Shizheng Wen

Shizheng Wen (闻仕政)

AI & Scientific Computing

PhD student @ ETH Zurich

shizheng.wen@sam.math.ethz.ch

Hi! I’m Shizheng, a doctoral student in the research group of Prof. Siddhartha Mishra at the Seminar for Applied Mathematics (SAM) at ETH Zurich. My research focuses on applied and computational mathematics, with a particular interest in developing solvers for partial differential equations (PDEs). I am passionate about advancing numerical methods and machine learning techniques for PDEs, including:

Neural Surrogates (NO and PINN) for PDE Solutions.
Differentiable Programming for Numerical Methods in PDEs.
PDE Foundation Models and their Applications.

In the past, I’ve had the honor of working with Prof. Earl Dowell at Duke University, Prof. Wanlin Guo and Prof. Xianglei Liu at NUAA.

PDEs are the language of natural science, governing everything from fluid dynamics to quantum mechanics. As an enthusiast of mathematics, physics, and biology, I love integrating multidisciplinary perspectives to tackle complex problems. If you’d like to connect or collaborate, feel free to reach out!

news

May 27, 2025	Paper posted at Arxiv: Geometry Aware Operator Transformer as an Efficient and Accurate Neural Surrogate for PDEs on Arbitrary Domains
Jan 31, 2025	Paper posted at Arxiv: RIGNO: A Graph-based framework for robust and accurate operator learning for PDEs on arbitrary domains
Apr 22, 2024	Paper accepted at IJMS: Phase-field simulation and machine learning of low-field magneto-elastocaloric effect in a multiferroic composite
Nov 13, 2023	Paper accepted at TAML: Feature identification in complex fluid flows by convolutional neural networks
Jul 28, 2022	Paper accepted at APL: A machine learning strategy for modeling and optimal design of near-field radiative heat transfer

selected publications

arxiv

Geometry Aware Operator Transformer as an Efficient and Accurate Neural Surrogate for PDEs on Arbitrary Domains

Shizheng Wen, Arsh Kumbhat, Levi Lingsch, Sepehr Mousavi, Yizhou Zhao, Praveen Chandrashekar, and Siddhartha Mishra

arXiv:2505.18781, 2025

Abs HTML Code Website

The very challenging task of learning solution operators of PDEs on arbitrary domains accurately and efficiently is of vital importance to engineering and industrial simulations. Despite the existence of many operator learning algorithms to approximate such PDEs, we find that accurate models are not necessarily computationally efficient and vice versa. We address this issue by proposing a geometry aware operator transformer (GAOT) for learning PDEs on arbitrary domains. GAOT combines novel multiscale attentional graph neural operator encoders and decoders, together with geometry embeddings and (vision) transformer processors to accurately map information about the domain and the inputs into a robust approximation of the PDE solution. Multiple innovations in the implementation of GAOT also ensure computational efficiency and scalability. We demonstrate this significant gain in both accuracy and efficiency of GAOT over several baselines on a large number of learning tasks from a diverse set of PDEs, including achieving state of the art performance on a large scale three-dimensional industrial CFD dataset.