Zobrazeno 1 - 10
of 332
pro vyhledávání: '"Narayan, Akil"'
Modern physics simulation often involves multiple functions of interests, and traditional numerical approaches are known to be complex and computationally costly. While machine learning-based surrogate models can offer significant cost reductions, mo
Externí odkaz:
http://arxiv.org/abs/2410.13794
Autor:
Lowery, Matthew, Turnage, John, Morrow, Zachary, Jakeman, John D., Narayan, Akil, Zhe, Shandian, Shankar, Varun
This paper introduces the Kernel Neural Operator (KNO), a novel operator learning technique that uses deep kernel-based integral operators in conjunction with quadrature for function-space approximation of operators (maps from functions to functions)
Externí odkaz:
http://arxiv.org/abs/2407.00809
We introduce the Transformed Generative Pre-Trained Physics-Informed Neural Networks (TGPT-PINN) for accomplishing nonlinear model order reduction (MOR) of transport-dominated partial differential equations in an MOR-integrating PINNs framework. Buil
Externí odkaz:
http://arxiv.org/abs/2403.03459
We present a novel and comparative analysis of finite element discretizations for a nonlinear Rosenau-Burgers model including a biharmonic term. We analyze both continuous and mixed finite element approaches, providing stability, existence, and uniqu
Externí odkaz:
http://arxiv.org/abs/2402.08926
Autor:
Berggren, Caleb C., Jiang, David, Wang, Y. F. Jack, Bergquist, Jake A., Rupp, Lindsay C., Liu, Zexin, MacLeod, Rob S., Narayan, Akil, Timmins, Lucas H.
Central to the clinical adoption of patient-specific modeling strategies is demonstrating that simulation results are reliable and safe. Simulation frameworks must be robust to uncertainty in model input(s), and levels of confidence should accompany
Externí odkaz:
http://arxiv.org/abs/2401.15047
The shallow water flow model is widely used to describe water flows in rivers, lakes, and coastal areas. Accounting for uncertainty in the corresponding transport-dominated nonlinear PDE models presents theoretical and numerical challenges that motiv
Externí odkaz:
http://arxiv.org/abs/2310.06229
Fourier Neural Operator (FNO) is a popular operator learning framework. It not only achieves the state-of-the-art performance in many tasks, but also is efficient in training and prediction. However, collecting training data for the FNO can be a cost
Externí odkaz:
http://arxiv.org/abs/2309.16971
Forward simulation-based uncertainty quantification that studies the distribution of quantities of interest (QoI) is a crucial component for computationally robust engineering design and prediction. There is a large body of literature devoted to accu
Externí odkaz:
http://arxiv.org/abs/2303.06422
Autor:
Li, Shibo, Penwarden, Michael, Xu, Yiming, Tillinghast, Conor, Narayan, Akil, Kirby, Robert M., Zhe, Shandian
Physics-informed neural networks (PINNs) are emerging as popular mesh-free solvers for partial differential equations (PDEs). Recent extensions decompose the domain, apply different PINNs to solve the problem in each subdomain, and stitch the subdoma
Externí odkaz:
http://arxiv.org/abs/2210.12669
Autor:
Cheng, Nuojin, Malik, Osman Asif, Xu, Yiming, Becker, Stephen, Doostan, Alireza, Narayan, Akil
Publikováno v:
SIAM/ASA Journal on Uncertainty Quantification, Vol. 12, Iss. 2 (2024)
Least squares regression is a ubiquitous tool for building emulators (a.k.a. surrogate models) of problems across science and engineering for purposes such as design space exploration and uncertainty quantification. When the regression data are gener
Externí odkaz:
http://arxiv.org/abs/2209.05705