59 papers
Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces
Khemraj Shukla, George Em Karniadakis
Deep Operator Networks (DeepONets; arXiv:1910.03193) typically encode an input function through point values on a fixed discretization. Building on the Topological DeepONet framewo…
Quantifying reticulocyte biomechanics in health and disease
Zhaojie Chai, Jianlu Zheng, He Li +2
Red blood cell (RBC) populations are mechanically heterogeneous, yet how this shapes transport, clogging, and rheology in confined environments remains unclear. We combine microflu…
Generalizable turbulence closures across bluff-body shapes by PINN-based solver-agnostic training
Zhen Zhang, Theo Käufer, Louise Ronglan +2
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 it…
ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms
Juan Diego Toscano, Daniel T. Chen, George Em Karniadakis
Progress in computational science depends on complex numerical workflows that must faithfully encode physical laws, yet translating conceptual insight into reliable code remains a…
Spectrally Safe Neural Operator Warm-Starts for Large-Scale Newton Solvers
Jaemin Oh, Youngkyu Lee, Jerome Darbon +1
Neural operators are increasingly used to warm-start Newton solvers for nonlinear PDEs, on the premise that a low test error places the initial guess inside the basin of attraction…
Agents' Last Exam
Yiyou Sun, Xinyang Han, Weichen Zhang +306
Recent AI systems have achieved strong results on a wide range of benchmarks, yet these gains have not translated into economically meaningful deployment across many professional d…