The identification of constitutive neural network models from heterogeneous full-field deformation data provides a robust alternative to traditional calibration methods based on homogeneous stress–strain experiments, particularly given the high dimensionality of trainable parameters. Existing approaches must balance generality, robustness, and computational efficiency: Conventional finite element model updating is broadly applicable but computationally demanding; weak-form methods offer efficiency but are sensitive to noise and data scarcity; neural operator models are highly expressive but require extensive training datasets. This work presents ADE-FEMU (Automatic-Differentiation-Enabled Finite Element Model Updating), an end-to-end differentiable framework that integrates a constitutive neural network model within a JAX-FEM nonlinear solver and identifies its parameters through gradient-based minimization of a measurement-mismatch loss, allowing for training on structural data with limited kinetic information. Thus, it can be considered as an extension of finite element model updating (FEMU) for hyperelastic materials, implemented within a GPU-accelerated, fully automatically differentiable finite element framework Newton tangent stiffness and loss gradients are computed automatically using forward- and reverse-mode automatic differentiation throughout the entire pipeline, thereby removing the need for analytic adjoints or offline surrogate models. ADE-FEMU is demonstrated for two architectures: a grey-box Constitutive Artificial Neural Network (CANN), a polyconvex, fully connected model with high flexibility, and a white-box CANN, an expert-system network with phenomenologically interpretable strain–energy terms. Focusing on incompressible isotropic hyperelasticity, ADE-FEMU is evaluated on three open experimental datasets: (1) full digital image correlation (DIC) of a perforated tensile specimen, (2) a reduced-data scenario with a one-dimensional stretch profile and global force–displacement curve, and (3) a heterogeneous matrix–inclusion system in which both phases’ constitutive laws are identified and generalized to twenty-two previously unseen samples. The grey-box CANN demonstrates superior performance with comprehensive, full-field, or heterogeneous data, whereas the interpretable white-box CANN is more reliable for model discovery from sparse datasets. The source code will be released upon publication.
Various nonparametric estimators for modelling the transition probabilities in multi-state models have been proposed, e.g., the Aalen-Johansen estimator, the landmark Aalen-Johansen estimator, and a hybrid Aalen-Johansen estimator. While the Aalen-Johansen estimator is generally only consistent under the rather restrictive Markov assumption, the landmark Aalen-Johansen estimator can handle non-Markov multi-state models. However, the landmark Aalen-Johansen estimator leads to a strict data reduction and, thus, to an increased variance. The hybrid Aalen-Johansen estimator serves as a compromise by, firstly, checking with a log-rank-based test whether the Markov assumption is satisfied. Secondly, landmarking is only applied if the Markov assumption is rejected. A new hybrid Aalen-Johansen estimator is proposed which uses a Cox model instead of the log-rank-based test to check the Markov assumption in the first step. Furthermore, the four estimators are compared in an extensive simulation study across Markov, semi-Markov, and distinct non-Markov settings. In order to get deep insights into the performance of the estimators, four different measures are considered: bias, variance, root mean squared error, and coverage rate. The main result of the simulation study is that the hybrid Aalen-Johansen estimators yield favourable results across various measures and settings.
Large-eddy simulations (LES) of a planar turbulent lean hydrogen-air jet flame at Re = 11000 are performed using a tabulated flamelet model based on mixture-averaged diffusion that incorporates detailed transport, including differential and preferential diffusion, wall heat loss, and thermodiffusion. The approach is extended to turbulent combustion in LES using a presumed-shape probability density function formulation that accounts for sub-filter effects. The flame exhibits a highly corrugated front, driven by local variations of mixture fraction induced by strong thermodiffusive transport. These effects significantly alter both the flame structure and morphology. The LES results are systematically compared to a reference direct numerical simulation across varying LES filters through different mesh resolutions to evaluate the predictive capability of the model. The LES accurately reproduces instantaneous flow structures and thermodiffusive effects. Global flame characteristics including flame length, surface area, and consumption speed, are well captured and show limited sensitivity to mesh resolution. The role of thermodiffusion is also examined, showing that its incorporation leads to a more reactive flame and should not be neglected in the formulation. Heat losses are incorporated into the tabulated chemistry framework for completeness but are found to have a negligible impact, consistent with the walls weak influence in the present configuration. Overall, the results demonstrate that the proposed approach provides reliable predictions of the main flame characteristics, with remaining discrepancies primarily associated with unresolved sub-filter effects that deserve further investigation.
The Fokker–Planck (FP) particle method accelerates rarefied-gas simulations by replacing the binary collisions of the commonly used Direct Simulation Monte Carlo (DSMC) algorithm with a drift–diffusion process. Like all particle methods, the FP method is inherently stochastic, which leads to statistical fluctuations in macroscopic quantities and necessitates large particle numbers for accurate results.In this work, we investigate the use of quasi-random numbers, which sample distributions more evenly and thereby reduce the variance. However, the standard quasi-Monte Carlo approach, in which the random inputs for each trajectory are generated from a single high-dimensional point, loses effectiveness in spatially discretized settings, where particle transport and boundary interactions lead to changing subsets of particles.To address this issue, we combine the FP method with the Array Randomized Quasi-Monte Carlo (Array-RQMC) technique, which reconstructs the low-discrepancy structure locally at each time step. We compare the proposed FP–Array-RQMC approach with established variance-reduction techniques in homogeneous and inhomogeneous problems. The method achieves improved convergence rates and yields smaller estimator errors for sufficiently large particle numbers.
The increased penetration of inverter-based resources is reducing system inertia and challenging traditional frequency modeling approaches based on a single global frequency. Accurate estimation of local bus frequencies has therefore become essential for dynamic analysis and control. This paper proposes a near real-time bus frequency estimation framework that combines the analytical structure of the frequency divider (FD) formulation with the distributed inference capability of the Gaussian belief propagation (GBP) algorithm. By representing the power system as a factor graph, the proposed method enables iterative and fully distributed computation of bus frequencies without matrix inversion. The proposed algorithm enables estimation on a much smaller time scale than classical approaches, allowing faster detection of frequency deviations. Simulation studies on standard test systems demonstrate that the GBP framework achieves the same accuracy as the classical FD, while offering improved scalability and suitability for distributed implementation.
