Related papers: Learning Hamiltonian Flow Maps: Mean Flow Consiste…

A recently proposed class of models attempts to learn latent dynamics from high-dimensional observations, like images, using priors informed by Hamiltonian mechanics. While these models have important potential applications in areas like…

We propose a framework to learn the time-dependent Hartree-Fock (TDHF) inter-electronic potential of a molecule from its electron density dynamics. Though the entire TDHF Hamiltonian, including the inter-electronic potential, can be…

The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of…

Modeling dynamical systems and unraveling their underlying causal relationships is central to many domains in the natural sciences. Various physical systems, such as those arising in cell biology, are inherently high-dimensional and…

Molecular dynamics (MD) simulates the time evolution of atomic systems governed by interatomic forces, and the fidelity of these simulations depends critically on the underlying force model. Classical force fields (CFFs) rely on fixed…

We propose a new approach to constructing a phase diagram using the effective Hamiltonian derived only from a single real-space image produced by scanning tunneling microscopy (STM). Currently, there have been two main methods to construct…

Flow Matching (FM) is a simulation-free method for learning a continuous and invertible flow to interpolate between two distributions, and in particular to generate data from noise. Inspired by the variational nature of the diffusion…

Robust and accurate perception of humans in their 3D scene context is essential for integrating robots into everyday environments. Existing approaches, however, often fail to predict plausible and accurate human motion estimates that are…

Fluid prediction is a long-standing challenge due to the intrinsic high-dimensional non-linear dynamics. Previous methods usually utilize the non-linear modeling capability of deep models to directly estimate velocity fields for future…

Molecular dynamics (MD) simulation is a widely used technique to simulate molecular systems, most commonly at the all-atom resolution where equations of motion are integrated with timesteps on the order of femtoseconds…

Understanding cellular trajectories via time-resolved single-cell transcriptomics is vital for studying development, regeneration, and disease. A key challenge is inferring continuous trajectories from discrete snapshots. Biological…

Metriplectic conditional flow matching (MCFM) learns dissipative dynamics without violating first principles. Neural surrogates often inject energy and destabilize long-horizon rollouts; MCFM instead builds the conservative-dissipative…

We construct a Hamiltonian whose dynamics simulate the dynamics of every other Hamiltonian up to exponentially long times in the system size. The Hamiltonian is time-independent, local, one-dimensional, and translation invariant. As a…

Flow matching (FM) is a family of training algorithms for fitting continuous normalizing flows (CNFs). Conditional flow matching (CFM) exploits the fact that the marginal vector field of a CNF can be learned by fitting least-squares…

Many experimental techniques aim at determining the Hamiltonian of a given system. The Hamiltonian describes the system's evolution in the absence of dissipation, and is often central to control or interpret an experiment. Here, we…

We introduce Riemannian Flow Matching Policies (RFMP), a novel model for learning and synthesizing robot visuomotor policies. RFMP leverages the efficient training and inference capabilities of flow matching methods. By design, RFMP…

Accurate traffic flow prediction remains a fundamental challenge in intelligent transportation systems, particularly in cross-domain, data-scarce scenarios where limited historical data hinders model training and generalisation. The complex…

The universal mathematical form of machine-learning potentials (MLPs) shifts the core of development of interatomic potentials to collecting proper training data. Ideally, the training set should encompass diverse local atomic environments…

We study the evolution, under convex Hamiltonian flows on cotangent bundles of compact manifolds, of certain distinguished subsets of the phase space. These subsets are generalizations of Lagrangian graphs, we call them pseudographs. They…

A popular way to plan trajectories in dynamic urban scenarios for Autonomous Vehicles is to rely on explicitly specified and hand crafted cost functions, coupled with random sampling in the trajectory space to find the minimum cost…