# Hybrid thermal modeling of additive manufacturing processes using physics-informed neural networks for temperature prediction and parameter identification

arXiv: https://arxiv.org/abs/2206.07756 · HTML: https://mlsanity.com/paper/2206.07756/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 43 references that are in the map.
- First posted on arXiv 15 Jun 2022.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [Machine learning for metal additive manufacturing: Predicting temperature and melt pool fluid dynamics using physics-informed neural networks](https://mlsanity.com/paper/2008.13547/) (2020)
- [Physics-Informed Neural Networks for Nonhomogeneous Material Identification in Elasticity Imaging](https://mlsanity.com/paper/2009.04525/) (2020)
- [Training multi-objective/multi-task collocation physics-informed neural network with student/teachers transfer learnings](https://mlsanity.com/paper/2107.11496/) (2021)

## Built on by (most cited first, 14 of 14)

- [Recent Advances and Applications of Machine Learning in Experimental Solid Mechanics: A Review](https://mlsanity.com/paper/2303.07647/) (2023)
- [Towards a Digital Twin Framework in Additive Manufacturing: Machine Learning and Bayesian Optimization for Time Series Process Optimization](https://mlsanity.com/paper/2402.17718/) (2024)
- [Physics-Informed Machine Learning of Argon Gas-Driven Melt Pool Dynamics](https://mlsanity.com/paper/2307.12304/) (2023)
- [Real-Time 2D Temperature Field Prediction in Metal Additive Manufacturing Using Physics-Informed Neural Networks](https://mlsanity.com/paper/2401.02403/) (2024)
- [Adapting Projection-Based Reduced-Order Models using Projected Gaussian Process](https://mlsanity.com/paper/2410.14090/) (2024)
- [Generative Machine Learning in Adaptive Control of Dynamic Manufacturing Processes: A Review](https://mlsanity.com/paper/2505.00210/) (2025)
- [MRF-PINN: A Multi-Receptive-Field convolutional physics-informed neural network for solving partial differential equations](https://mlsanity.com/paper/2209.03151/) (2022)
- [Computational, Data-Driven, and Physics-Informed Machine Learning Approaches for Microstructure Modeling in Metal Additive Manufacturing](https://mlsanity.com/paper/2505.01424/) (2025)
- [A Physics Informed Machine Learning Framework for Optimal Sensor Placement and Parameter Estimation](https://mlsanity.com/paper/2511.15543/) (2025)
- [Online Two-stage Thermal History Prediction Method for Metal Additive Manufacturing of Thin Walls](https://mlsanity.com/paper/2310.16125/) (2023)
- [Physics-Informed Machine Learning Regulated by Finite Element Analysis for Simulation Acceleration of Melt Pool Dynamics in Laser Powder Bed Fusion](https://mlsanity.com/paper/2506.20537/) (2025)
- [Stable Long-Horizon Spatiotemporal Prediction on Meshes Using Latent Multiscale Recurrent Graph Neural Networks](https://mlsanity.com/paper/2602.18146/) (2026)
- [Material-agnostic temperature field prediction for metal additive manufacturing via a parametric PINN framework](https://mlsanity.com/paper/2604.14562/) (2026)
- [FLARE: A Data-Efficient Surrogate for Predicting Displacement Fields in Directed Energy Deposition](https://mlsanity.com/paper/2604.16649/) (2026)

## Abstract (arXiv)

Understanding the thermal behavior of additive manufacturing (AM) processes is crucial for enhancing the quality control and enabling customized process design. Most purely physics-based computational models suffer from intensive computational costs and the need of calibrating unknown parameters, thus not suitable for online control and iterative design application. Data-driven models taking advantage of the latest developed computational tools can serve as a more efficient surrogate, but they are usually trained over a large amount of simulation data and often fail to effectively use small but high-quality experimental data. In this work, we developed a hybrid physics-based data-driven thermal modeling approach of AM processes using physics-informed neural networks. Specifically, partially observed temperature data measured from an infrared camera is combined with the physics laws to predict full-field temperature history and to discover unknown material and process parameters. In the numerical and experimental examples, the effectiveness of adding auxiliary training data and using the pretrained model on training efficiency and prediction accuracy, as well as the ability to identify unknown parameters with partially observed data, are demonstrated. The results show that the hybrid thermal model can effectively identify unknown parameters and capture the full-field temperature accurately, and thus it has the potential to be used in iterative process design and real-time process control of AM.