Author

G. Karniadakis

3 papers indexed here

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Open access Dec 2025

Hybrid Iterative Solvers With Geometry‐Aware Neural Preconditioners for Parametric PDEs

The convergence behavior of classical iterative solvers for parametric partial differential equations (PDEs) is often highly sensitive to the domain and specific discretization of PDEs. Previously, we introduced hybrid solvers by combining the classical solvers with neural operators for a specific geometry, but they te...

Youngkyu Lee, Francesc Levrero Florencio, Jay Pathak et al. · International Journal for Nu... · 5 citations · ⚡1

Preprint Aug 2026

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces

The Topological DeepONet framework is built on, replacing point samples by continuous linear functionals drawn from the continuous dual of a Hausdorff locally convex space, whose topology is generated by a point-separating family of seminorms rather than a single norm, and develops fixed and adaptive functional measure...

Khemraj Shukla, G. Karniadakis · 0 citations

Preprint Jul 2026

Generalizable turbulence closures across bluff-body shapes by PINN-based solver-agnostic training

Data-driven turbulence closures are usually calibrated by inverse methods that embed a CFD solver in the loop, tying the model to a particular discretization and requiring every iterate to yield a convergent solve. We instead train the closure inside a physics-informed neural network (PINN): the Reynolds-averaged Navie...

Zhen Zhang, T. Kaufer, Louise Ronglan et al. · 0 citations