PDEFlow: Autonomous Agentic PDE Pipelines for Neural Operator Learning and Solver-Free Inference
2026-07-06 • Machine Learning
Machine LearningArtificial Intelligence
AI summaryⓘ
The authors introduce PDEFlow, a system that automatically turns math problems involving ODEs and PDEs described by users into trained neural networks that can predict solutions quickly. Their method connects the steps of defining the problem, generating data using a solver, training neural operators, and making predictions without running solvers again. They use a natural language interface to understand user inputs and a modular setup that supports different neural network models, demonstrated here with Bayesian DeepONet. Tests show PDEFlow works on various equation types and helps automate physics and engineering tasks with less manual work.
PDE (Partial Differential Equation)ODE (Ordinary Differential Equation)neural operatorBayesian DeepONetfinite-element methodFEniCSxdata generationsolvermachine learning inferencescientific computing
Authors
Akshat Jani, Prathamesh Gadekar, Sakhinana Sagar Srinivas, Venkataramana Runkana
Abstract
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.