Related papers: Learning Interpolations between Boltzmann Densitie…
We study an idealized version of intermittent process leading the fluctuations of a stochastic dichotomous variable $\xi$. It consists of an overdamped and symmetric potential well with a cusp-like minimum. The right-hand and left-hand…
For three decades statistical mechanics has been providing a framework to analyse neural networks. However, the theoretically tractable models, e.g., perceptrons, random features models and kernel machines, or multi-index models and…
Motivated by applications in conditional sampling, given a probability measure $\mu$ and a diffeomorphism $\phi$, we consider the problem of simultaneously approximating $\phi$ and the pushforward $\phi_{\#}\mu$ by means of the flow of a…
A flow matching model learns a time-dependent vector field $v_t(x)$ that generates a probability path $\{ p_t \}_{0 \leq t \leq 1}$ that interpolates between a well-known noise distribution ($p_0$) and the data distribution ($p_1$). It can…
Learning probability models from data is at the heart of many machine learning endeavors, but is notoriously difficult due to the curse of dimensionality. We introduce a new framework for learning \emph{normalized} energy (log probability)…
A nonlinear Poisson--Boltzmann equation with transmission boundary conditions at the interface between two materials is investigated. The model describes the electrostatic potential generated by a vector of ion concentrations in a periodic…
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…
The three-dimensional Couette flow between parallel plates is addressed using mixed lattice Boltzmann models which implement the half-range and the full-range Gauss-Hermite quadratures on the Cartesian axes perpendicular and parallel to the…
Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only…
Inspired by DiPerna-Lions' work \cite{Diperna-Lions}, we study the renormalized solutions to the large-data Cauchy problem of the Boltzmann systems modeling mixture gases of monatomic and polyatomic species, in which the distribution…
Efficient sampling of unnormalized probability densities such as the Boltzmann distribution of molecular systems is a longstanding challenge. Next to conventional approaches like molecular dynamics or Markov chain Monte Carlo, variational…
We extend flow matching to ensembles of linear systems in both deterministic and stochastic settings. Averaging over system parameters induces memory leading to a non-Markovian interpolation problem for the stochastic case. In this setting,…
We tackle the problem of sampling from intractable high-dimensional density functions, a fundamental task that often appears in machine learning and statistics. We extend recent sampling-based approaches that leverage controlled stochastic…
In this article, we propose a generalized non-equilibrium chemical kinetics model from \textit{ab initio} simulation data obtained using accurate potential energy surfaces developed recently for the purpose of studying high-temperature air…
Iterative Gaussianization is a fixed-point iteration procedure that can transform any continuous random vector into a Gaussian one. Based on iterative Gaussianization, we propose a new type of normalizing flow model that enables both…
This paper studies the training-testing discrepancy (a.k.a. exposure bias) problem for improving the diffusion models. During training, the input of a prediction network at one training timestep is the corresponding ground-truth noisy data…
A simple and interpretable way to learn a dynamical system from data is to interpolate its vector-field with a kernel. In particular, this strategy is highly efficient (both in terms of accuracy and complexity) when the kernel is…
A crucial design decision for any robot learning pipeline is the choice of policy representation: what type of model should be used to generate the next set of robot actions? Owing to the inherent multi-modal nature of many robotic tasks,…
In recent years, diffusion models trained on equilibrium molecular distributions have proven effective for sampling biomolecules. Beyond direct sampling, the score of such a model can also be used to derive the forces that act on molecular…
The aim of this work is to study the electron transport in graphene with impurities by introducing a generalization of linear response theory for linear dispersion relations and spinor wave functions. Current response and density response…