Physics-informed machine learning (PIML) is a set of methods and tools that systematically
integrate machine learning (ML) algorithms with physical constraints and abstract …

Forecasting high-dimensional dynamical systems is a fundamental challenge in various
fields, such as geosciences and engineering. Neural Ordinary Differential Equations …

Abstract Universal Numerical Integrators (UNIs) can be defined as the coupling of a
universal approximator of functions (eg, artificial neural network) with some conventional …

We represent the optimal control functions by neural networks and solve optimal control
problems by deep learning techniques. Adjoint sensitivity analysis is applied to train the …

This paper focuses on learning the dynamics of time delay systems from trajectory data and
proposes the use of the maximal Lyapunov exponent (MLE) as an indicator to describe the …

Parameter estimation is one of the central challenges in computational biology. In this paper,
we present an approach to estimate model parameters and assess their identifiability in …

The term NeuralODE describes the structural combination of an Artificial Neural Network
(ANN) and a numerical solver for Ordinary Differential Equations (ODE), the former acts as …

Training dynamic models, such as neural ODEs, on long trajectories is a hard problem that
requires using various tricks, such as trajectory splitting, to make model training work in …

We propose a new model class aimed at predicting dynamical trajectories from high-
dimensional empirical data. This is done by combining variational autoencoders and (spatio …

Current battery modelling methodologies including equivalent circuital modelling and
electrochemical modelling do not maintain accuracy over diverse operating conditions of …