Related papers: Flow equations for Hamiltonians: Contrasting diffe…
This paper introduces equivariant hamiltonian flows, a method for learning expressive densities that are invariant with respect to a known Lie-algebra of local symmetry transformations while providing an equivariant representation of the…
Many-body perturbation theory provides a powerful framework to study the ground state and thermodynamic properties of nuclear matter as well as associated single-particle potentials and response functions within a systematic order-by-order…
Hamilton's equations with noise and friction possess a hidden supersymmetry, valid for time-independent as well as periodically time-dependent systems. It is used to derive topological properties of critical points and periodic trajectories…
T. Borrvall and J. Petersson [Topology optimization of fluids in Stokes flow, International Journal for Numerical Methods in Fluids 41 (1) (2003) 77--107] developed the first model for topology optimization of fluids in Stokes flow. They…
Scale separation is an important physical principle that has previously enabled algorithmic advances such as multigrid solvers. Previous work on normalizing flows has been able to utilize scale separation in the context of scalar field…
Flow models are a cornerstone of modern machine learning. They are generative models that progressively transform probability distributions according to learned dynamics. Specifically, they learn a continuous-time Markov process that…
We consider the Hamiltonian renormalisation group flow of discretised one-dimensional physical theories. In particular, we investigate the influence the choice of different embedding maps has on the RG flow and the resulting continuum…
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…
The observation of fluid-like behavior in nucleus-nucleus, proton-nucleus and high-multiplicity proton-proton collisions motivates systematic studies of how different measurements approach their fluid-dynamic limit. We have developed…
The isolation of pure samples of quark and gluon jets is of key interest at hadron colliders. Recent work has employed topic modeling to disentangle the underlying distributions in mixed samples obtained from experiments. However, current…
A positivity-preserving fractional algorithm is presented for solving the four-equation homogeneous relaxation model (HRM) with an arbitrary number of ideal gases and a liquid governed by the stiffened gas equation of state. The fractional…
Understanding turbulence is the key to our comprehension of many natural and technological flow processes. At the heart of this phenomenon lies its intricate multi-scale nature, describing the coupling between different-sized eddies in…
Sampling equilibrium distributions is fundamental to statistical mechanics. While flow matching has emerged as scalable state-of-the-art paradigm for generative modeling, its potential for equilibrium sampling in condensed-phase systems…
Novel constructions of empirical controllability and observability gramians for nonlinear systems for subsequent use in a balanced truncation style of model reduction are proposed. The new gramians are based on a generalisation of the…
Generative models based on dynamical equations such as flows and diffusions offer exceptional sample quality, but require computationally expensive numerical integration during inference. The advent of consistency models has enabled…
Business process models abstract complex business processes by representing them as graphical models. Their layout, solely determined by the modeler, affects their understandability. To support the construction of understandable models it…
Dynamics of ideal fluid with free surface can be effectively solved by perturbing the Hamiltonian in weak nonlinearity limit. However it is shown that perturbation theory, which includes third and fourth order terms in the Hamiltonian,…
The unique solvability and error analysis of the original Lagrange multiplier approach proposed in [8] for gradient flows is studied in this paper. We identify a necessary and sufficient condition that must be satisfied for the nonlinear…
Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. A…
We develop a formalism to discuss the properties of GENERIC systems in terms of corresponding Hamiltonians that appear in the characterization of large-deviation limits. We demonstrate how the GENERIC structure naturally arises from a…