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Found 10 papers, 0 papers with code
Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks
We use Physics-Informed Neural Networks (PINNs) to solve the discrete-time nonlinear observer state estimation problem.
Random Projection Neural Networks of Best Approximation: Convergence theory and practical applications
We investigate the concept of Best Approximation for Feedforward Neural Networks (FNN) and explore their convergence properties through the lens of Random Projection (RPNNs).
Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Points
We present a machine learning (ML)-assisted framework bridging manifold learning, neural networks, Gaussian processes, and Equation-Free multiscale modeling, for (a) detecting tipping points in the emergent behavior of complex systems, and (b) characterizing probabilities of rare events (here, catastrophic shifts) near them.
Slow Invariant Manifolds of Singularly Perturbed Systems via Physics-Informed Machine Learning
A comparison of the computational costs between symbolic, automatic and numerical approximation of the required derivatives in the learning process is also provided.
On the accuracy of interpolation based on single-layer artificial neural networks with a focus on defeating the Runge phenomenon
As expected, the accuracy of the approximation with a global polynomial increases only if the Chebychev nodes are considered.
Discrete-Time Nonlinear Feedback Linearization via Physics-Informed Machine Learning
We assess the performance of the proposed PIML approach via a benchmark nonlinear discrete map for which the feedback linearization transformation law can be derived analytically; the example is characterized by steep gradients, due to the presence of singularities, in the domain of interest.
Parsimonious Physics-Informed Random Projection Neural Networks for Initial-Value Problems of ODEs and index-1 DAEs
The unknown weights between the hidden and output layer are computed by Newton's iterations, using the Moore-Penrose pseudoinverse for low to medium, and sparse QR decomposition with regularization for medium to large scale systems.
Constructing coarse-scale bifurcation diagrams from spatio-temporal observations of microscopic simulations: A parsimonious machine learning approach
For our illustrations, we implemented the proposed method to construct the one-parameter bifurcation diagram of the 1D FitzHugh-Nagumo PDEs from data generated by $D1Q3$ Lattice Boltzmann simulations.
Numerical Solution of Stiff ODEs with Physics-Informed RPNNs
We propose a numerical method based on physics-informed Random Projection Neural Networks for the solution of Initial Value Problems (IVPs) of Ordinary Differential Equations (ODEs) with a focus on stiff problems.
Extreme learning machine collocation for the numerical solution of elliptic PDEs with sharp gradients
We show that a feedforward neural network with a single hidden layer with sigmoidal functions and fixed, random, internal weights and biases can be used to compute accurately a collocation solution.
Numerical Analysis Numerical Analysis
