11 papers
Symbolic Recovery of Differential Equations: The Identifiability Problem
Philipp Scholl, Aras Bacho, Holger Boche +1
Symbolic recovery of differential equations is the ambitious attempt at automating the derivation of governing equations with the use of machine learning techniques. In contrast to…
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…
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…
Error Estimation for Physics-informed Neural Networks Approximating Semilinear Wave Equations
Beatrice Lorenz, Aras Bacho, Gitta Kutyniok
This paper provides rigorous error bounds for physics-informed neural networks approximating the semilinear wave equation. We provide bounds for the generalization and training err…
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…
Humanity's Last Exam
Long Phan, Alice Gatti, Ziwen Han +1144
Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achi…