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A common trend in simulation-driven engineering applications is the ever-increasing size and complexity of the problem, where classical numerical methods typically suffer from significant computational time and huge memory cost. Methods based on artificial intelligence have been extensively investigated to accelerate partial differential equations (PDE) solvers using data-driven surrogates. However, most data-driven surrogates require an extremely large amount of training data. In this paper, we propose the Convolutional Hierarchical Deep Learning Neural Network-Tensor Decomposition (C-HiDeNN-TD) method, which can directly obtain surrogate models by solving large-scale space-time PDE without generating any offline training data. We compare the performance of the proposed method against classical numerical methods for extremely large-scale systems.

The evolution of artificial intelligence (AI) and neural network theories has revolutionized the way software is programmed, shifting from a hard-coded series of codes, Software 1.0, to a vast neural network, Software 2.0. However, this transition in engineering software has faced challenges such as data scarcity, multi-modality of data, low model accuracy, and slow inference. Here, we propose a new network based on interpolation theories and tensor decomposition, the interpolating neural network (INN) to open the new era of Engineering Software 2.0 that unifies training, solving, and calibration. Instead of interpolating training data, a common notion in computer science, INN interpolates grid points in the physical space whose coordinates and values are trainable. INN features orders of magnitude fewer trainable parameters (or degrees of freedom for solving), faster training/solving, less inference cost, smaller memory footprint, and higher model accuracy compared to multi-layer perceptron (MLP) or physics-informed neural networks (PINN). Various numerical experiments that cover computer science and engineering domains demonstrate that INN can solve over Zetta scale (10^{21}) partial differential equations and train/calibrate a dataset with extraordinary accuracy but fewer parameters using only a single graphics processing unit (GPU)., Comment: 9 pages, 2 figures

A digital twin (DT) is a virtual representation of physical process, products and/or systems that requires a high-fidelity computational model for continuous update through the integration of sensor data and user input. In the context of laser powder bed fusion (LPBF) additive manufacturing, a digital twin of the manufacturing process can offer predictions for the produced parts, diagnostics for manufacturing defects, as well as control capabilities. This paper introduces a parameterized physics-based digital twin (PPB-DT) for the statistical predictions of LPBF metal additive manufacturing process. We accomplish this by creating a high-fidelity computational model that accurately represents the melt pool phenomena and subsequently calibrating and validating it through controlled experiments. In PPB-DT, a mechanistic reduced-order method-driven stochastic calibration process is introduced, which enables the statistical predictions of the melt pool geometries and the identification of defects such as lack-of-fusion porosity and surface roughness, specifically for diagnostic applications. Leveraging data derived from this physics-based model and experiments, we have trained a machine learning-based digital twin (PPB-ML-DT) model for predicting, monitoring, and controlling melt pool geometries. These proposed digital twin models can be employed for predictions, control, optimization, and quality assurance within the LPBF process, ultimately expediting product development and certification in LPBF-based metal additive manufacturing., Comment: arXiv admin note: text overlap with arXiv:2208.02907

The extreme and repeated temperature variation during additive manufacturing of metal parts has a large effect on the resulting material microstructure and properties. The ability to accurately predict this temperature field in detail, and relate it quantitatively to structure and properties, is a key step in predicting part performance and optimizing process design. In this work, a finite element simulation of the Directed Energy Deposition (DED) process is used to predict the space- and time-dependent temperature field during the multi-layer build process for Inconel 718 walls. The thermal model is validated using the dynamic infrared (IR) images captured in situ during the DED builds, showing good agreement with experimental measurements. The relationship between predicted cooling rate, microstructural features, and mechanical properties is examined, and cooling rate alone is found to be insufficient in giving quantitative property predictions. Because machine learning offers an efficient way to identify important features from series data, we apply a 1D convolutional neural network (CNN) data-driven framework to automatically extract the dominant predictive features from simulated temperature history. The relationship between the CNN-extracted features and the mechanical properties is studied. To interpret how CNN performs in intermediate layers, we visualize the extracted features produced on each convolutional layer by a trained CNN. Our results show that the results predicted by the CNN agree well with experimental measurements and give insights into physical mechanisms of microstructure evolution and mechanical properties.