PDEFlow: Autonomous Agentic PDE Pipelines for Neural Operator Learning and Solver-Free Inference

Source

• Source name: arXiv
• Source kind: paper
• Authors / organization: Akshat Jani, Prathamesh Gadekar, Sakhinana Sagar Srinivas, Venkataramana Runkana
• Venue: arXiv: cs.LG
• Published: 2026-07-06
• Collected: 2026-07-07
• URL: http://arxiv.org/abs/2607.05134v1
• PDF: https://arxiv.org/pdf/2607.05134v1
• DOI: UNKNOWN

Plain-Language Brief

The paper presents PDEFlow, a framework that converts user-level descriptions of ODEs and PDEs into neural operator pipelines for autonomous agentic simulations. It includes stages for problem specification, data generation, operator training, and inference, with the ability to switch between different neural operators without altering the pipeline.

What the Document Says

• PDEFlow is an autonomous framework that converts natural-language input and user edits into validated problem specifications.
• It generates data for the configured governing-equation using FEniCSx finite-element backend and stores solutions as operator-ready tensors.
• The training and inference stages use a registry-based interface that allows different neural operators to be trained and deployed.
• In the current implementation, it uses a multi-branch Bayesian DeepONet.
• Experiments show PDEFlow can generate solver-backed datasets, train neural operators across steady and transient problem classes, and provide solver-free predictions from saved checkpoints.

Key Concepts Mentioned

• PDEFlow
• autonomous agentic framework
• ODE
• PDE
• data generation
• neural operator training
• checkpoint-based inference
• multi-branch Bayesian DeepONet

Claims Made by the Document

• PDEFlow can construct valid specifications.
• It generates solver-backed datasets.
• It trains neural operators across steady and transient problem classes.

Evidence Used

• The text describes the steps taken by PDEFlow to achieve these claims.

Methods / Approach

• stateful input graph
• FEniCSx finite-element backend
• registry-based interface
• multi-branch Bayesian DeepONet

Limitations Stated by the Authors

UNKNOWN

Limitations Noted by the Agent

Agent interpretation — not from the source.

UNKNOWN

Open Questions

UNKNOWN

Notes for Future Q&A

May include interpretation. Labeled where it does.

UNKNOWN

Raw Abstract / Excerpt

We present PDEFlow, an autonomous agentic framework that turns user-level ODE and PDE descriptions into solver-backed neural-operator pipelines. The workflow links problem specification, data generation, operator training, and checkpoint-based inference. A stateful input graph converts multi-turn natural-language input and user edits into validated problem specifications. The data-generation module then samples parameters, solves the configured governing-equation with FEniCSx finite-element backend, and stores the solutions as operator-ready tensors. The training and inference stages use a registry-based interface, allowing different neural operators to be trained and deployed without changing the surrounding pipeline. In the current implementation, we instantiate this interface with a multi-branch Bayesian DeepONet. Experiments on benchmark ODE and PDE tasks show that PDEFlow can construct valid specifications, generate solver-backed datasets, train neural operators across steady and transient problem classes, and provide solver-free predictions from saved checkpoints. The framework is designed for repeatable scientific and engineering workflows where many related physics configurations must be specified, simulated, learned, and queried with minimal manual intervention.