Lianghao Cao
A Computational Science, Engineering, and Mathematics Researcher
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About Me
About Me
I am a Postdoctoral Scholar Research Associate in Computing and Mathematical Sciences at the California Institute of Technology, hosted by Andrew M. Stuart. Before this position, I obtained a Ph.D. in Computational Science, Engineering, and Mathematics under the supervision of J. Tinsley Oden and Omar Ghattas at the Oden Institute of the University of Texas at Austin. A brief professional bio can be found here.
My research combines mechanistic modeling, uncertainty quantification, and scientific machine learning to enhance the reliability of physical simulations and support risk-aware decision-making. I have experience in using modeling and simulation to address challenges in polymer science, multiscale inelasticity, epidemiology, and geophysics. Read more about my research here.
I am seeking full-time research positions!
I am seeking full-time research positions!
I am applying to tenure-track positions in engineering, statistics/data science, or computational mathematics. Please also feel free to contact me about industry research positions.
Examples of Research Topics
Examples of Research Topics
Inhomogenous Polymers
Learn to predict patterns using microscopy data
Inverse Problems
Riemannian Manifold Hamiltonian Monte Carlo
Multiscale Modeling
Stress response of a crystal plasticity unit cell
Material Testing
Image data from uniaxial testing
Sequential
Decision- Making
Greedy approach for finding signal location
Updates
Updates
October 2026
My preprint titled "Hierarchical Laminates Cannot Reproduce All Effective Properties of Planar Two-Phase Composites: A Counterexample with a 16-Component Potential" is now available on arXiv [link]. It makes progresses on open problems in the theory of composites and calculus of variations. Please see [GitHub repo] for formal verification of the main results, a report on LLM-assisted research, and a step-by-step proof exercise with answers to digest the main results.
September 2026
Our preprint titled "Schur-Neural KF: Learned Schur-Consistent Corrections to the Extended Kalman Filter" is now available on arXiv. This paper has been accepted to the 65th IEEE Conference on Decision and Control (CDC 2026). This is a joint work with Min Kim, Soon-Jo Chung, and Andrew Stuart. [link]
September 2026
My preprint titled "On Prior-to-Posterior Stability in the Wasserstein Metric for Bayesian Inverse Problems" is now available on arXiv. [link]
Presentations
Presentations
October 2026
I will give an invited seminar talk at the Mathematical Data Science Seminar Series (2:30 PM ET, Monday, November 2nd). I presented operator learning and optimal experimental design for learning history-dependent constitutive models.
July 2026
I gave a contributed talk at WCCM-ECCOMAS 2026 in MS136A on Fundamental Concepts in Scientific ML (11:45-12:00, 14a, Friday, July 24th). I presented theoretical and numerical results on the operator learning of inelastic homogenization. [slides]
June 2026
I gave a contributed talk (Monday, June 22nd) at USNCTAM 2026, in the MS on Data-driven approaches for solid mechanics. I presented a method for efficiently and reliably learning inelastic constitutive laws from optimized experiments. [paper][slides]
See past updates and presentations here.
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