Results 91 to 100 of about 2,529,562 (187)

Numerical Analysis of HiPPO-LegS ODE for Deep State Space Models [PDF]

arXiv
In deep learning, the recently introduced state space models utilize HiPPO (High-order Polynomial Projection Operators) memory units to approximate continuous-time trajectories of input functions using ordinary differential equations (ODEs), and these techniques have shown empirical success in capturing long-range dependencies in long input sequences ...
arxiv  

Predicting Wind Turbine Blade Tip Deformation With Long Short‐Term Memory (LSTM) Models

Wind Energy, Volume 28, Issue 6, June 2025.
ABSTRACT Driven by the challenges in measuring blade deformations, this study presents a novel machine learning methodology to predict blade tip deformation using inflow wind data and operational parameters. Using a long short‐term memory (LSTM) model and a novel feature selection approach based on mutual information and recursive feature addition ...
Shubham Baisthakur, Breiffni Fitzgerald
wiley   +1 more source

Scattering for a particle interacting with a Bose gas [PDF]

arXiv, 2019
We study the asymptotic behavior of solutions to an ODE - Schr\"{o}dinger type system that models the interaction of a particle with a Bose gas. We show that the particle has a ballistic trajectory asymptotically, and that the wave function describing the Bose gas converges to a soliton in $L^{\infty}.$
arxiv  

From messianic subjectivity to immaculate objectivity: An etymology

Critical Quarterly, EarlyView.
Nick Groom
wiley   +1 more source

Spatial modeling of crime dynamics: Patch and reaction–diffusion compartmental systems

Mathematical Methods in the Applied Sciences, Volume 48, Issue 7, Page 7440-7459, 15 May 2025.
We study the dynamics of abstract models for crime evolution. The population is divided into three compartments, taking into account the participation in crime and incarceration. Individuals transit between the three segments, assuming that having more contact with criminally active people increases one's risk of learning and acquiring the same traits;
Julia Calatayud, Marc Jornet, Jorge Mateu   +2 more
wiley   +1 more source

Forward uncertainty quantification in random differential equation systems with delta‐impulsive terms: Theoretical study and applications

Mathematical Methods in the Applied Sciences, Volume 48, Issue 7, Page 7609-7629, 15 May 2025.
This contribution aims at studying a general class of random differential equations with Dirac‐delta impulse terms at a finite number of time instants. Our approach directly addresses calculating the so‐called first probability density function, from which all the relevant statistical information about the solution, a stochastic process, can be ...
Vicente J. Bevia, Juan C. Cortés, Rafael J. Villanueva   +2 more
wiley   +1 more source

Unification of Symmetries Inside Neural Networks: Transformer, Feedforward and Neural ODE [PDF]

arXiv
Understanding the inner workings of neural networks, including transformers, remains one of the most challenging puzzles in machine learning. This study introduces a novel approach by applying the principles of gauge symmetries, a key concept in physics, to neural network architectures. By regarding model functions as physical observables, we find that
arxiv  

Learning the Simplest Neural ODE [PDF]

arXiv
Since the advent of the ``Neural Ordinary Differential Equation (Neural ODE)'' paper, learning ODEs with deep learning has been applied to system identification, time-series forecasting, and related areas. Exploiting the diffeomorphic nature of ODE solution maps, neural ODEs has also enabled their use in generative modeling.
arxiv  

Continuous-time enclosures for uncertain implicit differential equations [PDF]

, 2015
Chachuat, B, Houska, B, Rayjaguru, J, Villanueva, ME   +3 more
core   +2 more sources

Mathematical modeling of tuberculosis using Caputo fractional derivative: a comparative analysis with real data. [PDF]

Sci Rep
Bhatter S, Kumawat S, Purohit SD, Suthar DL.   +3 more
europepmc   +1 more source