Agentic Exploration of PDE Spaces using Latent Foundation Models for Parameterized Simulations

TL;DR

This paper introduces a multi-agent LLM framework coupled with latent foundation models to autonomously explore PDE solution spaces, enabling efficient discovery of flow phenomena and scaling laws.

Contribution

It presents a novel coupling of multi-agent LLMs with LFMs to facilitate continuous, large-scale exploration of PDE parameter spaces without human intervention.

Findings

Discovered a two-mode structure for minimum displacement thickness.

Identified a linear scaling law for maximum momentum thickness.

Revealed dual-extrema landscape at flow regime transition.

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 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, enabling continuous exploration across governing PDE parameters and boundary conditions. The LFM serves as an on-demand surrogate simulator, allowing agents to query arbitrary parameter configurations at negligible cost. A hierarchical agent architecture orchestrates exploration through a closed loop of hypothesis, experimentation, analysis and verification, with a tool-modular interface requiring no user support. Applied to flow past tandem cylinders at Re = 500, the framework autonomously evaluates over 1,600 parameter-location pairs and discovers divergent scaling laws: a regime-dependent two-mode structure for minimum displacement thickness and a robust linear scaling for maximum momentum thickness, with both landscapes exhibiting a dual-extrema structure that emerges at the near-wake to co-shedding regime transition. The coupling of the learned physical representations with agentic reasoning establishes a general paradigm for automated scientific discovery in PDE-governed systems.