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.
We initiate the study of the phantom version of Maker-Breaker positional games. In a phantom game, the moves of one of the players are hidden from the other player, who still has the complete information. We look at the biased (a:b) Maker-PhantomBreaker games where the board is the edge set of the complete graph on n vertices, K_n, and Maker has no information about PhantomBreaker's choices of edges. We give randomized strategies for both players in four classical games: connectivity game, perfect matching game, mindegree-k game and Hamiltonicity game. In particular, we focus on characterizing all biases (a:b) for which Maker wins asymptotically almost surely.
The COSMO-SAC-Phi model developed by Soares et al. extends the COSMO-SAC activity-coefficient framework into a full equation of state by explicitly accounting for pressure effects. In this approach, pure substances and mixtures are represented as pseudo-mixtures consisting of the actual number of moles and an additional pseudo-component that describes free volume, or holes. In this work, we implement this extension within the openCOSMO-RS framework and evaluate it using a large and diverse set of molecules and binary systems. The resulting equation of state includes an extensive open-source parameter set with around 1800 pure-component entries, made freely available to the academic community. The four pure-component parameters were fitted to vapor-pressure and liquid-molar volume data for each substance. Model performance was assessed against two benchmark equation-of-state databases, one for pure compounds and one for binary mixtures, without introducing any binary interaction parameters. The resulting openCOSMO-RS-Phi model reproduces the accuracy of the original COSMO-SAC-Phi formulation while providing a fully open-source and accessible implementation for the scientific community. Beyond its immediate utility, it also establishes a foundation for future development of predictive EoS for electrolyte solutions.
This study presents a highly efficient and accurate approximate method based on a convergence acceleration parameter to approximate a nonlinear multidimensional aggregation population balance equation. Optimal tuning of the acceleration parameter significantly enhances solution quality over extended temporal domains and overcomes key limitations of existing approaches. Deeper mathematical insight is provided through a discussion of the existence of the proposed approach within the framework of a nonlinear aggregation model. Convergence analysis and error estimates are established using the fixed point theorem and the contractive mapping principle, thereby proving the existence of solutions to the aggregation model. The accuracy and efficiency of the proposed approach are demonstrated by computing approximate solutions for the number density function and its moments for physically relevant kernels. For analytically tractable kernels, results are validated against exact solutions. For complex size-dependent kernels, including polymerization, Ruckenstein-Pulvermacher, and shear kernels, the obtained results are compared with the existing finite volume scheme, homotopy analysis method, and optimal decomposition method. The results show that the proposed approach achieves higher accuracy in capturing number density functions and their integral moments while requiring significantly fewer series terms than existing methods.
Aggregation schemes provide a means to reduce the computational complexity of power system operation by reducing the number of devices that are considered individually. This can be achieved with tools of computational geometry, where the feasible set is projected onto the decision variables of the point of interconnection. Set projection is computationally expensive, especially in the context of multi-period power system operation. This calls for efficiency improvements via structure exploitation of set representations. This paper proposes efficient flexibility aggregation via constrained zonotopes. We evaluate the performance of the proposed method on a 15-bus distribution grid with time-dependent elements for up to 96 timesteps. The results suggest that the presented method significantly improves computation times compared to classic polytope projection approaches.
