skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Attention:

The NSF Public Access Repository (PAR) system and access will be unavailable from 11:00 PM ET on Thursday, January 15 until 2:00 AM ET on Friday, January 16 due to maintenance. We apologize for the inconvenience.


Title: Stochastically-Trained Physics-Informed Neural Networks: Application to Thermal Analysis in metal Laser Powder Bed Fusion
Modern digital manufacturing processes, such as additive manufacturing, are cyber-physical in nature and utilize complex, process-specific simulations for both design and manufacturing. Although computational simulations can be used to optimize these complex processes, they can take hours or days--an unreasonable cost for engineering teams leveraging iterative design processes. Hence, more rapid computational methods are necessary in areas where computation time presents a limiting factor. When existing data from historical examples is plentiful and reliable, supervised machine learning can be used to create surrogate models that can be evaluated orders of magnitude more rapidly than comparable finite element approaches. However, for applications that necessitate computationally- intensive simulations, even generating the training data necessary to train a supervised machine learning model can pose a significant barrier. Unsupervised methods, such as physics- informed neural networks, offer a shortcut in cases where training data is scarce or prohibitive. These novel neural networks are trained without the use of potentially expensive labels. Instead, physical principles are encoded directly into the loss function. This method substantially reduces the time required to develop a training dataset, while still achieving the evaluation speed that is typical of supervised machine learning surrogate models. We propose a new method for stochastically training and testing a convolutional physics-informed neural network using the transient 3D heat equation- to model temperature throughout a solid object over time. We demonstrate this approach by applying it to a transient thermal analysis model of the powder bed fusion manufacturing process.  more » « less
Award ID(s):
1825535
PAR ID:
10282641
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
International Design Engineering Technical Conferences
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Understanding thermal stress evolution in metal additive manufacturing (AM) is crucial for producing high-quality components. Recent advancements in machine learning (ML) have shown great potential for modeling complex multiphysics problems in metal AM. While physics-based simulations face the challenge of high computational costs, conventional data-driven ML models require large, labeled training datasets to achieve accurate predictions. Unfortunately, generating large datasets for ML model training through time-consuming experiments or high-fidelity simulations is highly expensive in metal AM. To address these challenges, this study introduces a physics-informed neural network (PINN) framework that incorporates governing physical laws into deep neural networks (NNs) to predict temperature and thermal stress evolution during the laser metal deposition (LMD) process. The study also discusses enhanced accuracy and efficiency of the PINN model when supplemented with small simulation data. Furthermore, it highlights the PINN transferability, enabling fast predictions with a set of new process parameters using a pre-trained PINN model as an online soft sensor, significantly reducing computation time compared to physics-based numerical models while maintaining accuracy. 
    more » « less
  2. Abstract Melt pool dynamics in metal additive manufacturing (AM) is critical to process stability, microstructure formation, and final properties of the printed materials. Physics-based simulation, including computational fluid dynamics (CFD), is the dominant approach to predict melt pool dynamics. However, the physics-based simulation approaches suffer from the inherent issue of very high computational cost. This paper provides a physics-informed machine learning method by integrating the conventional neural networks with the governing physical laws to predict the melt pool dynamics, such as temperature, velocity, and pressure, without using any training data on velocity and pressure. This approach avoids solving the nonlinear Navier–Stokes equation numerically, which significantly reduces the computational cost (if including the cost of velocity data generation). The difficult-to-determine parameters' values of the governing equations can also be inferred through data-driven discovery. In addition, the physics-informed neural network (PINN) architecture has been optimized for efficient model training. The data-efficient PINN model is attributed to the extra penalty by incorporating governing PDEs, initial conditions, and boundary conditions in the PINN model. 
    more » « less
  3. Lee, Jonghyun; Darve, Eric F.; Kitanidis, Peter K.; Mahoney, Michael W.; Karpatne, Anuj; Farthing, Matthew W.; Hesser, Tyler (Ed.)
    Modern design, control, and optimization often require multiple expensive simulations of highly nonlinear stiff models. These costs can be amortized by training a cheap surrogate of the full model, which can then be used repeatedly. Here we present a general data-driven method, the continuous time echo state network (CTESN), for generating surrogates of nonlinear ordinary differential equations with dynamics at widely separated timescales. We empirically demonstrate the ability to accelerate a physically motivated scalable model of a heating system by 98x while maintaining relative error of within 0.2 %. We showcase the ability for this surrogate to accurately handle highly stiff systems which have been shown to cause training failures with common surrogate methods such as Physics-Informed Neural Networks (PINNs), Long Short Term Memory (LSTM) networks, and discrete echo state networks (ESN). We show that our model captures fast transients as well as slow dynamics, while demonstrating that fixed time step machine learning techniques are unable to adequately capture the multi-rate behavior. Together this provides compelling evidence for the ability of CTESN surrogates to predict and accelerate highly stiff dynamical systems which are unable to be directly handled by previous scientific machine learning techniques. 
    more » « less
  4. Abstract The temperature history of an additively manufactured part plays a critical role in determining process–structure–property relationships in fusion-based additive manufacturing (AM) processes. Therefore, fast thermal simulation methods are needed for a variety of AM tasks, from temperature history prediction for part design and process planning to in situ temperature monitoring and control during manufacturing. However, conventional numerical simulation methods fall short in satisfying the strict requirements of time efficiency in these applications due to the large space and time scales of the required multiscale simulation. While data-driven surrogate models are of interest for their rapid computation capabilities, the performance of these models relies on the size and quality of the training data, which is often prohibitively expensive to create. Physics-informed neural networks (PINNs) mitigate the need for large datasets by imposing physical principles during the training process. This work investigates the use of a PINN to predict the time-varying temperature distribution in a part during manufacturing with laser powder bed fusion (L-PBF). Notably, the use of the PINN in this study enables the model to be trained solely on randomly synthesized data. These training data are both inexpensive to obtain, and the presence of stochasticity in the dataset improves the generalizability of the trained model. Results show that the PINN model achieves higher accuracy than a comparable artificial neural network trained on labeled data. Further, the PINN model trained in this work maintains high accuracy in predicting temperature for laser path scanning strategies unseen in the training data. 
    more » « less
  5. The inception of physics-constrained or physics-informed machine learning represents a paradigm shift, addressing the challenges associated with data scarcity and enhancing model interpretability. This innovative approach incorporates the fundamental laws of physics as constraints, guiding the training process of machine learning models. In this work, the physics-constrained convolutional recurrent neural network is further extended for solving spatial-temporal partial differential equations with arbitrary boundary conditions. Two notable advancements are introduced: the implementation of boundary conditions as soft constraints through finite difference-based differentiation, and the establishment of an adaptive weighting mechanism for the optimal allocation of weights to various losses. These enhancements significantly augment the network's ability to manage intricate boundary conditions and expedite the training process. The efficacy of the proposed model is validated through its application to two-dimensional phase transition, fluid dynamics, and reaction-diffusion problems, which are pivotal in materials modeling. Compared to traditional physics-constrained neural networks, the physics-constrained convolutional recurrent neural network demonstrates a tenfold increase in prediction accuracy within a similar computational budget. Moreover, the model's exceptional performance in extrapolating solutions for the Burgers' equation underscores its utility. Therefore, this research establishes the physics-constrained recurrent neural network as a viable surrogate model for sophisticated spatial-temporal PDE systems, particularly beneficial in scenarios plagued by sparse and noisy datasets. 
    more » « less