Neural Bridges in Complex Flows

Abstract: Predicting the behaviour of fluids in which microscopic structure matters remains an open challenge: fine-scale physics governs macroscopic observables, yet a fully resolved description is computationally prohibitive. I will outline a framework that links particle-scale and continuum descriptions through neural operators, providing a data-driven “bridge”. I will present the general strategy which is based on embedding discrete simulations into a reduced latent space, learning scale-transfer maps, and coupling the resulting surrogate with conventional CFD. Then I will specialise it to blood clot formation, a test-bed where multiscale interactions are unavoidable.
Recent work [1,2,3] shows that a DeepONet surrogate can reproduce LAMMPS-based platelet-like suspensions across capillary numbers spanning the physiological range, with relative errors below 5% on stress measures and a two-order-of-magnitude speed-up. These results support the feasibility of the overall scheme and suggest clear performance targets for future refinements.
I will close by sketching some research directions that build on this foundation: (i) two-way coupling with CFD to address rheological questions and thrombosis risk; (ii) richer particulate models incorporating cytoskeletal mechanics; (iii) alternative network architectures such as graph and transformer variants; and (iv) extension to reactive transport for drug delivery and platelet activation. Together, these directions aim to supply a flexible, verifiable toolset for multiscale fluid mechanics.

[1] Laudato, M., Manzari, L., & Shukla, K. (2024). High-Fidelity Description of Platelet Deformation Using a Neural Operator. arXiv preprint arXiv:2412.00747.
[2] Laudato, M., Manzari, L., & Shukla, K. (2025). Neural Operator Modeling of Platelet Geometry and Stress in Shear Flow. arXiv preprint arXiv:2503.12074.
[3] Laudato, M. (2025). Surrogate Prediction of Platelet Dynamics under Varying Capillary Number. In prepration.