Abstract Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode
model equations, like Partial Differential Equations (PDE), as a component of the neural …

We propose a very general framework for deriving rigorous bounds on the approximation
error for physics-informed neural networks (PINNs) and operator learning architectures such …

We make connections between complexity of training of physics-informed neural networks
(PINNs) and Kolmogorov n-width of the solution. Leveraging this connection, we then …

Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of
partial differential equation (PDE)-constrained optimization problems with initial conditions …

Recent work provides promising evidence that Physics-Informed Neural Networks (PINN)
can efficiently solve partial differential equations (PDE). However, previous works have …

We present a novel physics-informed system identification method to construct a passive
linear time-invariant system. In more detail, for a given quadratic energy functional …

We propose a new loss function for supervised and physics-informed training of neural
networks and operators that incorporates a posteriori error estimate. More specifically …

We consider the inverse problem to determine the number and locations of acoustic point
sources from single low-frequency partial data. The problem is particularly challenging in the …

Power systems are integrating uncertain generations, demanding transient analyses using
dynamic measurements. However, High-Resolution (HR) Phasor Measurement Units are …

Prediction error quantification in machine learning has been left out of most methodological
investigations of neural networks (NNs), for both purely data-driven and physics-informed …