Modeling and Computation in the Space of Language: Symbolic and LLM-Based Approaches

Vortrag von Prof. Dr. Haizhao Yang

Datum: 24.09.25  Zeit: 16.30 - 18.00  Raum: ETH HG G 19.2

Scientific modeling and computation traditionally rely on structured mathematics and hand-designed algorithms. In this talk, I propose a new perspective: treating both modeling and computation as processes operating within the space of natural language. I will introduce two complementary approaches that realize this vision. The first uses symbolic learning based on tree structures to generate mathematical expressions, where modeling is performed by constructing symbolic trees and computation is governed by operator rules. The Finite Expression Method (FEX) exemplifies this approach by discovering interpretable, high-accuracy solutions to PDEs and physical systems. The second approach employs large language models (LLMs) for automatic code generation and reasoning to translate scientific problem descriptions into formal mathematical models and executable solvers to solve these problems. As an example, the OptimAI framework demonstrates how multi-agent LLM collaboration enables reliable end-to-end optimization problem modeling and solving. Together, these methods point toward a unified paradigm where symbolic and language models form the foundation for interpretable, scalable scientific discovery and computation