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Xiaoyu Xie

Research Scientist @ Meta | PhD @ Northwestern University

Research

1. Data-driven discovery of universal laws

1.1 Dimensionless Learning (Dimensional Analysis + Machine Learning) for scientific discovery

Dimensionless learning combines fundamental physics principles with state-of-the-art machine learning techniques to solve scientific and engineering problems. By embedding the principle of dimensional invariance into a two-level machine learning scheme, it can automatically discover dominant dimensionless numbers and governing laws (scaling laws and differential equations) from noisy and scarce measurements.

1.2 Dimensionally invariant Neural Network (DimensionNet) for scientific discovery

The DimensionNet reduces the dimensionality of the original input parameters by automatically discovering a smaller set of governing dimensionless numbers and transforming the high-dimensional inputs to the dimensionless set.

  • 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. 
    Paper

2. Data-driven reduced-order modeling

Smooth and sparse latent dynamics in operator learning with jerk regularization

Spatiotemporal modeling is critical for understanding complex systems across various scientific and engineering disciplines, but governing equations are often not fully known or computationally intractable due to inherent system complexity. Data-driven reduced-order models (ROMs) offer a promising approach for fast and accurate spatiotemporal forecasting by computing solutions in a compressed latent space. However, these models often neglect temporal correlations between consecutive snapshots when constructing the latent space, leading to suboptimal compression, jagged latent trajectories, and limited extrapolation ability over time. To address these issues, this paper introduces a continuous operator learning framework that incorporates jerk regularization into the learning of the compressed latent space. This jerk regularization promotes smoothness and sparsity of latent space dynamics, which not only yields enhanced accuracy and convergence speed but also helps identify intrinsic latent space coordinates. Consisting of an implicit neural representation (INR)-based autoencoder and a neural ODE latent dynamics model, the framework allows for inference at any desired spatial or temporal resolution. The effectiveness of this framework is demonstrated through a two-dimensional unsteady flow problem governed by the Navier-Stokes equations, highlighting its potential to expedite high-fidelity simulations in various scientific and engineering applications.

  • Xie, X., Mowlavi, S., Benosman, M., (2024). Smooth and sparse latent dynamics in operator learning with jerk regularization. arXiv preprint arXiv:2402.15636.
    Paper (Accepted by NeurIPS 2025 Workshop ML4PS)

3. Machine Learning-based Digital Twin

AI-empowered scientific discovery and digital twin in additive manufacturing

Metal additive manufacturing provides remarkable flexibility in geometry and component design, but localized heating/cooling heterogeneity leads to spatial variations of as-built mechanical properties, significantly complicating the materials design process. To this end, we develop a mechanistic data-driven framework integrating wavelet transforms and convolutional neural networks to predict location-dependent mechanical properties over fabricated parts based on process-induced temperature sequences, i.e., thermal histories. The framework enables multiresolution analysis and importance analysis to reveal dominant mechanistic features underlying the additive manufacturing process, such as critical temperature ranges and fundamental thermal frequencies. We systematically compare the developed approach with other machine learning methods. The results demonstrate that the developed approach achieves reasonably good predictive capability using a small amount of noisy experimental data. It provides a concrete foundation for a revolutionary methodology that predicts spatial and temporal evolution of mechanical properties leveraging domain-specific knowledge and cutting-edge machine and deep learning technologies.

  • 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.
    Paper