Related papers: On Learning Hamiltonian Systems from Data
Urban transportation systems face increasing resilience challenges from extreme weather events, but current assessment methods rely on surface-level recovery indicators that miss hidden structural damage. Existing approaches cannot…
The partial Hamiltonian systems of the form $\dot q^i=\frac{\partial H}{\partial p_i}, \dot p^i=-\frac{\partial H}{\partial q_i}+\Gamma^i(t,q^i,p_i)$ arise widely in different fields of the applied mathematics. The partial Hamiltonian…
We investigate the problem of determining the Hamiltonian of a locally interacting open-quantum system. To do so, we construct model estimators based on inverting a set of stationary, or dynamical, Heisenberg-Langevin equations of motion…
In this paper we explore challenges in developing a topological framework in which machine learning can be used to robustly characterize global dynamics. Specifically, we focus on learning a useful discretization of the phase space of a…
A generic data-assisted control architecture within the port-Hamiltonian framework is proposed, introducing a physically meaningful observable that links conservative dynamics to all actuation, dissipation, and disturbance channels. A…
Data-driven methods for the identification of the governing equations of dynamical systems or the computation of reduced surrogate models play an increasingly important role in many application areas such as physics, chemistry, biology, and…
We study the phase space structures that control the transport in a classical Hamiltonian model for a chemical reaction. This model has been proposed to study the yield of products in an ultracold exothermic reaction. In the considered…
Obtaining the free energies of condensed phase chemical reactions remains computationally prohibitive for high-level quantum mechanical methods. We introduce a hierarchical machine learning framework that bridges this gap by distilling…
We present an approach to construct appropriate and efficient emulators for Hamiltonian flow maps. Intended future applications are long-term tracing of fast charged particles in accelerators and magnetic plasma confinement configurations.…
In this work, we introduce Dissipative SymODEN, a deep learning architecture which can infer the dynamics of a physical system with dissipation from observed state trajectories. To improve prediction accuracy while reducing network size,…
Non-Hermitian Hamiltonians provide an alternative perspective on the dynamics of quantum and classical systems coupled non-conservatively to an environment. Once primarily an interest of mathematical physicists, the theory of non-Hermitian…
Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…
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…
In this paper, we develop a framework to construct energy-preserving methods for multi-components Hamiltonian systems, combining the exponential integrator and the partitioned averaged vector field method. This leads to numerical schemes…
The relationships between port-Hamiltonian systems modeling and the notion of monotonicity are explored. The earlier introduced notion of incrementally port-Hamiltonian systems is extended to maximal cyclically monotone relations, together…
We present an adaptation of the so-called structural method \cite{CMM23} for Hamiltonian systems, and redesign the method for this specific context, which involves two coupled differential systems. Structural schemes decompose the problem…
The evolution of a large class of biological, physical and engineering systems can be studied through both dynamical systems theory and Hamiltonian mechanics. The former theory, in particular its specialization to study systems with…
We reconsider the fundamental problem of coarse-graining infinite-dimensional Hamiltonian dynamics to obtain a macroscopic system which includes dissipative mechanisms. In particular, we study the thermodynamical implications concerning…
We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian…
World models have recently re-emerged as a central paradigm for embodied intelligence, robotics, autonomous driving, and model-based reinforcement learning. However, current world model research is often dominated by three partially…