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
Predictive Modeling of
Inhomogenous Polymers
Numerical predictions of block copolymer thin film pattern before and after assimilating microscopy data
Fast and Scalable Methods for Uncertainty Quantification
Riemannian Manifold Hamiltonian Monte Carlo Sampling
Multiscale Modeling and Simulation
Micromechanics simulation of a two-scale viscoelastic material
Design Advanced Mechanical Testing of Materials
Image data obtained from uniaxial tests of a viscoelastic material
Updates
Updates
December 2025
Our paper titled "Derivative-Informed Fourier Neural Operator: Universal Approximation and Applications to PDE-Constrained Optimization" is now available on arXiv. This is a joint work with Boyuan John Yao, Dingcheng Luo, Nikola Kovachki, Thomas O'Leary-Roseberry, and Omar Ghattas. [link]
May 2025
Our paper titled "Derivative-Informed Neural Operator Acceleration of Geometric MCMC for Infinite-Dimensional Bayesian Inverse Problems" is published in the Journal of Machine Learning Research. [link]
March 2025
George Stepaniants, Margaret Trautner, and I organized a mini-symposium at SIAM CSE25 (MS249, Thursday, 2:10–3:25 pm and 4:20–5:35 pm). It focuses on data-driven methods for multiscale modeling and homogenization.
Presentations
Presentations
March 2026
I will give a talk at SIAM UQ26 in MS 89 (Monday, March 23, 6:00–6:25 PM) about my ongoing work regarding amortized sequential Bayesian inference and experimental design. See the abstract of the talk here.
October 2025
I gave a talk at PhysicsX on derivative-informed neural surrogates and their applications in accelerating Bayesian inversion [slides]. Open the slides in Adobe Acrobat for animations. Feedback is welcome!
October 2025
I gave a talk at a DDCR MURI meeting. I presented ongoing work on optimal experimental design for reliable learning of history-dependent constitutive laws [slides]. Open the slides in Adobe Acrobat for animations. Feedback is welcome!
See past updates and presentations here.
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