PDEFlow: Autonomous Agentic PDE Pipelines for Neural Operator Learning and Solver-Free Inference
For scientists and engineers, PDEFlow automates the repetitive pipeline from problem specification to neural operator inference, reducing manual intervention in multi-configuration physics workflows.
PDEFlow is an autonomous agentic framework that turns natural-language ODE/PDE descriptions into neural-operator pipelines, enabling solver-free inference. It successfully generates valid specifications, solver-backed datasets, and trains neural operators across steady and transient problems.
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.