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

• URL: http://arxiv.org/abs/2604.09584v1
• Date: Thu, 26 Feb 2026 20:39:45 GMT
• Title: Agentic Exploration of PDE Spaces using Latent Foundation Models for Parameterized Simulations
• Abstract summary: Flow and more broadly physical phenomena governed by partial differential equations (PDEs) are inherently continuous, high-dimensional and often chaotic in nature.<n>Traditionally, researchers have explored these rich PDE solution spaces using laboratory experiments and/or computationally expensive numerical simulations.<n>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.
• Score: 5.931951549967812
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• FUSE: FK-Steered Multi-Modal Flow Matching for Efficient Simulation-Based Posterior Estimation [47.3675633392999]
  We introduce FUSE (Feynman-Kac steered mUlti-modal flow matching for efficient Simulation-based posterior Estimation)<n>Unlike prior work, FUSE employs a dual-track architecture that preserves the distinct features of multimodal inputs while facilitating dynamic interaction.<n>Our approach outperforms state-of-the-art baselines on standard SBI benchmarks, producing posteriors that closely match ground-truth MCMC.
  arXiv  Detail & Related papers  (2026-07-06T15:59:18Z)
• OMNIFLOW: A Physics-Grounded Multimodal Agent for Generalized Scientific Reasoning [51.33849811496781]
  Large Language Models (LLMs) have demonstrated exceptional logical reasoning capabilities but frequently struggle with the continuous dynamics by Partial Differential Equations (PDEs)<n>We propose OMNIFLOW, a multimodal-symbolic architecture designed to ground frozen LLMs in fundamental physical laws without requiring domain-specific parameter updates.<n>We evaluate it on a benchmark spanning microscopic turbulence, theoretical Navier-Stokes, and macroscopic global weather forecasting.
  arXiv  Detail & Related papers  (2026-03-16T18:29:01Z)
• Out-of-distribution generalization of deep-learning surrogates for 2D PDE-generated dynamics in the small-data regime [1.9116784879310027]
  We study autoregressive deep-learning surrogates for two-dimensional PDE dynamics on periodic domains.<n>In small-data periodic 2D PDE settings, convolutional architectures with inductive biases aligned to locality remain strong contenders for accurate and moderately out-of-distribution-robust surrogate modeling.
  arXiv  Detail & Related papers  (2026-01-13T10:20:59Z)
• CompNO: A Novel Foundation Model approach for solving Partial Differential Equations [0.0]
  Partial differential equations govern a wide range of physical phenomena, but their numerical solution remains computationally demanding.<n>Recent Scientific Foundation Models (SFMs) aim to alleviate this cost by learning universal surrogates from large collections of simulated systems.<n>We introduce Compositional Neural Operators (CompNO), a compositional neural operator framework for parametric PDEs.
  arXiv  Detail & Related papers  (2026-01-12T10:04:48Z)
• Latent Twins [0.3078691410268859]
  We propose a unifying framework that creates a hidden surrogate in latent space for the underlying equations.<n>Latent Twins mirror mathematical systems in a learned latent space governed by operators.
  arXiv  Detail & Related papers  (2025-09-24T23:43:19Z)
• DREAMS: Density Functional Theory Based Research Engine for Agentic Materials Simulation [1.3821435284269523]
  We introduce the DFT-based Research Engine for Agentic Materials Screening (DREAMS)<n>DREAMS is a hierarchical, multi-agent framework for DFT simulation that combines a central Large Language Model (LLM) planner agent with domain-specific LLM agents.<n>We validate DREAMS capabilities on the Sol27LC lattice-constant benchmark, achieving average errors below 1% compared to the results of human DFT experts.
  arXiv  Detail & Related papers  (2025-07-18T15:26:04Z)
• Synthetic location trajectory generation using categorical diffusion models [50.809683239937584]
  Diffusion models (DPMs) have rapidly evolved to be one of the predominant generative models for the simulation of synthetic data. We propose using DPMs for the generation of synthetic individual location trajectories (ILTs) which are sequences of variables representing physical locations visited by individuals.
  arXiv  Detail & Related papers  (2024-02-19T15:57:39Z)
• Solving High-Dimensional PDEs with Latent Spectral Models [74.1011309005488]
  We present Latent Spectral Models (LSM) toward an efficient and precise solver for high-dimensional PDEs. Inspired by classical spectral methods in numerical analysis, we design a neural spectral block to solve PDEs in the latent space. LSM achieves consistent state-of-the-art and yields a relative gain of 11.5% averaged on seven benchmarks.
  arXiv  Detail & Related papers  (2023-01-30T04:58:40Z)
• Data-driven Control of Agent-based Models: an Equation/Variable-free Machine Learning Approach [0.0]
  We present an Equation/Variable free machine learning (EVFML) framework for the control of the collective dynamics of complex/multiscale systems. The proposed implementation consists of three steps: (A) from high-dimensional agent-based simulations, machine learning (in particular, non-linear manifold learning (DMs)) We exploit the Equation-free approach to perform numerical bifurcation analysis of the emergent dynamics. We design data-driven embedded wash-out controllers that drive the agent-based simulators to their intrinsic, imprecisely known, emergent open-loop unstable steady-states.
  arXiv  Detail & Related papers  (2022-07-12T18:16:22Z)
• Multi-fidelity Hierarchical Neural Processes [79.0284780825048]
  Multi-fidelity surrogate modeling reduces the computational cost by fusing different simulation outputs. We propose Multi-fidelity Hierarchical Neural Processes (MF-HNP), a unified neural latent variable model for multi-fidelity surrogate modeling. We evaluate MF-HNP on epidemiology and climate modeling tasks, achieving competitive performance in terms of accuracy and uncertainty estimation.
  arXiv  Detail & Related papers  (2022-06-10T04:54:13Z)
• Moser Flow: Divergence-based Generative Modeling on Manifolds [49.04974733536027]
  Moser Flow (MF) is a new class of generative models within the family of continuous normalizing flows (CNF) MF does not require invoking or backpropagating through an ODE solver during training. We demonstrate for the first time the use of flow models for sampling from general curved surfaces.
  arXiv  Detail & Related papers  (2021-08-18T09:00:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.