Artificial intelligence (AI), machine learning (ML), and data science are leading to a
promising transformative paradigm. ML, especially deep learning and physics-informed ML …

Physics-informed neural networks (PINNs) have recently been very successfully applied for
efficiently approximating inverse problems for partial differential equations (PDEs). We focus …

Physics-informed neural networks (PINNs) have recently been widely used for robust and
accurate approximation of partial differential equations (PDEs). We provide upper bounds …

Conventional reduced order modeling techniques such as the reduced basis (RB) method
(relying, eg, on proper orthogonal decomposition (POD)) may incur in severe limitations …

This review presents a modern perspective on dynamical systems in the context of current
goals and open challenges. In particular, our review focuses on the key challenges of …

Physics-informed neural networks (PINNs) have enabled significant improvements in
modelling physical processes described by partial differential equations (PDEs) and are in …

This work deals with the investigation of bifurcating fluid phenomena using a reduced order
modelling setting aided by artificial neural networks. We discuss the POD-NN approach …

We propose a novel mathematical and numerical model for cardiac electromechanics,
wherein biophysically detailed core models describe the different physical processes …

Nonlinear differential equations rarely admit closed-form solutions, thus requiring numerical
time-stepping algorithms to approximate solutions. Further, many systems characterized by …

We propose a machine learning-based method to build a system of differential equations
that approximates the dynamics of 3D electromechanical models for the human heart …