Results 11 to 20 of about 53,887 (179)

A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces

, 2019
The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding method developed to solve a variety of partial differential equations (PDEs) on smooth surfaces, using a closest point representation of the surface ...
Ling, L., Petras, A., Piret, C., Ruuth, S. J.   +3 more
core   +1 more source

On two aspects of the Painleve analysis

, 2013
We use the Calogero equation to illustrate the following two aspects of the Painleve analysis of nonlinear PDEs. First, if a nonlinear equation passes the Painleve test for integrability, the singular expansions of its solutions around characteristic ...
Sakovich, Sergei
core   +2 more sources

A mixed $\ell_1$ regularization approach for sparse simultaneous approximation of parameterized PDEs

, 2018
We present and analyze a novel sparse polynomial technique for the simultaneous approximation of parameterized partial differential equations (PDEs) with deterministic and stochastic inputs.
Dexter, Nick, Tran, Hoang, Webster, Clayton   +2 more
core   +1 more source

Mathematical analysis and numerical methods for a PDE model of a stock loan pricing problem

Journal of Mathematical Analysis and Applications, 2013
In the present paper, the stock loan pricing problem is addressed in the case when the accumulative dividend yield is returned to the borrower on redemption. The optimal regularity of the solution in anisotropic Sobolev spaces is analyzed, by applying obstacle problem techniques associated to hypoelliptic equations of Kolmogorov type.
PASCUCCI, ANDREA, M. Suarez Taboada, C. Vazquez   +2 more
openaire   +3 more sources

AutomataGPT: Transformer‐Based Forecasting and Ruleset Inference for Two‐Dimensional Cellular Automata

Advanced Science, EarlyView.
We introduce AutomataGPT, a generative pretrained transformer (GPT) trained on synthetic spatiotemporal data from 2D cellular automata to learn symbolic rules. Demonstrating strong performance on both forward and inverse tasks, AutomataGPT establishes a scalable, domain‐agnostic framework for interpretable modeling, paving the way for future ...
Jaime A. Berkovich, Noah S. David, Markus J. Buehler   +2 more
wiley   +1 more source

Mathematical analysis of PDE systems which govern fluid-structure interactive phenomena

Boletim da Sociedade Paranaense de Matemática, 2007
In this paper, we review and comment upon recently derived results for time dependent partial differential equation (PDE) models, which have been used to describe the various fluid-structure interactions which occur in nature. For these fluid-structure PDEs, this survey is particularly focused on the authors' results of (i) semigroup wellposedness, (ii)
Avalos, George, Triggiani, Roberto
openaire   +3 more sources

Spatial‐Wavelength Multiplexing Error‐Controlled Photonic Analog Computing System

Advanced Science, EarlyView.
A novel photonic integrated circuit prototype implementing the concept of general‐purpose analog computing and demonstrate its capability in radio frequency applications. The chip features a multichannel architecture and performs fully optical analog computation with frequency‐domain parallel processing. An FPGA‐based error‐correction algorithm aims to
Tao Zhu, Bowen Zhu, Shicheng Zhang, Keren Li, Xianchen Wu, Yazhi Pi, Jie Yan, Daigao Chen, Bingli Guo, Xi Xiao, Lei Wang, Xiaochuan Xu, Xuwei Xue, Shanguo Huang, Zizheng Cao, Shaohua Yu   +15 more
wiley   +1 more source

AI in chemical engineering: From promise to practice

AIChE Journal, EarlyView.
Abstract Artificial intelligence (AI) in chemical engineering has moved from promise to practice: physics‐aware (gray‐box) models are gaining traction, reinforcement learning complements model predictive control (MPC), and generative AI powers documentation, digitization, and safety workflows.
Jia Wei Chew, Ronnie Andersson, Thomas Bierweiler, Patrik Ryttestal, Torsten Wik   +4 more
wiley   +1 more source

An Improved Iterative HDG Approach for Partial Differential Equations

, 2017
We propose and analyze an iterative high-order hybridized discontinuous Galerkin (iHDG) discretization for linear partial differential equations. We improve our previous work (SIAM J. Sci. Comput. Vol. 39, No. 5, pp. S782--S808) in several directions: 1)
Bui-Thanh, Tan, Muralikrishnan, Sriramkrishnan, Tran, Minh-Binh   +2 more
core   +1 more source

“It Is Much Safer to Be Sparse than Connected”: Safe Control of Robotic Swarm Density Dynamics with PDE Optimization with State Constraints

Advanced Intelligent Systems, EarlyView.
This paper proposes a novel control framework to ensure safety of a robotic swarm. A feedback optimization controller is capable of driving the swarm toward a target density while keeping risk‐zone exposure below a safety threshold. Theory and experiments show how safety is more effectively achieved for sparsely connected swarms.
Longchen Niu, Gennaro Notomista
wiley   +1 more source