23 citations · 55 across the 18 of their papers we have counts for
19 papers
Agents' Last Exam
Yiyou Sun, Xinyang Han, Weichen Zhang +355
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…
Deflation-PINNs: Learning Multiple Solutions for PDEs and Landau-de Gennes
Sean Disarò, Ruma Rani Maity, Aras Bacho
Nonlinear Partial Differential Equations (PDEs) are ubiquitous in mathematical physics and engineering. Although Physics-Informed Neural Networks (PINNs) have emerged as a powerful…
KROM: Kernelized Reduced Order Modeling
Aras Bacho, Jonghyeon Lee, Houman Owhadi
We propose KROM, a kernel-based reduced-order framework for fast solution of nonlinear partial differential equations. KROM formulates PDE solution as a minimum-norm (Gaussian-proc…
What is a POLYNOMIAL-TIME Computable L2-Function?
Aras Bacho, Svetlana Selivanova, Martin Ziegler
We give two natural definitions of polynomial-time computability for L2 functions; and we show them incomparable (unless complexity class FP_1 includes #P_1).
Operator Learning at Machine Precision
Aras Bacho, Aleksei G. Sorokin, Xianjin Yang +6
Neural operator learning methods have garnered significant attention in scientific computing for their ability to approximate infinite-dimensional operators. However, increasing th…
Second-Order Parameterizations for the Complexity Theory of Integrable Functions
Aras Bacho, Martin Ziegler
We develop a unified second-order parameterized complexity theory for spaces of integrable functions. This generalizes the well-established case of second-order parameterized compl…