# Advanced Deep Operator Networks to Predict Multiphysics Solution Fields in Materials Processing and Additive Manufacturing

**Authors:** Shashank Kushwaha, Jaewan Park, Seid Koric, Junyan He, Iwona Jasiuk, Diab Abueidda  
**arXiv:** [2403.14795](https://arxiv.org/abs/2403.14795)  
**Date:** 2024-03-21  
**Summary page:** https://www.summarizepaper.com/en/paper/2403.14795v1/

## Key points

- Advanced variants of Deep Operator Network (DeepONet) architecture used for predicting thermal and mechanical solution fields in materials processing and additive manufacturing
- Newly devised DeepONet formulations incorporated sequential learning and Residual U-Net (ResUNet) architectures
- Trained to simultaneously forecast complete thermal and mechanical solution fields under variable conditions, loading histories, process parameters, and geometries
- Demonstrated efficacy in providing accurate solutions across different application areas
- Outperformed traditional finite-element analysis methods by several orders of magnitude
- Future studies will focus on incorporating data from every simulation time step into neural networks and exploring additive manufacturing for 3D structures
- Utilization of high-performance computing systems optimized for multi-scale computational frameworks
- Well-trained DeepONet architectures can serve as a surrogate for modeling complex real-world manufacturing processes
- Data and source code supporting the study will be made available in a public GitHub repository

## Summary

In this groundbreaking study, advanced variants of the Deep Operator Network (DeepONet) architecture were utilized to predict entire thermal and mechanical solution fields in materials processing and additive manufacturing. These newly devised DeepONet formulations incorporated sequential learning and Residual U-Net (ResUNet) architectures. They were trained for the first time to simultaneously forecast complete thermal and mechanical solution fields under variable loading conditions, loading histories, process parameters, and varying geometries. The research showcased the efficacy of DeepONets in providing accurate solutions across different application areas - from steel continuous casting with multiple visco-plastic constitutive laws to sequentially coupled direct energy deposition for additive manufacturing. Despite the complexity of spatially variable stress distributions, DeepONets demonstrated the ability to infer full-field temperature and stress solutions rapidly and efficiently. They outperformed traditional finite-element analysis (FEA) methods by several orders of magnitude. Looking ahead, future studies will focus on incorporating data from every simulation time step into neural networks to predict the complete history of solution fields. Additionally, there are plans to explore additive manufacturing for intricate 3D structures in order to accurately predict mechanical properties. The utilization of high-performance computing (HPC) systems will be further optimized to generate data from multi-scale computational frameworks encompassing micro and mesoscale phenomena. The research findings underscored that well-trained advanced DeepONet architectures can serve as a surrogate for modeling complex real-world manufacturing processes. This breakthrough opens up avenues for preliminary optimization, inverse analysis, sensitivity analysis, uncertainty quantification, online controls, digital twins creation, and other computationally intensive numerical analyses requiring multiphysics forward solution evaluations in domains with variable geometries and input parameters. To facilitate replication of results and promote transparency in research practices,the data and source code supporting this study will be made available in a public GitHub repository. Furthermore, the authors have declared no conflict of interest in conducting this study.