Transient Darcy inverse problem: training data, frozen DeepONet checkpoints, inverse-problem truths, and numerical reproduction artifacts

This record contains the frozen datasets, DeepONet checkpoints, inverse-problem inputs and machine-readable numerical products supporting the transient Darcy experiments in our study of learned forward operators and derivative-informed iterative inversion. The forward problem is the transient Darcy equation ∂p/∂t − ∇·(exp(m)∇p) = f on the unit square, with homogeneous no-flow boundary conditions and initial pressure p = 1. The source term represents injection and production wells. The inverse parameter m is the log-permeability field represented on a 120 × 120 nodal grid. The deposited finite-element data include log-permeability fields, corresponding pressure trajectories and exact discrete tangent, or Jacobian–vector, products. The frozen dataset is divided into: 20,000 training samples in 100 HDF5 shards; 2,000 validation samples in 10 HDF5 shards; and 2,000 independent test samples in 10 HDF5 shards. Each shard contains 200 samples, with pressure trajectories and labels for eight derivative directions selected from a frozen 32-direction empirical Karhunen–Loève basis. The independent test set was not used for training or checkpoint selection. The deposit also contains: the frozen derivative basis and sample manifest; two validation-selected standard DeepONet checkpoints trained on 20,000 samples, comprising a derivative-informed model and its pressure-only counterpart; a held-out inverse-problem truth, with clean observations generated using a finer spatial mesh and time discretisation than those used for training and exact inversion; paired 1%, 2% and 5% noisy versions of those observations; and checksummed numerical arrays and summaries used to generate the reported table, figures and numerical statements. The files support three levels of reproducibility. The small numerical-analysis bundle supplies the inputs for regenerating the reported Darcy table and figures. The frozen checkpoints, basis and truths support replay of the exact and surrogate Landweber inversion experiments. The full finite-element dataset supports retraining the declared model configurations and repeating validation selection and independent testing. Finished figures, tables and the manuscript are not included. The training data are divided across four ZIP archives solely to make large-file transfer and recovery more reliable. No HDF5 shard is divided between archives. Extracting all archives into the same parent directory reconstructs the documented data layout. File sizes and SHA-256 checksums are recorded in the accompanying manifests. The associated GitHub repository is: https://github.com/Marco-Iglesias-Nottingham/neural-operator-landweber-darcy Source code, environment specifications and reproduction instructions are available in the associated GitHub repository. The dataset version is 1.0.0. The data and numerical artifacts in this record are licensed under the Creative Commons Attribution 4.0 International licence.