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Conformal prediction provides a model-agnostic framework for uncertainty quantification with finite-sample validity guarantees, making it an attractive tool for constructing reliable prediction sets. However, existing approaches commonly…
In this paper, we establish a connection between the parameterization of flow-based and energy-based generative models, and present a new flow-based modeling approach called energy-based normalizing flow (EBFlow). We demonstrate that by…
Two models for quantum Brownian motion - the Oscillator Bath (OB) model and the Random-Band-Matrix (RBM) model - are compared and a relation between the spectral density function I(w) and the variance (Vab)^2 is established. The extension…
Conceptual hydrologic models remain the cornerstone of rainfall-runoff modeling, yet their calibration is often slow and numerically fragile. Most gradient-based parameter estimation methods rely on finite-difference approximations or…
In high-energy physics experiments, the trajectories of charged particles are reconstructed using track reconstruction algorithms. Such algorithms need to both identify the set of measurements from a single charged particle and to fit the…
Information flow provides a natural measure for the causal interaction between dynamical events. This study extends our previous rigorous formalism of componentwise information flow to the bulk information flow between two complex…
Flow Matching has recently emerged as a popular class of generative models for simulating a target distribution $\mu_1$ from samples drawn from a source distribution $\mu_0$. This framework relies on a fixed coupling between $\mu_0$ and…
Entropy stable schemes replicate an entropy inequality at the semi-discrete level. These schemes rely on an algebraic summation-by-parts (SBP) structure and a technique referred to as flux differencing. We provide simple and efficient…
We give a version of the usual Jacobian characterization of the defining ideal of the singular locus in the equal characteristic case: the new theorem is valid for essentially affine algebras over a complete local algebra over a mixed…
Data-carving methods perform selective inference by conditioning the distribution of data on the observed selection event. However, existing data-carving approaches typically require an analytically tractable characterization of the…
Understanding transport processes in complex nanoscale systems, like ionic conductivities in nanofluidic devices or heat conduction in low dimensional solids, poses the problem of examining fluctuations of currents within nonequilibrium…
A normalizing flow is an invertible mapping between an arbitrary probability distribution and a standard normal distribution; it can be used for density estimation and statistical inference. Computing the flow follows the change of…
By means of a novel variational approach and using dual maps techniques and general ideas of dynamical system theory we derive exact results about several models of transport flows, for which we also obtain a complete description of their…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…
Joint Embedding Predictive Architectures (JEPA) offer a scalable paradigm for self-supervised learning by predicting latent representations rather than reconstructing high-entropy observations. However, existing formulations rely on…
Generative modeling has emerged as a powerful paradigm for representation learning, but its direct applicability to challenging fields like medical imaging remains limited: mere generation, without task alignment, fails to provide a robust…
Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro-migration. Both continuous and stochastic dynamics are…
In this article, we present molecular dynamics study of the velocity autocorrelation function (VACF) of a Brownian particle. We compare the results of the simulation with the exact analytic predictions for a compressible fluid from [6] and…
We show that the flux-flow transport of the Josephson vortex lattice (JVL) in layered high-temperature superconductors provides a convenient probe for both components of quasiparticle conductivity, $\sigma_{c}$ and $\sigma_{ab}$. We found…
Biological function arises through the dynamical interactions of multiple subsystems, including those between brain areas, within gene regulatory networks, and more. A common approach to understanding these systems is to model the dynamics…