Lianghao Cao

computational engineering and applied mathematics researcher

My last name is pronounced ts'ao 

I am a Postdoctoral Scholar Research Associate in Computing and Mathematical Sciences at Caltech, sponsored by Andrew M. Stuart. Before this position, I was a Postdoctoral Fellow at  The Oden Institute, The University of Texas at Austin, where I obtained a Ph.D. in Computational Science, Engineering, and mathematics under the supervision of J. Tinsley Oden and Omar Ghattas.

My research addresses issues at the heart of computational engineering, sciences, and medicine: to understand, enhance, and control the quality, validity, and reliability of simulation-based predictions of complex physical systems. I have worked on various uncertainty quantification and optimization problems associated with models governed by parametric partial differential equations. I have extensively worked on application problems associated with computational polymer science. I am currently working on constitutive modeling for solid mechanics.

You can see more on my research page and publication page.


My preprint titled "Efficient geometric Markov chain Monte Carlo enabled by derivative-informed neural operator" is now available on arXiv. This is joint work with Tom O'Leary-Roseberry and Omar Ghattas. See a summary of this work on my research page. [link]

Our manuscript, "Bayesian model calibration for block copolymer self-assembly: Likelihood-free inference and expected information gain via measure transport", is now published in Journal of Computational Physics. Congratulations to Ricardo, Josh, Fengyi, Omar, Youssef, and Dr. Oden! [link]

The members of OPTIMUS and M2dt (Bassel, DC, and I) organized an MS at SIAM TX-LA titled "Mathematical and Computational Foundations of Predictive Digital Twins" (MS 33). We invited speakers from the research areas of model reduction, optimal control, and scientific machine learning to participate in our MS. The MS also included excellent talks on oceanic, biological, and robotic systems.

Our manuscript, "Bayesian model calibration for diblock copolymer thin film self-assembly using power spectrum of microscopy data and machine learning surrogate", is now published in Computer Methods in Applied Mechanics and Engineering. Congratulations to Keyi, Peng, Dr. Oden, and Omar! This manuscript is dedicated to Prof. Tom Hughes for his lifelong contributions to Computational Sciences and Engineering. [link]

You can see more news here.


I gave an Oden Institute Seminar talk on Dec. 12. I presented ongoing work on efficient geometric MCMC enabled by derivative-informed neural operators. The paper will be available on arXiv soon! Please feel free to contact me directly if you'd like to learn more about this work.

I gave a talk at the SIAM TX-LA regional meeting in MS29. I presented ongoing work on efficient geometric MCMC for PDE-constrained Bayesian inversion enabled by neural operators with parametric derivative training (DINO). Please feel free to contact me directly if you'd like to learn more about this work.

I gave an invited talk at ICIAM 2023 Tokyo. The talk was in the "Scientific Machine Learning for Inverse Problems" session. I presented works on error estimation and correction for neural operator acceleration of PDE-constrained Bayesian inverse problems. [slides][preprint] [journal]

I gave a lunch seminar at Caltech CMS on Aug. 2. I presented works on deriving self-consistent field theory for diblock copolymers and Bayesian parameter inference from microscopy data of diblock copolymer thin films. [slides] [thesis] [preprint]

You can see my old talks and slides here.