Related papers: Port-Hamiltonian Neural Networks for Learning Expl…
Non-Hermitian (NH) systems provide a fertile platform for quantum technologies, owing in part to their distinct dynamical phases. These systems can be characterized by the preservation or spontaneous breaking of parity-time reversal…
We propose Lagrangian Descriptors (LDs) as a diagnostic framework for evaluating neural network models of Hamiltonian systems beyond conventional trajectory-based metrics. Standard error measures quantify short-term predictive accuracy but…
Reconstructing the KAM dynamics diagram of Hamiltonian system from the time series of a limited number of parameters is an outstanding question in nonlinear science, especially when the Hamiltonian governing the system dynamics are unknown.…
Feed-forward neural networks (FNNs) work as standard building blocks in applying artificial intelligence (AI) to the physical world. They allow learning the dynamics of unknown physical systems (e.g., biological and chemical) {to predict…
Brains remain unrivaled in their ability to recognize and generate complex spatiotemporal patterns. While AI is able to reproduce some of these capabilities, deep learning algorithms remain largely at odds with our current understanding of…
In this paper, we identify a class of time-varying port-Hamiltonian systems that is suitable for studying problems at the intersection of statistical mechanics and control of physical systems. Those port-Hamiltonian systems are able to…
Training deep neural networks (DNNs) can be difficult due to the occurrence of vanishing/exploding gradients during weight optimization. To avoid this problem, we propose a class of DNNs stemming from the time discretization of Hamiltonian…
Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…
In this paper, we consider linear boundary port-Hamiltonian distributed parameter systems on a time-varying spatial domain. We derive the specific time-varying Dirac structure that these systems give rise to and use it to formally establish…
Time-reversal symmetry arises naturally as a structural property in many dynamical systems of interest. While the importance of hard-wiring symmetry is increasingly recognized in machine learning, to date this has eluded time-reversibility.…
Recurrent Neural Networks (RNNs) have shown great success in modeling time-dependent patterns, but there is limited research on their learned representations of latent temporal features and the emergence of these representations during…
We present a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our basic assumption is that the governing equations for the…
Important classes of active matter systems can be modeled using kinetic theories. However, kinetic theories can be high dimensional and challenging to simulate. Reduced-order representations based on tracking only low-order moments of the…
Learning accurate dynamics models is necessary for optimal, compliant control of robotic systems. Current approaches to white-box modeling using analytic parameterizations, or black-box modeling using neural networks, can suffer from high…
When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access to the full system state. This limits their use in partially…
Large-scale cyber-physical systems require that control policies are distributed, that is, that they only rely on local real-time measurements and communication with neighboring agents. Optimal Distributed Control (ODC) problems are,…
Realistic models of physical world rely on differentiable symmetries that, in turn, correspond to conservation laws. Recent works on Lagrangian and Hamiltonian neural networks show that the underlying symmetries of a system can be easily…
Despite successful seminal works on passive systems in the literature, learning free-form physical laws for controlled dynamical systems given experimental data is still an open problem. For decades, symbolic mathematical equations and…
A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing…
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,…