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Found 14 papers, 0 papers with code
A physics-informed neural network method for the approximation of slow invariant manifolds for the general class of stiff systems of ODEs
We present a physics-informed neural network (PINN) approach for the discovery of slow invariant manifolds (SIMs), for the most general class of fast/slow dynamical systems of ODEs.
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.
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.
Data-driven modelling of brain activity using neural networks, Diffusion Maps, and the Koopman operator
Importantly, we show that the proposed Koopman operator approach provides, for any practical purposes, equivalent results to the FNN-GH approach, thus bypassing the need to train a non-linear map and to use GH to extrapolate predictions in the ambient fMRI space; one can use instead the low-frequency truncation of the DMs function space of L^2-integrable functions, to predict the entire list of coordinate functions in the fMRI space and to solve the pre-image problem.
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.
Data-driven Control of Agent-based Models: an Equation/Variable-free Machine Learning Approach
We present an Equation/Variable free machine learning (EVFML) framework for the control of the collective dynamics of complex/multiscale systems modelled via microscopic/agent-based simulators.
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.
A biophysical network model reveals the link between deficient inhibitory cognitive control and major neurotransmitter and neural connectivity hypotheses in schizophrenia
We address a biophysical network dynamical model to study how the modulation of dopamine (DA) activity and related N-methyl-d-aspartate (NMDA) glutamate receptor activity as well as the emerging Pre-Frontal Cortex (PFC) functional connectivity network (FCN) affect inhibitory cognitive function in schizophrenia in an antisaccade task.
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
Construction of embedded fMRI resting state functional connectivity networks using manifold learning
We construct embedded functional connectivity networks (FCN) from benchmark resting-state functional magnetic resonance imaging (rsfMRI) data acquired from patients with schizophrenia and healthy controls based on linear and nonlinear manifold learning algorithms, namely, Multidimensional Scaling (MDS), Isometric Feature Mapping (ISOMAP) and Diffusion Maps.
