About

Wing Kam Liu is the Walter P. Murphy Professor of Mechanical Engineering and Civil and Environmental Engineering at Northwestern University, with courtesy appointments in Materials Science and Engineering. His research focuses on the development and application of mathematical scientific principles to understand and predict phenomena in engineering and materials science. Liu emphasizes mechanistic data science, which combines known scientific principles with newly collected data to facilitate new inventions and technological advancements. He has developed innovative AI platforms such as HiDeNN-AI, a mechanistic artificial intelligence software framework designed for rapid design, optimization, decision making, and discovery in scientific and engineering processes, including advanced manufacturing and material processing. Liu's contributions have been recognized through numerous prestigious awards, including the Gauss-Newton Medal from the International Association for Computational Mechanics, the Robert Henry Thurston Lecture Award from ASME, and the John von Neumann Medal from USACM. He has served in significant professional roles, such as Vice President of the International Association for Computational Mechanics and founding chair of the ASME Wide Nanotechnology Council. His work has had a substantial impact on computational mechanics, materials modeling, and additive manufacturing, making him a highly cited and influential researcher in his field.

Research topics

• Computer Science
• Artificial Intelligence
• Engineering
• Mathematics
• Machine Learning
• Materials science
• Mechanical engineering
• Physics
• Political Science
• Applied mathematics
• Structural engineering
• Composite material
• Mechanics
• Algorithm
• Law
• Thermodynamics
• Medicine

Selected publications

• Bayesian Interpolating Neural Network (B-INN): a scalable and reliable Bayesian model for large-scale physical systems

  ArXiv.org · 2026-01-30

  articleOpen accessSenior author

  Neural networks and machine learning models for uncertainty quantification suffer from limited scalability and poor reliability compared to their deterministic counterparts. In industry-scale active learning settings, where generating a single high-fidelity simulation may require days or weeks of computation and produce data volumes on the order of gigabytes, they quickly become impractical. This paper proposes a scalable and reliable Bayesian surrogate model, termed the Bayesian Interpolating Neural Network (B-INN). The B-INN combines high-order interpolation theory with tensor decomposition and alternating direction algorithm to enable effective dimensionality reduction without compromising predictive accuracy. We theoretically show that the function space of a B-INN is a subset of that of Gaussian processes, while its Bayesian inference exhibits linear complexity, $\mathcal{O}(N)$, with respect to the number of training samples. Numerical experiments demonstrate that B-INNs can be from 20 times to 10,000 times faster with a robust uncertainty estimation compared to Bayesian neural networks and Gaussian processes. These capabilities make B-INN a practical foundation for uncertainty-driven active learning in large-scale industrial simulations, where computational efficiency and robust uncertainty calibration are paramount.

  PublisherOA PDF

• CM-GAI: Continuum Mechanistic Generative Artificial Intelligence Theory for Data Dynamics

  Open MIND · 2026-01-28

  preprint

  Generative artificial intelligence (GAI) plays a fundamental role in high-impact AI-based systems such as SORA and AlphaFold. Currently, GAI shows limited capability in the specialized domains due to data scarcity. In this paper, we develop a continuum mechanics-based theoretical framework to generalize the optimal transport theory from pure mathematics, which can be used to describe the dynamics of data, realizing the generative tasks with a small amount of data. The developed theory is used to solve three typical problem involved in many mechanical designs and engineering applications: at material level, how to generate the stress-strain response outside the range of experimental conditions based on experimentally measured stress-strain data; at structure level, how to generate the temperature-dependent stress fields under the thermal loading; at system level, how to generate the plastic strain fields under transient dynamic loading. Our results show the proposed theory can complete the generation successfully, showing its potential to solve many difficult problems involved in engineering applications, not limited to mechanics problems, such as image generation. The present work shows that mechanics can provide new tools for computer science. The limitation of the proposed theory is also discussed.

