Related papers: Learning Stochastic Dynamical System via Flow Map …

We propose a numerical method for discovering unknown parameterized dynamical systems by using observational data of the state variables. Our method is built upon and extends the recent work of discovering unknown dynamical systems, in…

Modern machine learning models are typically trained via multi-pass stochastic gradient descent (SGD) with small batch sizes, and understanding their dynamics in high dimensions is of great interest. However, an analytical framework for…

Conditional flow matching (CFM) stands out as an efficient, simulation-free approach for training flow-based generative models, achieving remarkable performance for data generation. However, CFM is insufficient to ensure accuracy in…

Debiased machine learning estimators for smooth functionals in nonparametric models can exhibit substantial variability and instability, often leading practitioners to instead rely on parametric or semiparametric working models. Such…

Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great…

Flow matching (FM) learns vector fields by regressing stochastic velocity targets along intermediate distributions $p_t$. We identify a geometric optimization bottleneck in this regression problem: when the covariance $\Sigma_t$ of $p_t$ is…

Machine learning has affected the way in which many phenomena for various domains are modelled, one of these domains being that of structural dynamics. However, because machine-learning algorithms are problem-specific, they often fail to…

Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. Current GNN architectures assume ideal scenarios and ignore link…

Generative models that can model and predict sequences of future events can, in principle, learn to capture complex real-world phenomena, such as physical interactions. However, a central challenge in video prediction is that the future is…

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…

We address the problem of learning the parameters of a mean square stable switched linear systems (SLS) with unknown latent space dimension, or \textit{order}, from its noisy input--output data. In particular, we focus on learning a good…

This article presents an innovative approach to integrating port-Hamiltonian systems with neural network architectures, transitioning from deterministic to stochastic models. The study presents novel mathematical formulations and…

Flow Matching has emerged as a powerful framework for learning continuous transformations between distributions, enabling high-fidelity generative modeling. This work introduces Symmetrical Flow Matching (SymmFlow), a new formulation that…

In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without…

Recent efforts have extended the flow-matching framework to discrete generative modeling. One strand of models directly works with the continuous probabilities instead of discrete tokens, which we colloquially refer to as Continuous-State…

Accurate and efficient fluid flow models are essential for applications relating to many physical phenomena including geophysical, aerodynamic, and biological systems. While these flows may exhibit rich and multiscale dynamics, in many…

Stochastic Programming is a framework for modelling and solving problems of decision making under uncertainty. Stochastic Dynamic Programming is a branch of Stochastic Programming that takes a "functional equation" approach to the discovery…

We present a probabilistic framework for nonlinearities, based on doubly truncated Gaussian distributions. By setting the truncation points appropriately, we are able to generate various types of nonlinearities within a unified framework,…

The recently proposed Bayesian Flow Networks~(BFNs) show great potential in modeling parameter spaces, offering a unified strategy for handling continuous, discretized, and discrete data. However, BFNs cannot learn high-level semantic…

Machine learning (ML) is redefining what is possible in data-intensive fields of science and engineering. However, applying ML to problems in the physical sciences comes with a unique set of challenges: scientists want physically…