Accurate prediction of thermal evolution during Wire Arc Additive Manufacturing (WAAM) is essential for process control and defect reduction. High-fidelity simulations provide detailed temperature fields but are computationally expensive, limiting their use for parameter exploration and real-time optimization. In this work, we develop a simulation-based Reduced Order Model (ROM) that combines Proper Orthogonal Decomposition (POD) with XGBoost regression to efficiently predict thermocouple temperature evolution curves. The ROM is trained on a carefully designed set of 120 high-fidelity snapshots from a representative experimental setup and validated on both withheld snapshots and an independent experimental setup to assess its predictive performance under different experimental conditions. The model accurately reproduces temperature profiles and can predict thermal responses for parameter combinations not present in the training data. Leveraging the ROM’s computational efficiency, we systematically optimize key process parameters to identify configurations that enable simulations to reproduce experimental temperature curves with high fidelity. The results demonstrate that the ROM serves as an efficient calibration-oriented surrogate for high-fidelity simulations, facilitating rapid parameter exploration and optimization while substantially reducing computational cost. Highlights ∙ Developed and validated a physics-based thermal model resolving thermocouple temperature histories of WAAM processes. ∙ Developed a Machine Learning-based Reduced Order Model (ROM) for WAAM thermal predictions, enabling rapid exploration of process parameters to calibrate high-fidelity simulations against experimental temperature curves. ∙ ROM trained on only 120 high-fidelity simulation snapshots, demonstrating efficiency in small-data regimes. ∙ Validated across multiple experimental setups, showing robust predictive performance under varying experimental conditions.
The evolution of interfacial morphology in immiscible biphasic materials results from the combined effects of convection, deformation, capillary relaxation, coalescence, and topological rearrangements. Direct phase-field simulations can resolve these mechanisms at the microscopic scale, but their computational cost prevents their systematic use in process-scale simulations. This work proposes a micro–macro framework in which the diffuse interfacial geometry provided by a phase-field model is projected onto a second-order interfacial area tensor. The trace of this tensor measures the interfacial area density, while its deviatoric part characterizes the anisotropy of the interface-normal distribution. Periodic phase-field simulations are performed under simple shear and incompressible planar extension for different values of the dimensionless interface thickness ε and the phase-field Péclet number Pe. The resulting tensor histories are used to identify a reduced objective evolution law involving only three macroscopic parameters: the anisotropy relaxation time τ _a , the interfacial-area relaxation time τ _q , and the equilibrium interfacial area density Q_eq . A single parameter set is identified simultaneously from the shear and extension histories by minimizing the discrepancies associated with both the tensor deviator and its trace. Response surfaces are subsequently constructed to relate the identified macroscopic parameters to (ε ,Pe) . The approach is finally assessed in a simplified two-dimensional casting-filling application. The reduced evolution law is integrated along Lagrangian trajectories reconstructed by backward tracing, providing a spatial distribution of the interfacial area and orientation throughout the filled cavity. Direct phase-field calculations are also performed along representative trajectories located in divergent and convergent flow regions. The microscopic realizations exhibit fluctuations related to random initialization and discrete topological events, whereas the deterministic macroscopic model provides an effective morphological state around which these realizations are distributed. Although the macroscopic model cannot reproduce every microscopic overshoot or realization-specific anisotropy, it captures the dominant orientation, interfacial area level, and dependence on the accumulated flow history. The proposed framework therefore provides a computationally efficient connection between resolved phase-field microstructures and process-scale predictions of interfacial morphology.
Novel methodologies in machine learning enable non-destructive prediction of mechanical properties through the use of either material components or material imaging. Predictive technologies are continuously being developed in the field of mechanical and materials engineering. However, when it comes to inverse problems, the identification of the optimal microstructural content to create the material with the desired properties is often complicated and ill posed. In fact, the inverse problem is not unique, and multiple material combinations can lead to the desired properties. Working with biobased materials adds a layer of complexity to the inverse problem since in most cases biosourced components are mixtures rather than pure components. This work establishes a methodology for the prediction of material properties based on imaging of lignin-containing polyurethane rigid foams and solving the inverse problem by generating the required lignin-based formulation leading to the desired mechanical properties. The methodology employs a novel learnable kernel principal component analysis, based on the combination of the non-linear model order reduction technique with machine learning autoencoders mapping the physical data into a large dimensional space. The results are material generation through required mechanical properties, mechanical properties identification from microstructure imaging, microstructure generation from mechanical properties, and (bio)chemical combinations. The predictions of the mechanical properties are within less than 2.3
Physics-based reduced-order models are one of the key enablers for improving the predictive capabilities of digital twins, offering a balance between computational efficiency and physical fidelity. However, their efficiency for nonlinear problems remains a challenge because evaluating nonlinear operators in reduced dimensions can be very costly, and offline construction often requires many high-fidelity simulations. In this paper, we address this issue with a reduced-order modeling strategy for parametrized nonlinear partial differential equations that is efficient both online and offline. Offline efficiency is achieved using a greedy algorithm for reduced basis construction combined with a quasi-optimal hyper-reduction procedure called Reduced Basis Empirical Quadrature Procedure (RBEQP) [1]. Then, Gaussian process regression is integrated into the reduced-order model to learn the reduced coefficients and enhance online efficiency. Additionally, we evaluate the effectiveness of our proposed method on two model problems: a steady-state heat conduction problem with a nonlinear, temperature-dependent conductivity, and a neo-Hookean hyperelastic beam under self-weight load.
Accurate prediction of the efficiency of electromechanical powertrains is crucial for the development of electric vehicles. Until now, this has been done through time-consuming and costly test bench investigations in late development phases. To address this, digital modeling and development processes are implemented in the product development process. Although existing modeling approaches, such as simulations or classical data-driven models, are widely applied, they often suffer from limitations regarding prediction accuracy, prediction speed, or model size. To address this problem, this paper develops five different data-driven modeling approaches for digital twins, ranging from simple black-box models to hybrid grey-box approaches. In addition, a sixth modeling approach, a white-box model, was conducted as a reference to the other model approaches. Validation is based on recorded measurement data from a test bench setup of an electromechanical powertrain consisting of a permanent magnet synchronous machine and a multi-stage transmission. The evaluation includes classic error metrics such as mean absolute error and mean relative error, but also model size, training times, and prediction speeds. In addition, a quotient of output to input variables is included, which is used to evaluate the information content of the model structure. Despite a slightly increased error tolerance, the final bright-grey-model approach offers the best compromise between prediction accuracy, real-time capability, and a high output-to-input quotient. The results demonstrate that data-driven digital twins with physically informed structures enable early and real-time prediction of the efficiency of electromechanical powertrains.