  DOI

• Laser Powder Bed Fusion Melt Pool Dynamics for Different Geometric Variations and Powder Layer Heights: High-Fidelity Multiphysics Modeling vs 2025 NIST Experiments

  arXiv (Cornell University) · 2026-03-29

  preprintOpen access

  Metal Laser Powder Bed Fusion (PBF-LB/M) is a leading additive manufacturing technique in which part quality and grain morphology are highly dependent on process parameters. Numerous studies of process variations, such as laser power, scan speed, and spot diameter, have demonstrated that they strongly influence melt pool dynamics; however, the effects of powder layer height and geometric variations remain less well understood. In this article, we focus on variations in powder layer height and part geometry to study their influence on melt pool dynamics. We employed a high-fidelity multiphysics simulation framework based on the open source finite volume method (FVM) solver package `LaserBeamFoam' built on `OpenFOAM' to study the variations in different melt pool metrics -- melt pool depth, width, bead height, overlap depth, overlap width, solidified area, and dilution area. The solver captures coupled phenomena of heat transfer, fluid flow, vaporization, recoil pressure, Marangoni convection, and realistic laser reflection behavior to accurately model the melt pool dynamics. Simulations are performed for different powder layer heights and geometric dimensions for direct comparison with benchmark experiments conducted at the National Institute of Standards and Technology (NIST) in 2025. Quantitative validation against NIST experiment demonstrates excellent agreement in all the melt pool metrics. These results highlight the predictive capability of physics-based PBF-LB models, paving the way for process optimization, defect mitigation, and the integration of simulation into digital twin frameworks for additive manufacturing.

  PublisherDOI

• Bayesian Interpolating Neural Network (B-INN): a scalable and reliable Bayesian model for large-scale physical systems

  Open MIND · 2026-01-30

  preprintSenior author

  Neural networks and machine learning models for uncertainty quantification suffer from limited scalability and poor reliability compared to their deterministic counterparts. In industry-scale active learning settings, where generating a single high-fidelity simulation may require days or weeks of computation and produce data volumes on the order of gigabytes, they quickly become impractical. This paper proposes a scalable and reliable Bayesian surrogate model, termed the Bayesian Interpolating Neural Network (B-INN). The B-INN combines high-order interpolation theory with tensor decomposition and alternating direction algorithm to enable effective dimensionality reduction without compromising predictive accuracy. We theoretically show that the function space of a B-INN is a subset of that of Gaussian processes, while its Bayesian inference exhibits linear complexity, $\mathcal{O}(N)$, with respect to the number of training samples. Numerical experiments demonstrate that B-INNs can be from 20 times to 10,000 times faster with a robust uncertainty estimation compared to Bayesian neural networks and Gaussian processes. These capabilities make B-INN a practical foundation for uncertainty-driven active learning in large-scale industrial simulations, where computational efficiency and robust uncertainty calibration are paramount.

  DOI

• Laser Powder Bed Fusion Melt Pool Dynamics for Different Geometric Variations and Powder Layer Heights: High-Fidelity Multiphysics Modeling vs 2025 NIST Experiments

  arXiv (Cornell University) · 2026-03-29

  articleOpen access

  Metal Laser Powder Bed Fusion (PBF-LB/M) is a leading additive manufacturing technique in which part quality and grain morphology are highly dependent on process parameters. Numerous studies of process variations, such as laser power, scan speed, and spot diameter, have demonstrated that they strongly influence melt pool dynamics; however, the effects of powder layer height and geometric variations remain less well understood. In this article, we focus on variations in powder layer height and part geometry to study their influence on melt pool dynamics. We employed a high-fidelity multiphysics simulation framework based on the open source finite volume method (FVM) solver package `LaserBeamFoam' built on `OpenFOAM' to study the variations in different melt pool metrics -- melt pool depth, width, bead height, overlap depth, overlap width, solidified area, and dilution area. The solver captures coupled phenomena of heat transfer, fluid flow, vaporization, recoil pressure, Marangoni convection, and realistic laser reflection behavior to accurately model the melt pool dynamics. Simulations are performed for different powder layer heights and geometric dimensions for direct comparison with benchmark experiments conducted at the National Institute of Standards and Technology (NIST) in 2025. Quantitative validation against NIST experiment demonstrates excellent agreement in all the melt pool metrics. These results highlight the predictive capability of physics-based PBF-LB models, paving the way for process optimization, defect mitigation, and the integration of simulation into digital twin frameworks for additive manufacturing.

