Search Results (3,883)

Transient pore-air pressure in gas-loaded cover soils is difficult to observe between monitoring depths. We develop a coupled water–air inverse physics-informed neural network as a numerical proof of concept. Under a pre-calibrated constitutive model, three numerically sampled depths supply pore-air pressure, pore-water pressure, and saturation targets. An independent air-pressure field represents overpressure; the coupled balances constrain the joint state. On a one-dimensional same-equation benchmark, the full-window gas-pressure error is 0.0463. The data-only ablation reaches 0.0043, while the coupled residuals improve water pressure, saturation, and front monotonicity. Before the 495 s reference injection-base zero-stress crossing, gas-pressure error is 0.0448; on cells with positive reference effective stress, the stress-reduction error is 0.0450. Later states test numerical tracking under overload. The plane-model case fits two-dimensional FLAC2D training series with a one-dimensional residual omitting lateral transport, giving a responding-depth excess-overpressure error of 0.186. A residual-free line-M test evaluates architecture-only interpolation at 11 held-out depths. The configuration-specific Bishop post-process yields zero-to-seven-minute onset times and a 43% minimum-stress spread across three effective-stress parameter forms. These numerical fields support subsequent mechanical interpretation; physical validation requires measured interior states, and stability assessment requires a mechanical model. Full article

To address the constrained nonlinear guidance problem of simultaneously satisfying impact-angle, seeker field-of-view, and prescribed-initial-acceleration constraints during three-dimensional pre-terminal-to-terminal handover, a nonlinear line-of-sight-angle shaping guidance method is proposed. The LOS-angle profiles are parameterized by normalized relative range, with the pre-terminal acceleration imposed as an initial boundary condition of the terminal-guidance reference. Three-dimensional velocity geometry and lead-angle dynamics reveal a sequential solution for the initial LOS curvatures, yielding an explicit mapping from prescribed acceleration to curvature. Endpoint-vanishing shape functions regulate the intermediate field-of-view profile without changing the boundary conditions or acceleration-inheritance relationship. A dynamic-inversion law tracks the reconstructed reference lead angles. Theoretical analysis establishes exact acceleration inheritance, exponential tracking-error convergence, terminal impact-angle satisfaction, and field-of-view constraint satisfaction under a sufficient reference margin. Numerical simulations show that the proposed method nearly eliminates the acceleration mismatch at the switching instant compared with conventional polynomial shaping guidance. Closed-loop and Monte Carlo validations further demonstrate that this improvement remains pronounced in the presence of actuator dynamics and randomized handover conditions, while terminal accuracy and seeker visibility are consistently maintained. Full article

This study presents a synthetic proof-of-concept surrogate-assisted simulation–optimisation framework for identifying potentially mineralised locations using groundwater copper-isotope observations. The methodology adapts established groundwater contaminant-source characterisation principles, in which unknown source release histories are reconstructed from down gradient concentration measurements, to the investigation of concealed copper mineralisation. An isotope-informed MODFLOW–MT3DMS model was used to generate synthetic groundwater concentrations of Cu_Tot (total copper), ⁶³Cu, and ⁶⁵Cu for hypothetical mineralisation scenarios. Model responses were evaluated at 20 observation wells over five stress periods. These synthetic data were used to train, validate, and test a Gaussian Process Regression (GPR) surrogate model. The GPR model replicates the numerical simulator responses during testing. The test results show R² values exceeding 0.9998 and corresponding RMSE and MAE values of 0.03022 and 0.00571, respectively, indicating high predictive accuracy within the simulated parameter space. The trained surrogate was subsequently coupled with an Adaptive Simulated Annealing (ASA) algorithm to solve the inverse source-characterisation problem. The optimisation formulation contained 20 decision variables, representing time-varying source fluxes at four predefined candidate locations over five stress periods. Three candidates represented active synthetic mineral sources, whereas the fourth was intentionally assigned as an inactive dummy location to evaluate whether the framework could distinguish active from non-mineralised candidates. The optimisation converged in approximately 1080 s under the reported computational configuration. The reconstructed flux histories identified the three active candidates while assigning a near-zero flux to the dummy candidate. These results demonstrate that, under controlled synthetic conditions, isotope-informed inverse modelling can discriminate between predefined active and inactive candidate locations and reconstruct their temporal source strengths. However, the results do not constitute validation of a field-ready mineral-exploration method, because both the training and evaluation data were generated using the same underlying numerical framework. Subject to validation with independent field observations and more realistic geological, hydrogeochemical, and uncertainty representations, the proposed methodology could provide a computational screening and hypothesis-testing tool for prioritising prospective mineralised zones for further investigation. Full article

