Reaction-coefficient inverse problem: training data, frozen neural-operator checkpoints, inverse-problem truths, and paper artifacts

This record contains the frozen datasets, neural-operator checkpoints, inverse-problem inputs and machine-readable numerical products supporting the reaction-coefficient experiments in our study of learned forward operators and derivative-informed iterative inversion. The forward problem is the elliptic reaction equation −Δp + mp = 1 on the unit square, with homogeneous Dirichlet boundary conditions. The inverse parameter m is the physical reaction coefficient represented on a 120 × 120 nodal grid. The deposited finite-element data include coefficient fields, corresponding pressure solutions and exact tangent, or Jacobian–vector, products. The frozen dataset is divided into: 10,000 training samples in 16 HDF5 shards; 2,500 validation samples in 4 HDF5 shards; and 2,500 independent test samples in 4 HDF5 shards. Each shard contains sampled coefficient fields, exact finite-element forward solutions and labels for 16 covariance-scaled derivative directions. The independent test set was not used for optimisation, hyperparameter selection or checkpoint selection. The deposit also contains: the frozen 16-direction derivative basis; quadrature-weighted input-PCA and output-POD bases for training budgets of 1,000, 5,000 and 10,000 samples; 32 validation-selected checkpoints covering FNO, DeepONet, GenFNO and GenDeepONet architectures, including derivative-informed headline models, forward-only counterparts and controlled ablations; the clean T1 held-out training-distribution truth and structured T2 two-inclusion truth; paired 1%, 2% and 5% noisy versions of T1 and T2; and checksummed machine-readable summaries used to generate the reported tables, figures and numerical statements. The files support three levels of reproducibility. The small paper-product bundle regenerates the reported Reaction tables and figures. The frozen checkpoints, bases and truths support replay of the exact and surrogate Landweber inversion experiments. The full finite-element dataset supports rebuilding reduced bases, retraining the declared model configurations, and repeating validation selection and independent testing. 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 project layout. File sizes and SHA-256 checksums are recorded in the accompanying manifests. Source code, environment specifications and reproduction instructions are available in the associated GitHub repository: https://github.com/Marco-Iglesias-Nottingham/neural-operator-landweber-reaction The corresponding verified software release is version v1.0.1. The data and numerical artifacts in this record are licensed under the Creative Commons Attribution 4.0 International licence.