Related papers: Lagrangian Flow Matching: A Least-Action Framework…
Fitting probabilistic models to data is often difficult, due to the general intractability of the partition function and its derivatives. Here we propose a new parameter estimation technique that does not require computing an intractable…
Flow-based Generative Models (FGMs) effectively transform noise into complex data distributions. Incorporating Optimal Transport (OT) to couple noise and data during FGM training has been shown to improve the straightness of flow…
Stable concurrent learning and control of dynamical systems is the subject of adaptive control. Despite being an established field with many practical applications and a rich theory, much of the development in adaptive control for nonlinear…
The matching principles behind optimal transport (OT) play an increasingly important role in machine learning, a trend which can be observed when OT is used to disambiguate datasets in applications (e.g. single-cell genomics) or used to…
Lagrangian stochastic models are widely used to predict and analyze turbulent dispersion in complex environments, such as in various terrestrial and marine canopy flows. However, due to a lack of empirical data, it is still not understood…
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…
This paper focuses on the alignment of flow matching models with human preferences. A promising way is fine-tuning by directly backpropagating reward gradients through the differentiable generation process of flow matching. However,…
Population dynamics is the study of temporal and spatial variation in the size of populations of organisms and is a major part of population ecology. One of the main difficulties in analyzing population dynamics is that we can only obtain…
Modeling interactive driving behaviors in complex scenarios remains a fundamental challenge for autonomous driving planning. Learning-based approaches attempt to address this challenge with advanced generative models, removing the…
We give a geometrical interpretation for the principle of stationary action in classical Lagrangian particle mechanics. In a nutshell, the difference of the action along a path and its variation effectively ``counts'' the possible…
We consider a novel approach for the enhancement of fluid mixing via pure stirring strategies building upon the Least Action Principle (LAP) for incompressible flows. The LAP is formally analogous to the Benamou--Brenier formulation of…
Flow models parameterized as time-dependent velocity fields can generate data from noise by integrating an ODE. These models are often trained using flow matching, i.e. by sampling random pairs of noise and target points…
Flow matching has emerged as a powerful framework for generative modeling through continuous normalizing flows. We investigate a potential topological constraint: when the prior distribution and target distribution have mismatched topology…
Model-based controllers can offer strong guarantees on stability and convergence by relying on physically accurate dynamic models. However, these are rarely available for high-dimensional mechanical systems such as deformable objects or…
Flow matching (FM) constructs continuous-time ODE samplers by prescribing probability paths between a base distribution and a target distribution. In this note, we study FM through the lens of finite-sample plug-in estimation. In addition…
Continual learning in robotics seeks systems that can constantly adapt to changing environments and tasks, mirroring human adaptability. A key challenge is refining dynamics models, essential for planning and control, while addressing…
This work is an analytical calculation of the path probability for random dynamics of mechanical system described by Langevin equation with Gaussian noise. The result shows an exponential dependence of the probability on the action. In the…
We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate in infinite-dimensional spaces. Our approach works by first defining a path of probability…
Recent advances in reaction prediction have achieved near-saturated accuracy on standard benchmarks (e.g., USPTO), yet most state-of-the-art models formulate the task as a one-shot mapping from reactants to products, offering limited…
Physics-Informed Neural Networks (PINNs) have gained widespread popularity for solving inverse and forward problems across a range of scientific and engineering domains. However, most existing PINN frameworks are limited to the Eulerian…