Source-linked AI summary
Machine learning for metal additive manufacturing: Predicting temperature and melt pool fluid dynamics using physics-informed neural networks
Qiming Zhu, Zeliang Liu, Jinhui Yan
TL;DR
Metal AM modeling is limited by the expense of obtaining large labeled datasets and by the complexity of high-fidelity process simulations. The paper develops a PINN that combines data with momentum, mass, and energy conservation and introduces hard Dirichlet boundary enforcement. Applied to representative metal-manufacturing problems, the framework accurately predicts temperature and melt pool dynamics with limited labeled data, while remaining incomplete for several metal AM phenomena.
Problem
Deep learning for metal AM is challenged by the scarcity and expense of labeled experimental and high-fidelity simulation data.
Method
The paper uses a physics-informed neural network that embeds momentum, mass, and energy conservation and applies a Heaviside-based hard treatment of Dirichlet boundary conditions.
Results
The PINN accurately predicts temperature and melt pool fluid dynamics using a small amount of labeled training data across two representative metal manufacturing problems.
Takeaways & Limitations
The initial results demonstrate PINN potential for modeling complicated metal AM processes without relying on big data.
Takeaways & Limitations
The model does not resolve ambient gas, melt-pool free-surface deformation, or evaporation phenomena.
Abstract
from arXiv · showhide
The recent explosion of machine learning (ML) and artificial intelligence (AI) shows great potential in the breakthrough of metal additive manufacturing (AM) process modeling. However, the success of conventional machine learning tools in data science is primarily attributed to the unprecedented large amount of labeled data-sets (big data), which can be either obtained by experiments or first-principle simulations. Unfortunately, these labeled data-sets are expensive to obtain in AM due to the high expense of the AM experiments and prohibitive computational cost of high-fidelity simulations. We propose a physics-informed neural network (PINN) framework that fuses both data and first physical principles, including conservation laws of momentum, mass, and energy, into the neural network to inform the learning processes. To the best knowledge of the authors, this is the first application of PINN to three dimensional AM processes modeling. Besides, we propose a hard-type approach for Dirichlet boundary conditions (BCs) based on a Heaviside function, which can not only enforce the BCs but also accelerate the learning process. The PINN framework is applied to two representative metal manufacturing problems, including the 2018 NIST AM-Benchmark test series. We carefully assess the performance of the PINN model by comparing the predictions with available experimental data and high-fidelity simulation results. The investigations show that the PINN, owed to the additional physical knowledge, can accurately predict the temperature and melt pool dynamics during metal AM processes with only a moderate amount of labeled data-sets. The foray of PINN to metal AM shows the great potential of physics-informed deep learning for broader applications to advanced manufacturing.
1. Introduction
Metal AM modeling needs reliable process-structure-property relationships, but conventional high-fidelity simulations and data-driven learning are costly because the process is complex and labeled data are scarce. The paper introduces a PINN framework that combines conservation-law knowledge with limited data to predict temperature and melt pool dynamics.
- Metal AM adoption is limited by a lack of reliable process-structure-property relationships.
- Thermal-fluid simulation must represent coupled mass, flow, and heat exchanges across gas, liquid, and solid phases.
- High-fidelity numerical methods require sophisticated discretization, coupling, boundary-condition, and solver treatments, consuming substantial HPC resources.
- Deep learning for AM is constrained because experimental measurements and high-fidelity simulations are expensive sources of large labeled datasets.
- The proposed PINN fuses momentum, mass, and energy conservation with a fully connected neural network to reduce reliance on labeled data.
- The framework is demonstrated on two representative manufacturing problems, including the 2018 NIST AM-Benchmark test series.
2. Methods
The method models metal AM thermal-fluid behavior with coupled conservation-law PDEs and a fully connected neural network. Its loss combines labeled-data agreement with PDE residuals, while a Heaviside-based hard treatment enforces Dirichlet boundary conditions.
- Governing partial differential equations: The governing model assumes equal constant solid and liquid density, negligible vaporization effects, and a flat melt-pool top surface.
- Governing partial differential equations: The thermal-fluid formulation couples momentum, mass, and energy conservation through PDEs.
- Governing partial differential equations: Dirichlet conditions prescribe velocity, pressure, and temperature, while Neumann conditions prescribe traction and heat flux.
- Governing partial differential equations: Liquid fraction is zero in the solid, one in the liquid, and linear across the mushy zone, with material properties interpolated between phases.
