Fredholm neural networks
Within the family of explainable machine-learning, we present Fredholm neural networks
(Fredholm NNs), deep neural networks (DNNs) which replicate fixed point iterations for the …
(Fredholm NNs), deep neural networks (DNNs) which replicate fixed point iterations for the …
Quantification of total uncertainty in the physics-informed reconstruction of CVSim-6 physiology
When predicting physical phenomena through simulation, quantification of the total
uncertainty due to multiple sources is as crucial as making sure the underlying numerical …
uncertainty due to multiple sources is as crucial as making sure the underlying numerical …
Stability Analysis of Physics-Informed Neural Networks for Stiff Linear Differential Equations
We present a stability analysis of Physics-Informed Neural Networks (PINNs) coupled with
random projections, for the numerical solution of (stiff) linear differential equations. For our …
random projections, for the numerical solution of (stiff) linear differential equations. For our …
GRINNs: Godunov-Riemann Informed Neural Networks for Learning Hyperbolic Conservation Laws
DG Patsatzis, M di Bernardo, L Russo… - arXiv preprint arXiv …, 2024 - arxiv.org
We present GRINNs: numerical analysis-informed neural networks for the solution of inverse
problems of non-linear systems of conservation laws. GRINNs are based on high-resolution …
problems of non-linear systems of conservation laws. GRINNs are based on high-resolution …
Fourier PINNs: From Strong Boundary Conditions to Adaptive Fourier Bases
Interest is rising in Physics-Informed Neural Networks (PINNs) as a mesh-free alternative to
traditional numerical solvers for partial differential equations (PDEs). However, PINNs often …
traditional numerical solvers for partial differential equations (PDEs). However, PINNs often …