in Lattice Field Theory

Neural generative samplers for lattice field theory can be costly to train and evaluate. When they miss modes or assign them incorrect relative weights, biased observables do not reveal which collective variables are responsible. We project a trained flow-matching velocity onto vector fields built from lattice operators and Fourier modes. In two-dimensional lattice $ϕ^4$ theory, the projection separates changes in the overall magnetization from the lowest nonzero-momentum fluctuations and guides an explicit invertible proposal that treats them separately. Allowing the amplitude of the lowest nonzero-momentum fluctuations to depend on the magnetization improves the overlap between the proposal and target distributions, while the same two-parameter modification at higher momenta gives smaller improvements. The Metropolis--Hastings correction defines a Markov chain with the target Boltzmann distribution as its stationary law, and the normalized proposal density yields finite-volume partition-function estimates consistent with an independent HMC calculation. At the larger tested volume, the overlap between the proposal and target distributions deteriorates substantially, limiting the range over which the same parameterization remains effective.

hep-lat↗

arXiv2026

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). We further derive a shared-bridge round-trip NHMC--MH kernel and prove that its configuration-space transition preserves the Boltzmann target. On double-well, finite-volume lattice $ϕ^4$, compact non-Abelian gauge, and Lennard--Jones cluster 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 a molecular-dynamics prior and learned-force path proposal.

cs.LG↗

arXiv2026

Stochastic Path Sampler For Lattice Field Theory

In lattice field theory, target distributions are known only up to normalization, (\tildeπ(ϕ)\propto e^{-S(ϕ)}), while the partition function is intractable. Markov chain Monte Carlo simulations often become inefficient near phase transitions or the continuum limit due to critical slowing down. In this work, we propose a novel sampler based on nonequilibrium thermodynamics, called Stochastic Path Sampler (SPS), which can generate configurations for the unnormalized target distribution without requiring training data. The central idea of SPS is to establish a trajectory-level balance for learnable forward and backward stochastic dynamics between two equilibrium states, namely the prior and target distributions. This is achieved by minimizing the path-space variational free energy, equivalently an entropy-production upper bound, defined by the log-ratio of forward and auxiliary backward trajectory measures, thereby enhancing the reversibility of the forward and backward processes. The learned forward process provides independent proposals, which are subsequently corrected by an extended-space Independence Metropolis--Hastings step. In two-dimensional (ϕ^4) theory, we demonstrate that our neural sampler can achieve the same sampling quality as HMC but with a much shorter autocorrelation time in the critical region. This sampler offers a stochastic-quantization-inspired route to data-free proposal construction for lattice field theory by leveraging a variational free-energy principle derived from path-space irreversibility.

hep-lat↗

arXiv2025

Variational Autoregressive Networks Applied to $ϕ^4$ Field Theory Systems

We combine reinforcement learning with variational autoregressive networks (VANs) to perform data-free training and sampling for the discrete Ising model and the continuous $ϕ^4$ scalar field theory. We quantify the complexity of the target distribution via the KL divergence between the magnetization distribution and a reference Gaussian distribution, and observe that configurations with smaller KL divergence typically require fewer training steps. Motivated by this observation, we investigate transfer learning and show that fine-tuning models pretrained at a single value of $κ$ can reduce training time compared with training from a Gaussian field. In addition, inspired by single-site and cluster Monte Carlo updates, we introduce single-site and block Metropolis--Hastings (MH) updates on top of VAN proposals. These MH corrections systematically reduce the residual bias of pure VAN sampling in the parameter range we study, while maintaining high sampling efficiency in terms of the effective sample size (ESS). For both the Ising model and the $ϕ^4$ theory, our results agree with standard Monte Carlo benchmarks within errors, and no clear critical slowing down is observed in the explored parameter ranges.

hep-lat↗

arXiv2025

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.

eess.SP↗