KAN-ODEs: Kolmogorov–Arnold network ordinary differential equations for learning dynamical systems and hidden physics
Abstract Kolmogorov–Arnold networks (KANs) as an alternative to multi-layer perceptrons
(MLPs) are a recent development demonstrating strong potential for data-driven modeling …
(MLPs) are a recent development demonstrating strong potential for data-driven modeling …
Nonlinearsolve. jl: High-performance and robust solvers for systems of nonlinear equations in julia
Efficiently solving nonlinear equations underpins numerous scientific and engineering
disciplines, yet scaling these solutions for complex system models remains a challenge. This …
disciplines, yet scaling these solutions for complex system models remains a challenge. This …
Discretize first, filter next: learning divergence-consistent closure models for large-eddy simulation
SD Agdestein, B Sanderse - arXiv preprint arXiv:2403.18088, 2024 - arxiv.org
We propose a new neural network based large eddy simulation framework for the
incompressible Navier-Stokes equations based on the paradigm" discretize first, filter and …
incompressible Navier-Stokes equations based on the paradigm" discretize first, filter and …
Locally regularized neural differential equations: some black boxes were meant to remain closed!
Abstract Neural Differential Equations have become an important modeling framework due
to their ability to adapt to new problems automatically. Training a neural differential equation …
to their ability to adapt to new problems automatically. Training a neural differential equation …
Recurrent networks recognize patterns with low-dimensional oscillations
KT Murray - arXiv preprint arXiv:2310.07908, 2023 - arxiv.org
This study proposes a novel dynamical mechanism for pattern recognition discovered by
interpreting a recurrent neural network (RNN) trained on a simple task inspired by the SET …
interpreting a recurrent neural network (RNN) trained on a simple task inspired by the SET …
Continuous deep equilibrium models: Training neural odes faster by integrating them to infinity
Implicit models separate the definition of a layer from the description of its solution process.
While implicit layers allow features such as depth to adapt automatically to new scenarios …
While implicit layers allow features such as depth to adapt automatically to new scenarios …
Symmetry constrained neural networks for detection and localization of damage in metal plates
J Amarel, C Rudolf, A Iliopoulos, J Michopoulos… - arXiv preprint arXiv …, 2024 - arxiv.org
The present paper is concerned with deep learning techniques applied to detection and
localization of damage in a thin aluminum plate. We used data generated on a tabletop …
localization of damage in a thin aluminum plate. We used data generated on a tabletop …
Learning residual dynamics via physics-augmented neural networks: Application to vapor compression cycles
R Chinchilla, VM Deshpande… - 2023 American …, 2023 - ieeexplore.ieee.org
In order to improve the control performance of vapor compression cycles (VCCs), it is often
necessary to construct accurate dynamical models of the underlying thermo-fluid dynamics …
necessary to construct accurate dynamical models of the underlying thermo-fluid dynamics …
Optimal Experimental Design for Universal Differential Equations
C Plate, CJ Martensen, S Sager - arXiv preprint arXiv:2408.07143, 2024 - arxiv.org
Complex dynamic systems are typically either modeled using expert knowledge in the form
of differential equations, or via data-driven universal approximation models such as artificial …
of differential equations, or via data-driven universal approximation models such as artificial …
Higher-Order Automatic Differentiation and Its Applications
S Tan - 2023 - dspace.mit.edu
Differentiable programming is a new paradigm for modeling and optimization in many fields
of science and engineering, and automatic differentiation (AD) algorithms are at the heart of …
of science and engineering, and automatic differentiation (AD) algorithms are at the heart of …