BLISS: A Dataset and Benchmark for the Buckling of Imperfect Spherical Shells

Machine-learning (ML) surrogates are increasingly used to predict how a structure responds to its geometry. However, existing scientific-ML benchmarks rarely use a change in the physical mechanism itself as the source of a distribution shift. Their shifts come from random splits, new initial conditions or held-out ranges of sampled inputs. Here, we introduce BLISS, a dataset and benchmark of 8,528 imperfect hemispherical shells simulated with finite elements until collapse, in which an instability creates the shift. A small change in geometry, two defects moving close enough to interact, changes how the shell collapses. Models map the surface with its defects to three outputs of the collapse, the collapse load (knockdown factor), the displacement field and the failure site where collapse starts. Within distribution, as on existing benchmarks, the best models reach a field $R^2$ of 0.985 and find 98% of clear failure sites. With deeper defects they lose the failure site where defects interact. Trained on shells with far-apart defects and tested on shells with close defects, every model that reads the shell geometry scores below a constant prediction of the average training shell on the field. Moving a single pair of defects from $25^{\circ }$ to $10^{\circ }$ apart lowers the collapse load by 14% in the solver, while the models predict almost no change. Five dense examples recover most of the field of two models, and the choice between two nearly equal failure sites stays close to chance. Our simulations match eight physical tests within 3.3%. Code, scorer and data-access instructions are available at https://anonymous.4open.science/w/BLISS-3388/.