Machine Learning · Scientific Computing

Levi Lingsch

Doctoral researcher in Applied Mathematics at the ETH AI Center and the Computational and Applied Mathematics Laboratory (CAMLab), ETH Zurich

ETH AI Center Doctoral Fellow Operator Learning Neuro-Symbolic PDEs PDE Foundation Models

I develop flexible machine-learning methods for the physical sciences: operator learning for multimodal and irregularly sampled scientific data, neuro-symbolic discovery of the governing equations themselves, and discrete tokenizers that compress physical fields — building toward foundation models for partial differential equations.

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About

Learning the language of physical systems

I am an ETH AI Center Doctoral Fellow and a doctoral researcher in the Computational and Applied Mathematics Laboratory (CAMLab) at ETH Zurich, my home group. I am supervised by Siddhartha Mishra (ETH Zurich) and Sebastian Schemm (Cambridge). My work sits at the intersection of machine learning and computational science: I design models that learn maps between function spaces, recover the symbolic structure of physical laws, and form discrete representations of continuous physics.

My research is supported by a research award from IBM, and I collaborate actively with IBM Research. A through-line of my recent work is moving from bespoke surrogates toward general, reusable models: operators that ingest heterogeneous and irregularly sampled inputs, methods that infer the governing equations rather than only their solutions, and tokenizers that capture the fine-grained detail needed to resolve fluid dynamics, weather and climate, and other physical systems. My ongoing work develops a foundation model for partial differential equations built on this tokenization paradigm.

I like ideas at the edge of what should work. I am happy to collaborate on ambitious, uncertain directions where the failure modes are as instructive as the wins.

Research interests

What I work on

Flexible operator learning

Operators that learn PDE dynamics from multimodal, irregularly sampled, and geometry-varying data, generalizing across resolutions and arbitrary domains.

Neuro-symbolic PDEs

Inferring the governing equations themselves — recovering closed-form and symbolic descriptions of physical systems, not only their numerical solutions.