Generality and robustness of learned simulators under severe changes

Determine the extent to which learned simulators for continuum mechanics can generalize to severe changes in domain geometry, boundary conditions, and constitutive laws while maintaining robustness (i.e., avoiding hallucinations) and accuracy during inference.

Background

The paper investigates whether foundation model principles can be applied to learned simulators in continuum mechanics (solid and fluid). While learned simulators provide fast inference and have shown success in specific tasks, their reliability depends on training data quality and they risk producing physically meaningless outputs due to complex loss landscapes.

A central bottleneck highlighted is the lack of generality: models trained on particular setups often underperform when the domain geometry, boundary conditions, or material constitutive laws change. The authors frame the question of generalization—especially zero-shot or minimal adaptation scenarios—as a key unresolved issue, motivating their worst-case evaluation strategy and adaptation techniques (e.g., transfer learning and thermodynamic inductive biases).

References

Although so-called ``learned simulators'' have shown some success when applied to specific tasks, it remains to be studied to what extent they are able to undergo severe changes in domain shape, boundary conditions and/or constitutive laws and still provide robust (i.e., hallucination-free) and accurate results.

— On the feasibility of foundational models for the simulation of physical phenomena  (2410.14645 - Tierz et al., 2024) in Abstract (page 1)

Because a continuous, weakly organized precursor space cannot be enumerated by a catalog of weather regimes, this motivates directly sampling the trajectory distribution---a capability that arbitrary conditioning unlocks but one that forces the question of whether every generated trajectory is physically admissible.

— Extremes on Rewind: Generating 1,000-Member Ensembles Initialized at a Final Condition  (2608.19008 - Lin et al., 19 Aug 2026) in Discussion section

Mitigating rollout instability and distribution shifts for non-periodic, non-stationary problems remains an open challenge.

— From Numerical Simulators of PDEs to Neural Emulators and Back  (2608.24547 - Koehler, 25 Aug 2026) in Section 10, “Limitations and Open Questions”

Consequently, \cref{tab:cylinder-generalization-aggregate} neither confirms nor refutes whether the reductions in wall, inlet, and weak-mass diagnostics observed during physics-adapter selection transfer to these additional conditions.

— Physics-Guided Generative Surrogates for Parametric Rarefied Flows with Neural-Field Auto-Decoders: A Pipeline-Level Study of Flow Matching and Diffusion  (2608.25454 - Qi et al., 26 Aug 2026) in Section 5, Subsection “Rarefied cylinder flow,” Subsection “Aggregate results over additional conditions”

Furthermore, it remains an open question how to automatically enforce mixed boundary conditions on arbitrary domains that are defined separately on a partition $\Gamma_1 \cup \dots \cup \Gamma_J = \partial \Omega$ with operator learning.

— Enforcing Dirichlet Boundary Conditions in Operator Learning  (2608.27256 - Stuart et al., 27 Aug 2026) in Section 6, Conclusion