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We use parsimonious diffusion maps (PDMs) to discover the latent dynamics of high-fidelity Navier-Stokes simulations with a focus on the 2D fluidic pinball problem. By varying the Reynolds number, different flow regimes emerge, ranging from…

The present study presents a novel application for normalizing flows for domain adaptation. The study investigates the ability of flow based neural networks to improve signal extraction of $\Lambda$ Hyperons at CLAS12. Normalizing Flows can…

Foundational language models show a remarkable ability to learn new concepts during inference via context data. However, similar work for images lag behind. To address this challenge, we introduce FLoWN, a flow matching model that learns to…

Through examples of coordinate and probability transformation between different distributions, the basic principle of normalizing flow is introduced in a simple and concise manner. From the perspective of the distribution of random variable…

Incorporating geometric inductive biases into models can aid interpretability and generalization, but encoding to a specific geometric structure can be challenging due to the imposed topological constraints. In this paper, we theoretically…

In this article we show that the phase-ordering scaling state for binary fluids is not necessarily unique and that local correlations in the initial conditions can be responsible for selecting the scaling state. We describe a new scaling…

Normalizing flows model complex probability distributions by combining a base distribution with a series of bijective neural networks. State-of-the-art architectures rely on coupling and autoregressive transformations to lift up invertible…

The assignment flow recently introduced in the J. Math. Imaging and Vision 58/2 (2017), constitutes a high-dimensional dynamical system that evolves on an elementary statistical manifold and performs contextual labeling (classification) of…

Normalizing Flows (NFs) are universal density estimators based on Neural Networks. However, this universality is limited: the density's support needs to be diffeomorphic to a Euclidean space. In this paper, we propose a novel method to…

Density estimation and reliable prediction regions for outputs are crucial in supervised and unsupervised learning. While conformal prediction effectively generates coverage-guaranteed regions, it struggles with multi-dimensional outputs…

Deep neural networks have been demonstrated to achieve phenomenal success in many domains, and yet their inner mechanisms are not well understood. In this paper, we investigate the curvature of image manifolds, i.e., the manifold deviation…

Deep generative frameworks including GANs and normalizing flow models have proven successful at filling in missing values in partially observed data samples by effectively learning -- either explicitly or implicitly -- complex,…

Autoencoders have long been considered a nonlinear extension of Principal Component Analysis (PCA). Prior studies have demonstrated that linear autoencoders (LAEs) can recover the ordered, axis-aligned principal components of PCA by…

Renormalisation group flows of the bosonic nonlinear \sigma-model are governed, perturbatively, at different orders of \alpha', by the perturbatively evaluated \beta--functions. In regions where \frac{\alpha'}{R_c^2} << 1 the flow equations…

The objective of this paper is to design novel multi-layer neural network architectures for multiscale simulations of flows taking into account the observed data and physical modeling concepts. Our approaches use deep learning concepts…

The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo…

To better understand the overlapping modular organization of large networks with respect to flow, here we introduce the map equation for overlapping modules. In this information-theoretic framework, we use the correspondence between…

Mapping between discrete and continuous distributions is a difficult task and many have had to resort to heuristical approaches. We propose a tessellation-based approach that directly learns quantization boundaries in a continuous space,…

Normalizing flows can transform a simple prior probability distribution into a more complex target distribution. Here, we evaluate the ability and efficiency of generative machine learning methods to sample the Boltzmann distribution of an…

Data arrives at our senses as a continuous stream, smoothly transforming from one instant to the next. These smooth transformations can be viewed as continuous symmetries of the environment that we inhabit, defining equivalence relations…