Agentic Exploration of PDE Spaces using Latent Foundation Models for Parameterized Simulations
Summary: arXiv:2604.09584v1 Announce Type: new
Abstract: Flow physics and more broadly physical phenomena governed by partial differential equations (PDEs), are inherently continuous, high-dimensional and often chaotic in nature. Traditionally, researchers have explored these rich spatiotemporal PDE solution spaces using laboratory experiments and/or computationally expensive numerical simulations. This severely limits automated and large-scale exploration, unlike domains such as drug discovery or materials science, where discrete, tokenizable representations naturally interface with large language models.
We address this challenge by coupling multi-agent LLMs with latent foundation models (LFMs), a generative model over parametrised simulations, that learns explicit, compact and disentangled latent representations of flow fields. This innovative approach enables continuous exploration across governing PDE parameters and boundary conditions.
Key Features of the Framework
- Surrogate Simulation: The LFM acts as an on-demand surrogate simulator, allowing agents to query arbitrary parameter configurations at negligible computational cost.
- Hierarchical Agent Architecture: The framework features a hierarchical agent architecture that orchestrates exploration through a closed loop of hypothesis, experimentation, analysis, and verification.
- Tool-Modular Interface: The system is equipped with a tool-modular interface that requires no user support, enhancing its usability in various scientific applications.
Application and Findings
In a practical application, this framework was tested on the flow past tandem cylinders at a Reynolds number (Re) of 500. The system autonomously evaluated over 1,600 parameter-location pairs, resulting in significant discoveries regarding flow characteristics:
- Divergent Scaling Laws: The exploration revealed a regime-dependent two-mode structure for minimum displacement thickness.
- Momentum Thickness Scaling: A robust linear scaling was found for maximum momentum thickness.
- Dual-Extrema Structure: Both landscapes exhibited a dual-extrema structure that emerges at the transition from the near-wake to the co-shedding regime.
Conclusion
The coupling of learned physical representations with agentic reasoning in this innovative framework establishes a general paradigm for automated scientific discovery in PDE-governed systems. As automation becomes increasingly vital in scientific research, this approach presents a significant leap forward, enabling researchers to explore complex physical phenomena more efficiently and effectively.
This research opens up new avenues for future studies, particularly in fields that require extensive parameter exploration and data analysis. By leveraging the capabilities of LFMs and multi-agent systems, the potential for breakthroughs in understanding complex flow dynamics and other PDE-related phenomena is immense.