Journal Articles:
- Xie, X., Samaei, A., Guo, J., Liu, W. K., & Gan, Z., (2022). Data-driven discovery of dimensionless numbers and governing laws from scarce measurements. Nature Communications, 13, 7562. https://doi.org/10.1038/s41467-022-35084-w
- Xie, X., Bennett, J., Saha, S., Lu, Y., Cao, J., Liu, W. K., & Gan, Z. (2021). Mechanistic data-driven prediction of as-built mechanical properties in metal additive manufacturing. npj Computational Materials, 7(1), 1–12. https://doi.org/10.1038/s41524-021-00568-8
- Park, C., Saha, S., Guo, J., Zhang, H., Xie, X., Bessa, M. A., Qian, D., Chen, W., Wagner, G., Cao, J. & Liu, W. K. (2026). Interpolating Neural Networks for Accurate and Resource-Efficient Predictive Artificial Intelligence. Nature Communications, 16, 8753. https://doi.org/10.1038/s41467-025-63790-8
- Samaei, A., Leonor, J. P., Gan, Z., Sang, Z., Xie, X., Simonds, B. J., Liu, W. K. & Wagner, G. J. (2024). Benchmark study of melt pool and keyhole dynamics, laser absorptance, and porosity in additive manufacturing of Ti-6Al-4V. Progress in Additive Manufacturing, 1–25. https://doi.org/10.1007/s40964-024-00579-7
- Li, Y., Mojumder, S., Lu, Y., Al Amin, A., Guo, J., Xie, X., Chen, W., Wagner, G. J., Cao, J. & Liu, W. K. (2024). Statistical parameterized physics-based machine learning digital shadow models for laser powder bed fusion process. Additive Manufacturing, 87, 104214. https://doi.org/10.1016/j.addma.2024.104214
- Amin, A., Li, Y., Lu, Y., Xie, X., Mojumder, S., Gan, Z., Wagner, G., & Liu, W. K. (2023). Physics Guided Heat Source for Quantitative Prediction of the Laser Track Measurements of IN718 in 2022 NIST AM Benchmark Test. npj Computational Materials, 10, 37. https://doi.org/10.1038/s41524-024-01198-6
- Shao, J., Samaei, A., Xue, T., Xie, X., Guo, S., Cao, J., MacDonald, B., & Gan, Z. (2023). Additive friction stir deposition of metallic materials: process, structure and properties. Materials & Design, 234, 112356. https://doi.org/10.1016/j.matdes.2023.112356
- Xue, T., Liao, S., Gan, Z., Park, C., Xie, X., Liu, W. K., & Cao, J. (2023). JAX-FEM: A differentiable GPU-accelerated 3D finite element solver for automatic inverse design and mechanistic data science. Computer Physics Communications, 108802. https://doi.org/10.1016/j.cpc.2023.108802
- Mozaffar, M., Liao, S., Xie, X., Saha, S., Park, C., Cao, J., Liu, W. K., & Gan, Z. (2022). Mechanistic artificial intelligence (Mechanistic-AI) for modeling, design, and control of advanced manufacturing processes: Current state and perspectives. Journal of Materials Processing Technology, 117485. https://doi.org/10.1016/j.jmatprotec.2022.117485
- Saha, S., Gan, Z., Cheng, L., Gao, J., Kafka, O. L., Xie, X., Li, H., Tajdari, M., Kim, H. A., & Liu, W. K. (2021). Hierarchical Deep Learning Neural Network (HiDeNN): An artificial intelligence (AI) framework for computational science and engineering. Computer Methods in Applied Mechanics and Engineering, 373, 113452. https://doi.org/10.1016/j.cma.2020.113452
- Zhang, L., Yu, G., Li, S., He, X., Xie, X., Xia, C., Ning, W., & Zheng, C. (2019). The effect of laser surface melting on grain refinement of phase separated Cu-Cr alloy. Optics & Laser Technology, 119, 105577. https://doi.org/10.1016/j.optlastec.2019.105577
Conference Papers:
- Xie, X., Mowlavi, S., & Benosman, M. (2025). Smooth and sparse latent dynamics in operator learning with jerk regularization. NeurIPS 2025 Workshop ML4PS. https://arxiv.org/abs/2402.15636
- Guo, J., Xie, X., Park, C., Zhang, H., Politis, M., Domel, G., Hughes, T. J., & Liu, W. K. (2025). Interpolating Neural Network–Tensor Decomposition (INN-TD): a scalable and interpretable approach for large-scale physics-based problems. arXiv preprint arXiv:2503.02041. (International Conference on Machine Learning (ICML)). https://arxiv.org/abs/2503.02041
- Guo, J., Park, C., Xie, X., Sang, Z., Wagner, G. J., & Liu, W. K. (2024). Convolutional Hierarchical Deep Learning Neural Networks–Tensor Decomposition (C-HiDeNN-TD): a scalable surrogate modeling approach for large-scale physical systems. arXiv preprint arXiv:2409.00329. (NeurIPS 2024 Workshop D3S3). https://arxiv.org/abs/2409.00329
Patents:
- Mowlavi, S., Xie, X., & Benosman, M., Mitsubishi Electric Research Laboratories, Inc., 2025. Physics-Informed Smooth Operator Learning for High-Dimensional Systems Prediction and Control. U.S. Patent Application 18/20250146695, filed November 6, 2023.
- Liu, W. K., Saha, S., Mojumder, S., Suarez, D. A., Lu, Y., Li, H., Xie, X. & Gan, Z. (2024). U.S. Patent Application No. 18/286,619.
- Yu, G., Xie, X., et al. An evaluation method for the relationship between plasma and final modification effect during laser modification, CN 106296649 A, (Granted patent; Chinese patent)
Talks
- Xie, X., Samaei, A., Guo, J., Gan, Z., Liu, W., Data-driven discovery of dimensionless numbers and governing laws from scarce measurements, Scientific Machine Learning Webinar, Carnegie Mellon University, March, 2023.
- Xie, X., Gan, Z., Liu, W., Dimensionless learning for discovering new dimensionless numbers, 16th U.S. National Congress on Computational Mechanics (USNCCM16), July 25-29, 2021, Virtual Event.
- Xie, X., Gan, Z., Saha, S., Liu, W., Mechanistic digital twin of metal additive manufacturing, Mechanistic Machine Learning and Digital Twins for Computational Science, Engineering & Technology (MMLDT-CSET 2021), Sep. 2021, San Diego, USA.
Codes
- PyDimension: A Python package for automatically data-driven scientific discovery;
- PyDimension Documentation: Online documentation and tutorials for PyDimension;