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

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…

Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical numerical solvers are typically employed to compute the…

One-step generative modeling seeks to generate high-quality data samples in a single function evaluation, significantly improving efficiency over traditional diffusion or flow-based models. In this work, we introduce Modular MeanFlow (MMF),…

Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulations. Geometric integrators are widely used for this purpose,…

We introduce ImitationFlow, a novel Deep generative model that allows learning complex globally stable, stochastic, nonlinear dynamics. Our approach extends the Normalizing Flows framework to learn stable Stochastic Differential Equations.…

Generative models for sequential data often struggle with sparsely sampled and high-dimensional trajectories, typically reducing the learning of dynamics to pairwise transitions. We propose Interpolative Multi-Marginal Flow Matching…

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…

We develop a computational method to learn a molecular Hamiltonian matrix from matrix-valued time series of the electron density. As we demonstrate for three small molecules, the resulting Hamiltonians can be used for electron density…

Flow Matching enables simulation-free training of generative models on Riemannian manifolds, yet sampling typically still relies on numerically integrating a probability-flow ODE. We propose Riemannian MeanFlow (RMF), extending MeanFlow to…

Simulating transition dynamics between metastable states is a fundamental challenge in dynamical systems and stochastic processes with wide real-world applications in understanding protein folding, chemical reactions and neural activities.…

Diffusion and flow models have become the dominant paradigm for generative modeling on Riemannian manifolds, with successful applications in protein backbone generation and DNA sequence design. However, these methods require tens to…

The Hamiltonian formalism plays a central role in classical and quantum physics. Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful…

Maps of dynamics are effective representations of motion patterns learned from prior observations, with recent research demonstrating their ability to enhance various downstream tasks such as human-aware robot navigation, long-term human…

Mainstream flow matching methods typically focus on learning the local velocity field, which inherently requires multiple integration steps during generation. In contrast, Mean Velocity Flow models establish a relationship between the local…

Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and…

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.…

We propose \emph{Euler Mean Flows (EMF)}, a flow-based generative framework for one-step and few-step generation that enforces long-range trajectory consistency with minimal sampling cost. The key idea of EMF is to replace the trajectory…

Matching objectives underpin the success of modern generative models and rely on constructing conditional paths that transform a source distribution into a target distribution. Despite being a fundamental building block, conditional paths…

We introduce a robust framework for learning various generalized Hamiltonian dynamics from noisy, sparse phase-space data and in an unsupervised manner based on variational Bayesian inference. Although conservative, dissipative, and…

Density functional theory (DFT) is a fundamental method for simulating quantum chemical properties, but it remains expensive due to the iterative self-consistent field (SCF) process required to solve the Kohn-Sham equations. Recently, deep…