Infinite Numbers, introduced in preceding studies as functional expressions φ(ξ) of a distinguished infinity unit ξ, are here given a rigorous germ-based foundation within a Hardy-field setting. The real system is realized as an ordered non-Archimedean field canonically isomorphic to the chosen Hardy field, while complex Infinite Numbers arise by complexification. Equality is defined by eventual equality rather than asymptotic equivalence, thereby retaining lower-order and nonzero infinitesimal contributions. Within stated admissibility conditions, the principal arithmetic, differential, partially defined integral, and retained-transform operations of the preceding framework receive rigorous interpretations. The theory further establishes conditions relating discrete accumulation to asymptotic antiderivative representations and proves that the retained bilateral-transform family is injective on C(ℝ) along every fixed vertical line, yielding a well-defined inverse on its range. Two applications illustrate the framework. For a nonlinear boundary-value problem on the real line, retained finite symmetric transforms remain applicable despite the absence of a common classical bilateral region of convergence, leading to an explicit heteroclinic solution and nonzero infinitesimal endpoint corrections. A discrete-series limit illustrates the accumulation theorem and is independently verified by a classical estimate. Full article

We study a nonlinear system of two Langevin differential equations, each governed by $\psi$-Hilfer fractional derivatives acting through a p-Laplacian and coupled to one another both through the nonlinearities and through the boundary data. The latter consist of antiperiodic relations connecting an interior node $\eta \in (a,b)$ with the endpoint b, alongside Lebesgue–Stieltjes integrals in which the terminal value of each unknown is expressed through the other. An integral relation, in which every constant generated by the successive inversion of the two $\psi$-Hilfer operators is computed explicitly, is derived and proved to be equivalent to the boundary value problem, leading to a coupled Hammerstein-type fixed-point formulation. Since $\psi$-Hilfer solutions may develop an algebraic singularity at the left endpoint, the natural functional framework is a product of weighted Banach spaces, and all estimates are performed in the associated weighted norms, with the convexity of the p-Laplacian entering the computations at several key points. Viewing the resulting solution operator as one completely continuous map, we obtain at least one solution from Schaefer’s fixed-point theorem, along with an explicit a priori radius. Two worked examples close the paper: one with $p=2$ and one with $p=\frac{3}{2}$. In each, the hypotheses of the main theorem are verified explicitly, and every constant they require is evaluated numerically. Full article

Cloud-model hyper-entropy can be overestimated when a scale-inflated subpopulation broadens the tails. We develop a quantile-based estimator that removes location and common scale before recovering cloud shape. Influence normalization balances the selected contrasts, and a prespecified correction addresses centered scale inflation. The theory proves global injectivity of the shape-contrast map for every positive shape ratio, establishes local stability under data and numerical-score perturbations, derives a mixed-rate limit for the singular cloud center, and gives boundary-projected and fixed-positive finite-step limits for the contamination correction. Independently checked numerical integration supports the reference calculations. Simulations and real-data-calibrated semi-synthetic experiments show a clean-sample efficiency cost and improved recovery under moderate scale inflation. A controlled loss ablation attributes the observed gains to the structural construction and weighting rather than active Huber clipping. Benchmark applications illustrate how the estimator can be integrated into a cloud-clustering workflow. Full article

We analyse inversion of the viscosity ratio M in the Buckley–Leverett equation, distinguishing structural identifiability, observation-operator conditioning, and numerical estimation error. The Riemann solution gives $M=4s^2-4s$ from the shock speed s, with relative condition number $\kappa \left(M\right)=2\sqrt{1+M}/(\sqrt{1+M}-1)$, which diverges as $M\downarrow 0$. The continuum physics objective admits exact solution–parameter pairs for every $M>0$, so identifying the true ratio requires observations. We examine numerical recovery using a viscous physics-informed neural network (PINN) with positive parameterisation and 30 paired repetitions per setting. At $M=3$, the median parameter error decreases from $514.25\%$ without observations to $6.13\%$ with 25 noisy observations. Additional data decrease the median field error, while median parameter errors are nonmonotone. Over $M\in [0.25,10]$, $\kappa$ decreases from $18.94$ to $2.86$, whereas the smooth-branch Cramér–Rao relative scale for 50 scattered observations with $5\%$ Gaussian noise levels off near $7\%$. Shock crossings supply additional nonregular information. Finite-network physics losses remain small across the tested ratios, with different orderings on training and held-out points. Scalar controls assess finite-resolution viscous-model discrepancy; complementary PINN tests show poorer recovery as the front sharpens. Recovery accuracy therefore depends jointly on the observation operator, regularisation, and numerical estimator. Full article