- Physical informed neural network (PINN) for Thermal-fluid flows: The PINN uses a fully connected deep network mapping manufacturing parameters and space-time collocation points to velocity, pressure, and temperature fields.
- Loss function design: The loss combines mean-squared labeled-data discrepancies with residual constraints from momentum, mass, and energy PDEs.
- Loss function design: A hard Dirichlet treatment embeds prescribed boundary values through a Heaviside construction, automatically satisfying them without an additional constraint.
- Loss function design: Neumann boundary conditions incorporate surface tension and laser effects through additional loss terms, and training uses Adam to improve convergence speed.
3. Applications
The applications evaluate PINNs on unlabeled aluminum solidification and three-dimensional NIST metal AM benchmarks. The framework produces accurate thermal-fluid predictions, with hard Dirichlet enforcement improving learning and low-resolution PINN results remaining accurate relative to FEM.
- 3.1. Solidification of aluminum in a graphite mold without labeled data: The aluminum solidification case uses energy conservation to train a PINN without labeled data and predicts temperature from 5 s to 10 s.The setup models heat transfer from liquid aluminum into a graphite mold and tracks the solid-liquid interface.
- 3.1. Solidification of aluminum in a graphite mold without labeled data: The hard Dirichlet-boundary approach accelerates learning and produces more accurate temperature predictions than the soft approach.Figure 4 compares learning speed and temperature distributions at 10 s.
- 3.1. Solidification of aluminum in a graphite mold without labeled data: PINN and FEM show similar convergence rates, but PINN retains high accuracy at low resolution while standard FEM shows noticeable discrepancy.The comparison uses four collocation-point counts and four equivalent FEM resolutions.
- 3.2. NIST AM-bench test series: The NIST AM-Bench application predicts temperature, melt pool fluid dynamics, melt pool dimensions, and cooling rates for three-dimensional metal AM processes.The study uses an IN625 substrate and three laser-parameter cases from the NIST benchmark.
- 3.2. NIST AM-bench test series: For case B, PINN and FEM predictions of temperature, melt pool length, and melt pool fluid velocity agree well with available experimental data.The PINN generates predictions similar to FEM while using a moderate amount of training data.
- 3.2. NIST AM-bench test series: Melt pool-length discrepancies for PINN are 9.7%, 5.1%, and 2.9% in cases A, B, and C, respectively, compared with NIST measurements.The reported discrepancies are similar to those of FEM and Gan et al.’s predictions.
4. Conclusion
The paper demonstrates that PINNs can predict metal AM temperature and melt pool fluid dynamics from limited labeled data while incorporating physical knowledge. It also introduces a hard Dirichlet-boundary-condition approach and identifies important modeling limits.
- PINNs accurately predict temperature and melt pool fluid dynamics in metal AM using only a small amount of labeled training data.
- The proposed SciML framework predicts temperature, pressure, and velocity fields without relying on big data.
- The hard Dirichlet-boundary-condition approach exactly imposes prescribed values and accelerates learning.
- The initial results demonstrate PINN potential for modeling complicated metal AM processes, while conventional numerical tools remain principal methods.
- The current model omits ambient gas, free-surface deformation, and evaporation, although these effects are considered noncrucial for the studied applications.
6. Appendix: High-fidelity FEM thermal-fluid simulations
The high-fidelity FEM thermal-fluid simulations use a residual-based variational multi-scale formulation to solve coupled velocity, pressure, and temperature fields. The NIST AM-Bench simulations use a finely refined tetrahedral mesh and fully coupled numerical solution procedures.
- The RBVMS formulation solves the Navier–Stokes and energy conservation equations for velocity, pressure, and temperature fields.Testing functions belong to W, while the unknown fields belong to V.
- The thermal-energy equation includes transient, advective, and latent-heat terms involving temperature and liquid-fraction contributions.
- The formulation stabilizes momentum, continuity, and energy residuals using corresponding parameters τM, τC, and τT.The text also situates VMS alongside ALE-VMS and ST-VMS techniques used in fluid-dynamics applications.
- NIST AM-Bench FEM simulations use 4,464,276 tetrahedral elements with local refinement around the moving laser.Figure 11 shows the employed mesh.
- The NIST simulations solve velocity, pressure, and temperature fully coupled, using generalized-α time integration with Δt = 1 × 10−6 s.Newton’s method linearizes the nonlinear equations, and GMRES with block preconditioning solves the resulting linear systems.