Additive Friction Stir Deposition (AFSD) is an emerging metal additive manufacturing process gaining increased attention due to its solid-state processing nature, resulting in desirable mechanical properties and the capability of fabricating large parts. To understand the multi-physics nature of the process, modeling of thermal distribution and material velocity during processing is imperative, which can be addressed by solving the related partial differential equations (PDEs). However, complex coupled PDEs entail inaccuracies and slowness in utilizing the existing numerical methods, such as the Finite Volume Method (FVM). This work proposes a neural network-based method, coupled Physics Informed Neural Network (coPINN), as a fast and accurate mesh-free solution for predicting the thermomechanical states during the AFSD process. In the case studies, the proposed coPINN accurately predicts the velocity and temperature distribution for a steady-state non-linear coupled fluid dynamics-heat transfer model of the AFSD process faster than the existing FVM. Comprehensive comparisons with residual errors show the proposed method’s trustworthiness in handling coupled physics, non-linearity, and mixed boundary conditions. In addition, the solutions of our approach show better conformance with the actual experimental data than the FVM-based solver. Overall, this work shows more efficient neural network-based solutions of a PDEs-based model than a traditional numerical method.

This paper proposes a Geometry-Aware Physics Informed PointNet (GeoPIPN), a deep learning-based fast prediction model for solving Partial Differential Equations (PDE) acrossunseenadditive manufacturing (AM) geometries. Thermal distributions in AM parts are crucial and governed by diffusion models in the form of PDEs, which dictate their spatial and temporal behavior. Proper thermal distribution control ensures desired material properties, uniform microstructure, and dimensional accuracy – key to AM part quality and reliability. Existing thermal modeling primarily utilizes numerical solvers, namely, the Finite Element Methods (FEM), which are computationally costly for the fast-paced, iterative geometric design phase. Furthermore, these methods are tailored to a specific part geometry, requiring rerunning for each new geometry, making them inefficient for designs that change frequently. Our GeoPIPN considers various part geometries, represented as point clouds, as input, and is trained in a physics-informed setting where the learning objective combines PDE residual loss, boundary condition loss, and measurement-based loss from sparse sensor locations. During the training, both geometry-aware global and boundary features, as well as point-wise local features, are learned. The resulting GeoPIPN can predict the thermal distribution for a new AM part geometry at inference time without rerunning the FEM simulations. In the case studies, we demonstrate the superior performance of our GeoPIPN over benchmark methods on 2D AM test problems. Consequently, GeoPIPN offers an efficient solution for fast and accurate AM design iteration in 2D settings and provides a foundation for future extensions to fully 3D AM problems.

Exploring the outer atmosphere of the sun has remained a significant bottleneck in astrophysics, given the intricate magnetic formations that significantly influence diverse solar events. Magnetohydrodynamics (MHD) simulations allow us to model the complex interactions between the sun’s plasma, magnetic fields, and the surrounding environment. However, MHD simulation is extremely time-consuming, taking days or weeks for simulation. The goal of this study is to accelerate coronal magnetic field simulation using deep learning, specifically, the Fourier Neural Operator (FNO). FNO has been proven to be an ideal tool for scientific computing and discovery in the literature. In this paper, we proposed a global-local Fourier Neural Operator (GL-FNO) that contains two branches of FNOs: the global FNO branch takes downsampled input to reconstruct global features while the local FNO branch takes original resolution input to capture fine details. The performance of the GL-FNO is compared with state-of-the-art deep learning methods, including FNO, U-NO, U-FNO, Vision Transformer, CNN-RNN, and CNN-LSTM, to demonstrate its accuracy, computational efficiency, and scalability. Furthermore, physics-based analysis from domain experts is also performed to demonstrate the reliability of GL-FNO. The results show that GL-FNO not only accelerates the MHD simulation (a few seconds for prediction, more than ×20,000 speed up) but also provides reliable prediction capabilities, thus greatly contributing to the understanding of space weather dynamics. Our code implementation is available at https://github.com/Yutao-0718/GL-FNO.

Differential equations are fundamental in modeling numerous physical systems, including thermal, manufacturing, and meteorological systems. Traditionally, numerical methods often approximate the solutions of complex systems modeled by differential equations. With the advent of modern deep learning, Physics-informed Neural Networks (PINNs) are evolving as a new paradigm for solving differential equations with a pseudo-closed form solution. Unlike numerical methods, the PINNs can solve the differential equations mesh-free, integrate the experimental data, and resolve challenging inverse problems. However, one of the limitations of PINNs is the poor training caused by using the activation functions designed typically for purely data-driven problems. This work proposes a scalable tanh-based activation function for PINNs to improve learning the solutions of differential equations. The proposed Self-scalable tanh (Stan) function is smooth, non-saturating, and has a trainable parameter. It can allow an easy flow of gradients and enable systematic scaling of the input-output mapping during training. Various forward problems to solve differential equations and inverse problems to find the parameters of differential equations demonstrate that the Stan activation function can achieve better training and more accurate predictions than the existing activation functions for PINN in the literature.