Related papers: Applications of Machine Learning to Modelling and …

Physics-informed deep learning models have emerged as powerful tools for learning dynamical systems. These models directly encode physical principles into network architectures. However, systematic benchmarking of these approaches across…

Lattice Hamiltonian systems underpin models across condensed matter, nonlinear optics, and biophysics, yet learning their dynamics from data is obstructed by two unknowns: the interaction topology and whether node dynamics are homogeneous.…

We propose a deep neural network architecture designed such that its output forms an invertible symplectomorphism of the input. This design draws an analogy to the real-valued non-volume-preserving (real NVP) method used in normalizing flow…

Conventional neural networks are universal function approximators, but because they are unaware of underlying symmetries or physical laws, they may need impractically many training data to approximate nonlinear dynamics. Recently introduced…

Predicting optoelectronic properties of large-scale atomistic systems under realistic conditions is crucial for rational materials design, yet computationally prohibitive with first-principles simulations. Recent neural network models have…

Identifying the underlying dynamics of physical systems can be challenging when only provided with observational data. In this work, we consider systems that can be modelled as first-order ordinary differential equations. By assuming a…

Hybrid machine learning combines physical knowledge with data-driven models to enhance interpretability and performance. In this context, Port-Hamiltonian Systems (PHS), which generalize Hamiltonian mechanics to describe open,…

Understanding natural symmetries is key to making sense of our complex and ever-changing world. Recent work has shown that neural networks can learn such symmetries directly from data using Hamiltonian Neural Networks (HNNs). But HNNs…

Attempts to apply Neural Networks (NN) to a wide range of research problems have been ubiquitous and plentiful in recent literature. Particularly, the use of deep NNs for understanding complex physical and chemical phenomena has opened a…

Dynamic analysis of structures subjected to earthquake excitation is a time-consuming process, particularly in the case of extremely small time step required, or in the presence of high geometric and material nonlinearity. Performing…

Data-driven approaches are increasingly popular for identifying dynamical systems due to improved accuracy and availability of sensor data. However, relying solely on data for identification does not guarantee that the identified systems…

This paper revisits building machine learning algorithms that involve interactions between entities, such as those between financial assets in an actively managed portfolio, or interactions between users in a social network. Our goal is to…

In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast and accurate. In this paper, we propose…

Hamiltonian systems with multiple timescales arise in molecular dynamics, classical mechanics, and theoretical physics. Long-time numerical integration of such systems requires resolving fast dynamics with very small time steps, which…

The observation and description of collective excitations in solids is a fundamental issue when seeking to understand the physics of a many-body system. Analysis of these excitations is usually carried out by measuring the dynamical…

Port-Hamiltonian neural networks have shown promising results in the identification of nonlinear dynamics of complex systems, as their combination of physical principles with data-driven learning allows for accurate modelling. However, due…

To accurately compute data-based prediction of Hamiltonian systems, especially the long-term evolution of such systems, it is essential to utilize methods that preserve the structure of the equations over time. We consider a case that is…

The ability to predict trajectories of surrounding agents and obstacles is a crucial component in many robotic applications. Data-driven approaches are commonly adopted for state prediction in scenarios where the underlying dynamics are…

Understanding real-world dynamical phenomena remains a challenging task. Across various scientific disciplines, machine learning has advanced as the go-to technology to analyze nonlinear dynamical systems, identify patterns in big data, and…

Discovering a suitable coordinate transformation for nonlinear systems enables the construction of simpler models, facilitating prediction, control, and optimization for complex nonlinear systems. To that end, Koopman operator theory offers…