GINTO: Geometry-informed transformer neural operator for fluid flows on arbitrary domains

Abstract

Generalizing neural operators across varying geometries remains a central challenge in scientific machine learning. While most operator-learning frameworks assume fixed geometries and parametric variability in boundary conditions or coefficients, many fluid-dynamics problems require prediction across distinct domains. In this work, we introduce the Geometry-informed transformer neural operator (GINTO), a physics-informed architecture that reformulates the physics-informed neural transformer operator (PINTO) paradigm for domain-geometry generalization. The proposed model uses a spatial representation of obstacle geometry encoded as point clouds and propagates geometric information to interior evaluation points through stacked linear cross-attention blocks. The approach is based on a point-wise collocation representation and does not require a structured or unstructured body-fitted mesh, geometric parameterization, or domain alignment. Training requires neither data nor reference solutions, physical consistency is enforced through residual minimization of the steady incompressible Navier–Stokes equations. To systematically study geometric generalization, we introduce a composite geometric distance metric and construct training subsets with controlled coverage of the geometric space. Numerical experiments demonstrate that extrapolation accuracy strongly depends on geometric diversity in the training set. Increasing coverage yields substantial improvements up to a saturation regime, beyond which gains become marginal. Compared with the original PINTO architecture, the proposed model achieves comparable accuracy while delivering a 7–10-fold reduction in training time on the benchmark problems considered in this study, thereby enabling large-scale experiments with diverse geometry sets. The results establish geometry-conditioned transformer operators as a scalable and physically consistent surrogate modeling framework for fluid flows on arbitrary domains, with relevance to shape optimization and geometry-driven simulation tasks. The code and experiments are available in the open-source framework MultiPINN at https://github.com/labadt/multipinn.