  PublisherOA PDF

• MultiLevel variational MultiScale (ML-VMS) framework for large-scale simulation

  Computer Methods in Applied Mechanics and Engineering · 2026-02-13 · 1 citations

  articleSenior authorCorresponding
  PublisherDOI

• CM-GAI: Continuum Mechanistic Generative Artificial Intelligence Theory for Data Dynamics

  ArXiv.org · 2026-01-28

  articleOpen access

  Generative artificial intelligence (GAI) plays a fundamental role in high-impact AI-based systems such as SORA and AlphaFold. Currently, GAI shows limited capability in the specialized domains due to data scarcity. In this paper, we develop a continuum mechanics-based theoretical framework to generalize the optimal transport theory from pure mathematics, which can be used to describe the dynamics of data, realizing the generative tasks with a small amount of data. The developed theory is used to solve three typical problem involved in many mechanical designs and engineering applications: at material level, how to generate the stress-strain response outside the range of experimental conditions based on experimentally measured stress-strain data; at structure level, how to generate the temperature-dependent stress fields under the thermal loading; at system level, how to generate the plastic strain fields under transient dynamic loading. Our results show the proposed theory can complete the generation successfully, showing its potential to solve many difficult problems involved in engineering applications, not limited to mechanics problems, such as image generation. The present work shows that mechanics can provide new tools for computer science. The limitation of the proposed theory is also discussed.

  PublisherOA PDF

• Time-marching multi-level variational multiscale tensor decomposition algorithm for heat conduction with moving heat source

  Computational Mechanics · 2026-03-10

  articleSenior author
  PublisherDOI

• Efficient GPU-computing simulation platform JAX-PF for differentiable phase field model

  arXiv (Cornell University) · 2025-12-29

  preprintOpen access

  We present JAX-PF, an open-source, GPU-accelerated, and differentiable Phase Field (PF) software package, supporting both explicit and implicit time stepping schemes. Leveraging the modern computing architecture JAX, JAX-PF achieves high performance through array programming and GPU acceleration, delivering ~5x speedup over PRISMS-PF with MPI (24 CPU cores) for systems with ~4.19 million degrees of freedom using explicit schemes, and scaling efficiently with implicit schemes for large-size problems. Furthermore, a key feature of JAX-PF is automatic differentiation (AD), eliminating manual derivations of free-energy functionals and Jacobians. Beyond forward simulations, JAX-PF demonstrates its potential in inverse design by providing sensitivities for gradient-based optimization. We demonstrate, for the first time, the calibration of PF material parameters using AD-based sensitivities, highlighting its capability for high-dimensional inverse problems. By combining efficiency, flexibility, and full differentiability, JAX-PF offers a fast, practical, and integrated tool for forward simulation and inverse design, advancing co-designing of material and manufacturing processes and supporting the goals of the Materials Genome Initiative.

  PublisherDOI

• A Framework for Supervised and Unsupervised Segmentation and Classification of Materials Microstructure Images

  SSRN Electronic Journal · 2025-01-01 · 1 citations

  preprintOpen access
  PublisherDOI

Recent grants

• Computational Multiresolution Mechanics of Solids and Structures

  NSF · $150k · 2008–2011

• Manipulating Nanoparticle-Modified Melt Pool Dynamics in Additive Manufacturing

  NSF · $874k · 2019–2024

• Data-driven Multiscale Damage and Failure Prediction

  NSF · $569k · 2018–2022

• Wafer-scale bio/nano filament assembly for chem/bio sensors

  NSF · $300k · 2005–2008

Frequent coauthors

• Ted Belytschko

  61 shared

• Gregory J. Wagner

  Northwestern University

  46 shared

• Shan Tang

  China Jiliang University

  35 shared

• Shaofan Li

  University of California, Berkeley

  34 shared

• Ying Li

  33 shared

• Zhengtao Gan

  The University of Texas at El Paso

  32 shared

• Jian Cao

  31 shared

• Dong Qian

  The University of Texas at Dallas

  30 shared

Awards & honors

• Gauss-Newton Medal, the highest award given by the Internati…
• Robert Henry Thurston Lecture Award, American Society of Mec…
• John von Neumann Medal, the highest award given by USACM (20…
• Computational Mechanics Award, Japan Society of Mechanical E…
• ASME Gustus L. Larson Memorial Award (1995)