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pro vyhledávání: '"Kirby, Robert"'
Physics-informed neural networks (PINNs) are an increasingly popular class of techniques for the numerical solution of partial differential equations (PDEs), where neural networks are trained using loss functions regularized by relevant PDE terms to
Externí odkaz:
http://arxiv.org/abs/2410.03573
Interest is rising in Physics-Informed Neural Networks (PINNs) as a mesh-free alternative to traditional numerical solvers for partial differential equations (PDEs). However, PINNs often struggle to learn high-frequency and multi-scale target solutio
Externí odkaz:
http://arxiv.org/abs/2410.03496
FIAT (the FInite element Automatic Tabulator) provides a powerful Python library for the generation and evaluation of finite element basis functions on a reference element. This release paper describes recent improvements to FIAT aimed at improving i
Externí odkaz:
http://arxiv.org/abs/2408.03565
Autor:
Song, Jialin, Swope, Aidan, Kirby, Robert, Roy, Rajarshi, Godil, Saad, Raiman, Jonathan, Catanzaro, Bryan
Automatically designing fast and space-efficient digital circuits is challenging because circuits are discrete, must exactly implement the desired logic, and are costly to simulate. We address these challenges with CircuitVAE, a search algorithm that
Externí odkaz:
http://arxiv.org/abs/2406.09535
This paper proposes a novel deep symbolic regression approach to enhance the robustness and interpretability of data-driven mathematical expression discovery. Despite the success of the state-of-the-art method, DSR, it is built on recurrent neural ne
Externí odkaz:
http://arxiv.org/abs/2406.06751
We present polynomial-augmented neural networks (PANNs), a novel machine learning architecture that combines deep neural networks (DNNs) with a polynomial approximant. PANNs combine the strengths of DNNs (flexibility and efficiency in higher-dimensio
Externí odkaz:
http://arxiv.org/abs/2406.02336
Autor:
Kirby, Robert C., MacLachlan, Scott P.
Irksome is a library based on the Unified Form Language (UFL) that enables automated generation of Runge--Kutta methods for time-stepping finite element spatial discretizations of partial differential equations (PDE). Allowing users to express semidi
Externí odkaz:
http://arxiv.org/abs/2403.08084
Physics-informed machine learning (PIML) as a means of solving partial differential equations (PDE) has garnered much attention in the Computational Science and Engineering (CS&E) world. This topic encompasses a broad array of methods and models aime
Externí odkaz:
http://arxiv.org/abs/2402.11126
Autor:
Kirby, Robert C., Shapero, Daniel
Solutions to many important partial differential equations satisfy bounds constraints, but approximations computed by finite element or finite difference methods typically fail to respect the same conditions. Chang and Nakshatrala enforce such bounds
Externí odkaz:
http://arxiv.org/abs/2311.05880
Publikováno v:
The Twelfth International Conference on Learning Representations (ICLR 2024)
Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs). However, PINNs often struggle to solve high-frequency and multi-scale PDE
Externí odkaz:
http://arxiv.org/abs/2311.04465