Related papers: Learning Stochastic Dynamical System via Flow Map …

Modeling and identification of high-dimensional stochastic processes is ubiquitous in many fields. In particular, there is a growing interest in modeling stochastic processes with simple and interpretable structures. In many applications,…

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…

Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…

Filtering - the task of estimating the conditional distribution for states of a dynamical system given partial and noisy observations - is important in many areas of science and engineering, including weather and climate prediction.…

Stochastic diffusion is the noisy and uncertain process through which dynamics like epidemics, or agents like animal species, disperse over a larger area. Understanding these processes is becoming increasingly important as we attempt to…

Stochastic fluid-fluid models (SFFMs) offer powerful modeling ability for a wide range of real-life systems of significance. The existing theoretical framework for this class of models is in terms of operator-analytic methods. For the first…

New technologies for recording the activity of large neural populations during complex behavior provide exciting opportunities for investigating the neural computations that underlie perception, cognition, and decision-making. Nonlinear…

In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality…

Generative Flow Networks (GFlowNets) are a new family of probabilistic samplers where an agent learns a stochastic policy for generating complex combinatorial structure through a series of decision-making steps. Despite being inspired from…

In this work we explore the advantages of end-to-end learning of multilayer maps offered by feed forward neural-networks (FFNN) for learning and predicting dynamics from transient fluid flow data.While machine learning in general depends on…

In this paper, we propose a probabilistic physics-guided framework, termed Physics-guided Deep Markov Model (PgDMM). The framework targets the inference of the characteristics and latent structure of nonlinear dynamical systems from…

We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…

Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…

We analyze in a closed form the learning dynamics of stochastic gradient descent (SGD) for a single-layer neural network classifying a high-dimensional Gaussian mixture where each cluster is assigned one of two labels. This problem provides…

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the…

Regressing the vector field of a dynamical system from a finite number of observed states is a natural way to learn surrogate models for such systems. A simple and interpretable way to learn a dynamical system from data is to interpolate…

Unsupervised structure learning in high-dimensional time series data has attracted a lot of research interests. For example, segmenting and labelling high dimensional time series can be helpful in behavior understanding and medical…

This work addresses the problem of learning the dynamics of high-dimensional probability densities over time using unlabeled samples, without assuming access to trajectory information. We introduce two-parameter flows that learn only…

ML-based systems are software systems that incorporates machine learning components such as Deep Neural Networks (DNNs) or Large Language Models (LLMs). While such systems enable advanced features such as high performance computer vision,…

For modelling geophysical systems, large-scale processes are described through a set of coarse-grained dynamical equations while small-scale processes are represented via parameterizations. This work proposes a method for identifying the…