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

Computer Science > Artificial Intelligence [Submitted on 26 Feb 2026] Agentic Exploration of PDE Spaces using Latent Foundation Models for Parameterized Simulations Abhijeet Vishwasrao, Francisco Giral, Mahmoud Golestanian, Federica Tonti, Andrea Arroyo Ramo, Adrian Lozano-Duran, Steven L. Brunton, Sergio Hoyas, Soledad Le Clainche, Hector Gomez, Ricardo Vinuesa 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. Subjects: Artificial Intelligence (cs.AI); Computer Vision and Pattern Recognition (cs.CV) Cite as: arXiv:2604.09584 [cs.AI]   (or arXiv:2604.09584v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2604.09584 Focus to learn more Submission history From: Abhijeet Vishwasrao [view email] [v1] Thu, 26 Feb 2026 20:39:45 UTC (1,507 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-04 Change to browse by: cs cs.CV References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)