active magnetic mapping

This paper addresses the trajectory optimization of mobile sensors for Bayesian inverse problems, aiming to minimize the posterior uncertainty of parameters in linear partial differential equation (PDE) models. Method: We propose a continuous-observation-based optimal experimental design framework: (i) deriving a closed-form gradient expression of the posterior covariance matrix with respect to the sensor trajectory; (ii) constructing a differentiable objective functional that converges uniformly under temporal discretization refinement; and (iii) incorporating obstacle-avoidance constraints and control parameterization to ensure physical realizability. The method integrates Bayesian inference, linear PDE modeling, and optimal experimental design theory, and solves the resulting constrained nonconvex optimization problem efficiently via an interior-point method. Results: Evaluated on initial condition inversion for a convection–diffusion equation, the optimized trajectories significantly reduce parameter estimation uncertainty while demonstrating computational robustness and engineering practicality.

This study addresses the challenge of accurately locating survivors within the critical 72-hour window following building collapse, where limited knowledge of internal rubble structure impedes rescue efforts. The authors propose an active sensing approach employing a drone-mounted array of quantum magnetometers, integrating quantum-grade magnetic sensing with Bayesian active learning for the first time. They develop an end-to-end simulation framework that encompasses physical collapse modeling (based on Unreal Engine), dipole magnetic field approximation via triangular surface elements, and Gaussian process regression–driven spatial magnetic field reconstruction. Experimental results demonstrate effective recovery of magnetic signals ranging from sub-picotesla to sub-nanotesla levels at approximately one meter above the rubble surface. A three-sensor array achieves optimal structural correlation within fewer than 100 sampling iterations, validating the method’s feasibility and efficiency for void detection in disaster scenarios.

研究利用稀疏性解决高维度下的伊辛模型采样及贝叶斯稀疏线性回归问题，提出新的高效采样方法。

In GNSS-denied environments, real-time large-scale terrain mapping via online Gaussian process (GP) regression is hindered by the cubic computational complexity of standard GP inference, which scales prohibitively with map size. Method: This paper proposes a recursive Bayesian estimation framework based on locally supported basis functions. Its core innovation is a novel “global grid + local activation” mechanism: GP updates and inference are performed exclusively within neighborhoods of measurement or query points, decoupling computational cost from total map area. Contribution/Results: The method achieves strictly spatially scalable GP terrain mapping—computational complexity is constant per update, with no boundary effects. Evaluated on magnetic terrain mapping and magnetic SLAM, it delivers a 3.2× speedup over full GP while preserving equivalent accuracy and reducing memory footprint by two orders of magnitude, enabling real-time, large-area online mapping.

Optimizing sparse sensor placement for high-dimensional, low-rank real-world data remains challenging due to complex inter-sensor correlations and measurement uncertainty. Method: We propose a data-driven statistical physics framework that maps sensor configurations onto an Ising model—explicitly encoding both pointwise measurement variance and inter-sensor coupling effects. Leveraging the empirical covariance matrix, we construct a thermodynamic potential landscape and derive an interpretable energy function. The method integrates gappy Proper Orthogonal Decomposition (POD) with a QR-inspired interactive tensor estimation strategy. Contribution/Results: Our approach enables robust state reconstruction under noise, dynamic reconfiguration, failure prognosis, and incremental replacement assessment, while providing full visualization of sensor synergy. Evaluated on fluid flow and climate datasets, it reduces reconstruction error by 32% compared to conventional methods. Crucially, it moves beyond the classical single-optimal-configuration paradigm, delivering a scalable, physically interpretable optimization framework for sparse sensing systems.

This study addresses the challenge of modeling uncertainty in spatial random fields arising from irregular sampling and missing data in Earth sciences. The authors propose an asymptotically unbiased spectral maximum likelihood estimation framework that explicitly incorporates the geometry of the sampling design, accommodating complex scenarios such as non-rectangular domains and instrument trajectories. Built upon the assumption of a stationary, isotropic Gaussian field and employing a Matérn covariance model, the method leverages an increasing-domain sampling strategy and provides closed-form uncertainty quantification. Theoretical analysis and numerical experiments demonstrate that increasing-domain sampling substantially reduces both bias and variance in parameter estimates compared to infill (dense) sampling. Furthermore, the work systematically evaluates the influence of covariance priors on field characterization and confirms the superior fitting performance of the Matérn class of models.

This work addresses the challenges of low sampling efficiency and high computational cost in high-dimensional Bayesian calibration. It proposes a unified framework that integrates active subspace methods with surrogate modeling to construct a surrogate of the mismatch function in a low-dimensional latent space. The approach jointly quantifies observational noise, model discrepancy, and surrogate uncertainty, while remaining compatible with any deterministic bijective likelihood transformation. By explicitly accounting for the uncertainty associated with active subspace identification, the method substantially reduces computational overhead without sacrificing accuracy in characterizing the posterior distribution of calibration parameters, thereby enabling efficient and robust high-dimensional Bayesian calibration.

This work addresses the challenge of parameter optimization in computer model calibration, where the goal is to minimize discrepancies between multidimensional model outputs and observed data. The authors propose a novel root-finding paradigm that reformulates calibration as a root-search problem by constructing signed-residual-based Kriging or stochastic Kriging surrogates. Their approach integrates a sequential search space reduction strategy with a new acquisition function compatible with first-order optimizers. Notably, it guarantees algorithmic robustness even when roots may not exist—a scenario unaddressed by prior methods. Empirical evaluations demonstrate that the proposed method significantly outperforms conventional calibration techniques across both data-driven and physics-based modeling tasks, achieving higher computational efficiency while enhancing solution robustness.

This work addresses the truncation errors inherent in conventional methods for three-dimensional magnetic field reconstruction in inaccessible regions by proposing a physics-informed neural network (PINN) framework that integrates Maxwell’s equations. The approach embeds the divergence-free and curl-free conditions of the magnetic field directly into the loss function, enforcing global physical consistency. Innovatively, explicit physical residual losses are introduced at measurement points, replacing traditional random collocation sampling and substantially enhancing model accuracy. Numerical simulations demonstrate reconstruction errors on the order of 10⁻⁴, representing a tenfold improvement over existing PINN-based methods. Experimental validation further confirms a relative accuracy better than 0.1% (approximately 10⁻³) under ambient conditions, meeting the stringent requirements of high-precision physical experiments.

This work addresses the limitations of traditional Gaussian assumptions in accurately representing complex uncertainties, which often lead to information loss and reduced accuracy in multi-stage measurement and control processes. To overcome these challenges, the paper proposes a scalable precision framework based on Gaussian Mixture Models (GMMs), leveraging GMMs as universal approximators of probability density functions. The approach integrates closed-form uncertainty propagation algorithms with memory-efficient computational strategies, thereby transcending the representational constraints of Gaussian methods while maintaining computational tractability. Experimental evaluations in manufacturing and metrology scenarios—such as circular factories—demonstrate that the proposed method significantly enhances the fidelity of uncertainty characterization and propagation, outperforming conventional Gaussian-based techniques.