Magnetic Resonance Imaging (MRI) is an imaging technique that provides detailed structural and functional information about organs and tissues. To support the validation of MRI measurement techniques and provide a tool for scanner benchmarking, we develop an MRI simulator exploiting graphics processing units (GPUs) for computational acceleration. The GPU-Accelerated MRI Simulator (GAMS) enables us to generate synthetic images with high-resolution detail for quantitative estimation of relaxation times. GAMS is designed to reproduce the entire MRI image acquisition pipeline, including the definition of the MRI pulse sequence in a standard Pulseq format, the input of the digital phantom and its voxelization, the time integration of the Bloch equation at voxel level, and the processing of the derived k-space for image synthesis. The Bloch equation solver is implemented in CUDA Fortran, using GPUs to increase computational efficiency. The solver accuracy is tested in simple cases by comparison with analytical solutions and with the open-source Jülich Extensible MRI Simulator (JEMRIS). GAMS is applied to an inverse reconstruction problem to estimate the relaxation properties of a calibration phantom, starting with synthetic data. Then, it is used to reproduce the imaging process of a high-resolution digital brain phantom, generating realistic images under diverse MRI pulse sequences, which enable differentiation of tissues based on relaxation properties and/or proton density. The results demonstrate GAMS’s ability to generate synthetic images of complex anatomical structures comparable to those acquired with real MRI scanners and to reliably quantify sample relaxation properties. The simulator is also characterized by high computational efficiency, extensibility for multi-GPU implementation, and cross-platform compatibility. These features make GAMS a valuable tool for the metrological assessment of quantitative MRI (qMRI) and the testing of new pulse sequences for qMRI technique development. Full article

Inverse synthetic aperture radar (ISAR) imaging enables high-resolution two-dimensional reconstruction of non-cooperative moving targets, serving as a crucial tool for radar target recognition and situational awareness. The radar network faces the coupled optimization problem of spatial matching and temporal sequencing in order to execute multi-target ISAR imaging tasks. Firstly, the spatial matching scheme directly determines the observational geometric relationship, significantly affecting the two-dimensional resolution and image quality of ISAR imaging. Secondly, the temporal domain sequencing scheme sets the starting time of each imaging task. It dynamically changes the coherent integration time (CIT) of the task and influences the overall scheduling efficiency. Traditional methods can only obtain suboptimal allocation schemes, with low imaging utility, and the running time significantly increases when facing large-scale scenarios. In response to the above issues, this paper designs quality functions and efficiency functions to quantify the quality of spatial domain matching and the execution efficiency in the temporal domain. It also combines task priority to design a utility function for balancing quality and efficiency, and a joint allocation constraint optimization model for multi-target ISAR spatio-temporal resource scheduling under utility maximization is constructed. At the same time, the proximal policy optimization (PPO) is introduced to realize sequential online decision-making for the coupled scheduling of spatio-temporal resources, and a complete resource allocation scheme is generated step by step. Experimental results in a double-scale simulation scenario show that the proposed algorithm has stronger training convergence stability compared to the Double Deep Q-Network (DDQN) algorithm, and outperforms the random policy algorithm (RPA), genetic algorithm (GA), and particle swarm optimization (PSO) in imaging utility, with reasonable running time, demonstrating that the proposed algorithm balances optimization accuracy and real-time solution efficiency. Full article

Prebaked anodes are critical consumables in primary aluminum electrolysis, where their internal integrity dictates cell efficiency and operational stability. Conventional defect characterization relies on destructive sampling, which inherently causes material degradation and offers poor reproducibility. Existing nondestructive evaluation (NDE) techniques are frequently limited by prohibitive costs and poor in-situ scalability. To address these challenges, this study proposes a nondestructive imaging strategy using open electrical impedance tomography (OEIT). In the DC limit employed here, the method is equivalent to open electrical resistance tomography (OERT): a constant direct current is injected, so that only the resistive contrast of the anode is exploited. A dedicated OEIT mathematical model for prebaked anodes is established, systematically detailing the signal acquisition scheme, forward problem formulation, and inverse problem regularization. By integrating conventional image reconstruction algorithms, a customized measurement procedure and a specific inversion algorithm are developed to enable the visual reconstruction of internal anomalies. The efficacy of the proposed methodology is examined through numerical simulations and benchtop experiments. Results indicate that, for the two defects examined, the approach can localize defects in the in-plane directions and approximately recover their morphology, providing a preliminary basis for further development toward online inspection. Full article

In nonlinear mechatronic systems with multiple coupled actuators, the allocation of control inputs affects both the feedback-system structure and the required actuator effort. This paper develops an operator-based nonlinear multi-input control framework within the robust right coprime factorization (RRCF) structure for systems with more actuator inputs than controlled outputs. The original multi-input plant is represented through a reduced-output formulation, and the control allocation is described by a mapping that selects a right inverse of the input-coupling. Specifically, the actuator inputs are determined by minimizing the quadratic voltage-based control-effort objective subject to the prescribed coupling relation and actuator constraints. Under the ideal allocation condition, the nominal Bezout Identity is preserved, while robust stability in the presence of plant perturbations, coupling uncertainty, and allocation errors is guaranteed when the generalized Lipschitz condition derived for the optimized RRCF system is satisfied. The proposed framework is applied to a vibrating plate actuated by multiple piezoelectric elements. For this application, the constrained two-input allocation problem is reduced to a scalar piecewise optimization problem and solved by a finite-candidate selection procedure. Comparative experiments show that the proposed approach achieves stronger vibration suppression, a lower voltage-based control-effort metric, and a more balanced allocation among the actuators. These results demonstrate the effectiveness of integrating constrained multi-input allocation with the operator-based robust control framework. Full article

