WangRuocheng/QuanONet-Data

PDE Operator Learning Dataset

Dataset Summary

This dataset serves as a comprehensive benchmark for Scientific Machine Learning (SciML) and Operator Learning. It contains a diverse collection of 1D and 2D physics field mappings designed to evaluate and train deep learning surrogate models, such as DeepONets and Fourier Neural Operators (FNOs). The data covers a wide spectrum of physical scenarios, ranging from linear and nonlinear dynamic systems to fluid mechanics, reaction-diffusion processes, and macroscopic traffic flow, testing the models' capacity to learn mappings between infinite-dimensional function spaces.

Dataset Structure & Physics Background

2D Partial Differential Equations (PDEs)

This category focuses on 2D spatial (or 1D spatial combined with 1D temporal) field evolutions.

• Darcy Operator: A classic benchmark in operator learning that describes steady-state fluid flow through porous media governed by an elliptic PDE. The primary task is to map input permeability fields to output pressure fields.
• Advection Operator: This models the transport and convection of substances or energy under fluid flow, requiring the network to map an initial waveform to its future temporal evolution.
• RDiffusion (Reaction-Diffusion) Operator: Captures the complex process where substances transform via local chemical reactions while diffusing through space (often resulting in phenomena like Turing patterns). The model must map initial concentration fields or source terms to their spatiotemporal distributions.

1D PDEs and Operators

This subset involves 1D spatial domains or 1D time-series dynamic systems, testing both physical phenomena and foundational mathematical transformations.

• Physical Systems: The Burgers Operator is a standard 1D nonlinear PDE used to simulate fluid dynamics, specifically the formation and dissipation of shock waves, mapping initial velocity profiles to future states. Similarly, the LWR Operator represents the Lighthill-Whitham-Richards macroscopic traffic flow model, predicting future traffic density and congestion waves based on initial density distributions.
• Mathematical & Dynamic Operators: To evaluate pure mathematical mapping capabilities, the Inverse Operator tests the model's ability to learn smooth integral mappings (the inverse of derivatives). The Identity Operator serves as a baseline sanity check to ensure the architecture can achieve lossless information transmission from input to output. Finally, the Homogeneous and Nonlinear Operators provide generalized ODE benchmarks to test the network's structural capacity to fit linear systems with homogeneous conditions and highly complex nonlinear functional mappings.

Potential Use Cases

Neural Operator Benchmarking: Training and evaluating architectures like FNOs, DeepONets, or newer attention-based operators. PINN Baselines: Serving as a pure data-driven baseline to compare against or augment Physics-Informed Neural Networks. Scientific Computing Acceleration: Building highly efficient deep learning surrogates to accelerate traditional numerical solvers like Finite Element Method (FEM) or Finite Difference Method (FDM).

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