2026-10-06T16:12:17Z https://api.figshare.com/v2/oai

oai:figshare.com:article/33428968 2026-09-27T09:24:54Z category_29815 category_26770 category_29224 item_type_3 month_year_09_2026

<b>Dataset and Source Code for "</b>Physics-Corrected Boundary Neural Operators for Three-Dimensional Fractional Thermoelasticity with Curved Boundary Elements and Hierarchical Solvers<b>"</b> Mohamed Abdelsabour Fahmy (10769228) Numerical solution of differential and integral equations Numerical modelling and mechanical characterisation Numerical computation and mathematical software Boundary neural operator boundary element method scientific machine learning fractional memory thermoelasticity topology generalization hierarchical matrices <p dir="ltr">This repository accompanies the manuscript <i>“Physics-corrected boundary neural operators with causal memory and hierarchical 3D integral solvers.”</i> The study develops a modular scientific machine-learning framework in which neural operators generate boundary-field initial guesses that are subsequently corrected using boundary-integral residual iterations. The approach combines boundary neural operators, causal sum-of-exponentials memory for hereditary dynamics, GMRES/Krylov-based physics correction, curved mixed P1/P0 boundary elements for three-dimensional elastostatics, and hierarchical H/H² matrix representations for large boundary-integral operators.</p><p dir="ltr">The numerical study evaluates the framework through a hierarchy of complementary benchmarks. These include geometry-disjoint two-dimensional boundary-learning problems, structured fractional-memory validation against L1 and Mittag–Leffler references, free-form three-dimensional boundary-memory problems involving genus-zero, toroidal, disconnected and internal-cavity geometries, curved-element Kelvin–Somigliana mechanics, large-scale scalar boundary-integral compression, and full-vector Kelvin operator compression. The free-form three-dimensional benchmark contains 30 geometries split into 18 training, 4 validation and 8 test geometries, with all internal-cavity geometries withheld from training.</p><p dir="ltr">Representative results show that eight boundary-integral correction iterations reduced the mean FNO boundary-flux error from 6.513% to 0.589% on unseen two-dimensional geometries. In the free-form three-dimensional test set, four GMRES iterations reduced the mean flux error to 0.3757%, while a 24-step causal rollout achieved an aggregate flux error of 0.1908%. At N=12,000N=12{,}000, compressed Kelvin displacement and traction operators achieved storage reductions of 28.06× and 25.20×, respectively, with sampled matrix–vector multiplication errors below 0.2%.</p><p dir="ltr">The repository is intended to support reproducibility and reuse of the computational methodology. It includes or is designed to include benchmark definitions, geometry and split information, numerical data underlying figures and tables, trained-model checkpoints, sum-of-exponentials configurations, boundary-integral and Kelvin–Somigliana solver components, hierarchical matrix routines, configuration files, scripts for reproducing reported results, and environment information. The manuscript treats the demonstrated capabilities as complementary modules rather than claiming a single fully integrated large-NN, topology-diverse fractional thermoelastic solver.</p> 2026-09-27T09:24:54Z Dataset Dataset 10.6084/m9.figshare.33428968.v3 https://figshare.com/articles/dataset/_p_dir_ltr_b_Dataset_and_Source_Code_for_b_b_Physics-corrected_boundary_neural_operators_with_causal_memory_and_hierarchical_3D_integral_solvers_b_p_/33428968 CC BY 4.0