Related papers: Generative framework for dimensionality reduction …

Reconstructing the equation of motion and thus the network topology of a system from time series is a very important problem. Although many powerful methods have been developed, it remains a great challenge to deal with systems in high…

In this era of data deluge, many signal processing and machine learning tasks are faced with high-dimensional datasets, including images, videos, as well as time series generated from social, commercial and brain network interactions. Their…

Networks of interconnected agents are essential to study complex networked systems' state evolution, stability, resilience, and control. Nevertheless, the high dimensionality and nonlinear dynamics are vital factors preventing us from…

We propose a novel modular inference approach combining two different generative models -- generative adversarial networks (GAN) and normalizing flows -- to approximate the posterior distribution of physics-based Bayesian inverse problems…

We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…

We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…

In this work, we present GAROM, a new approach for reduced order modelling (ROM) based on generative adversarial networks (GANs). GANs have the potential to learn data distribution and generate more realistic data. While widely applied in…

The quality of data representation in deep learning methods is directly related to the prior model imposed on the representations; however, generally used fixed priors are not capable of adjusting to the context in the data. To address this…

A powerful approach for understanding neural population dynamics is to extract low-dimensional trajectories from population recordings using dimensionality reduction methods. Current approaches for dimensionality reduction on neural data…

Despite the remarkable success of generative adversarial networks, their performance seems less impressive for diverse training sets, requiring learning of discontinuous mapping functions. Though multi-mode prior or multi-generator models…

Many networks in nature and applications have an approximate low-rank structure in the sense that their connectivity structure is dominated by a few dimensions. It is natural to expect that dynamics on such networks would also be…

We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…

The topological information is essential for studying the relationship between nodes in a network. Recently, Network Representation Learning (NRL), which projects a network into a low-dimensional vector space, has been shown their…

Classical nonlinear dimensionality reduction (NLDR) techniques like t-SNE, Isomap, and LLE excel at creating low-dimensional embeddings for data visualization but fundamentally lack the ability to map these embeddings back to the original…

Generative design problems often encompass complex action spaces that may be divergent over time, contain state-dependent constraints, or involve hybrid (discrete and continuous) domains. To address those challenges, this work introduces…

Gaussian graphical models are widely utilized to infer and visualize networks of dependencies between continuous variables. However, inferring the graph is difficult when the sample size is small compared to the number of variables. To…

We present a non-convex optimization algorithm metaheuristic, based on the training of a deep generative network, which enables effective searching within continuous, ultra-high dimensional landscapes. During network training, populations…

Random network models, constrained to reproduce specific statistical features, are often used to represent and analyze network data and their mathematical descriptions. Chief among them, the configuration model constrains random networks by…

Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…

In dynamical systems reconstruction (DSR) we seek to infer from time series measurements a generative model of the underlying dynamical process. This is a prime objective in any scientific discipline, where we are particularly interested in…