In the intelligent operation and maintenance of core process equipment in semiconductor manufacturing, the thickness and morphological parameters of sub-micron multilayer transparent films on wafer surfaces are critical quality indicators that govern device performance and yield. White Light Interferometry (WLI) enables the high-precision measurement of thin-film thickness and topography parameters, and is widely deployed in high-precision manufacturing fields such as semiconductors. However, when measuring sub-micron multilayer transparent films, WLI faces challenges including low computational efficiency, severe parameter coupling, and non-unique solutions, making it difficult to meet the demands of high-throughput online inspection. To address these issues, this paper proposes a deep learning-based method for decoupling and optimizing WLI signals through inverse modeling. The approach establishes an innovative hybrid intelligent framework: first, a training dataset is generated based on interferometric system modeling and simulation; then, a classification model is employed to intelligently categorize the acquired interference signals, decomposing the complex multimodal inversion problem into several sub-problems with simpler patterns. Next, for each signal category, a specialized closed-loop deep network model is designed and trained. This network integrates an inverse prediction network with a forward reconstruction network in series. During training, both prediction error and reconstruction error are jointly used as the loss function, ensuring solution uniqueness and physical consistency, thereby enhancing inversion reliability and robustness. This research provides an effective solution for high-precision online optical measurement of complex thin-film structures, offering significant theoretical value and broad industrial application prospects. Full article

The limited length and structural evolution of time series for water-sector energy consumption constrain reliable multi-step forecasting. To address this problem, this research proposed a gate-recycling fractional-order grey model named GRGM(r,k,1), based on a finite-memory accumulation operator. The parameter $r$ governed geometric attenuation within the active gate, whereas the integer gate length $k$ determined the range of direct historical participation. Their separation decoupled attenuation intensity from memory span. The operator admitted exact recursive inversion. Theoretical analysis established the nonsingularity of the accumulation operator, derived operator-norm and condition-number bounds, and demonstrated finite direct perturbation support and relevant boundary relations. Empirical validation combined fixed-origin, rolling-origin, and external tests against four benchmark models. For Chinese water production and supply energy consumption, GRGM(r,k,1) achieved test MAPE and sMAPE values of 0.99% and 1.00%, respectively. Its test MAPE values for the desalination and wastewater-treatment datasets are 0.68% and 2.60%. The forecasts further indicate sustained consumption growth with a declining annual growth rate. The results suggest that gate recycling provided an interpretable fractional-order mechanism for short-sample grey forecasting by jointly regulating information attenuation and finite memory. Full article

The design of sensible heat storage contains an optimization process of a careful choice or an original design of materials and composites for their particular parts, components, and layers. Especially high thermal capacity and appropriate thermal conductivity, together with fire resistance, are required. In such a process, a reliable procedure of evaluation of material parameters from experimental data is needed. This article demonstrates the development of such a procedure for the case of hot-wire probes on cylindrical measurement configurations. The classical nonlinear least-squares approach, based on the semi-analytic formulas for the evolution of temperature in time, is compared with a hybrid genetic algorithm, as a representative of soft-computing approaches. Full article

Unmanned aerial vehicle (UAV)-assisted data collection from battery-constrained Internet of Things (IoT) devices faces a fundamental trade-off between communication reliability and device energy depletion. This paper jointly optimizes UAV trajectory, user association, and radio resource management (RRM) to minimize the uplink weighted sum transmit powers, where each device’s weight is dynamically and inversely related to its residual energy, while treating UAV propulsion energy as a feasibility constraint. To circumvent the initialization trap of conventional alternating optimization (AO), we propose a two-layer non-alternating framework. The inner layer solves the per-slot RRM problem analytically via KKT conditions for a fixed UAV position, yielding analytical power allocation and a unique bandwidth solution, while user association is determined by an incremental greedy algorithm. The outer layer formulates trajectory planning (TP) as a Markov decision process (MDP), enabling single-pass trajectory synthesis without cross-layer iteration, thereby inherently avoiding initialization sensitivity. The framework supports the genetic algorithm (GA) and limited depth-first search (DFS) as trajectory solvers, with the deep Q-network (DQN) as a promising future extension, each offering distinct optimality–complexity trade-offs. Simulation results show that the proposed scheme consistently outperforms conventional iterative baselines across various network configurations. Full article