Related papers: Particle Dynamics for Latent-Variable Energy-Based…
Deep directed generative models have attracted much attention recently due to their expressive representation power and the ability of ancestral sampling. One major difficulty of learning directed models with many latent variables is the…
Charged particle dynamics under the influence of electromagnetic fields is a challenging spatiotemporal problem. Many high performance physics-based simulators for predicting behavior in a charged particle beam are computationally…
Expectation-Maximization (EM) is a prominent approach for parameter estimation of hidden (aka latent) variable models. Given the full batch of data, EM forms an upper-bound of the negative log-likelihood of the model at each iteration and…
Energy-based models (EBMs) provide a powerful and flexible way of learning a joint probability distribution over data by constructing an energy surface. This energy surface enables insight extraction and conditional sampling. We apply EBMs…
Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape,…
Latent variable models (LVMs) represent observed variables by parameterized functions of latent variables. Prominent examples of LVMs for unsupervised learning are probabilistic PCA or probabilistic SC which both assume a weighted linear…
We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…
Energy-based modeling is a promising approach to unsupervised learning, which yields many downstream applications from a single model. The main difficulty in learning energy-based models with the "contrastive approaches" is the generation…
We introduce a physics-driven deep latent variable model (PDDLVM) to learn simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of parametric partial differential equations (PDEs). Our formulation…
Chaotic dynamical systems exhibit strong sensitivity to initial conditions and often contain unresolved multiscale processes, making deterministic forecasting fundamentally limited. Generative models offer an appealing alternative by…
We analyze some parabolic PDEs with different drift terms which are gradient flows in the Wasserstein space and consider the corresponding discrete-in-time JKO scheme. We prove with optimal transport techniques how to control the L p and L…
Large language models (LLMs) trained via KL-regularized reinforcement learning demonstrate strong instruction following, self-correction, and reasoning abilities. Yet their theoretical underpinnings remain limited. We exploit the…
In this paper we introduce a modified lattice Boltzmann model (LBM) with the capability of mimicking a fluid system with dynamic heterogeneities. The physical system is modeled as a one-dimensional fluid, interacting with finite-lifetime…
Amortised inference enables scalable learning of sequential latent-variable models (LVMs) with the evidence lower bound (ELBO). In this setting, variational posteriors are often only partially conditioned. While the true posteriors depend,…
The classical (overdamped) Langevin dynamics provide a natural algorithm for sampling from its invariant measure, which uniquely minimizes an energy functional over the space of probability measures, and which concentrates around the…
Given nonstationary data from molecular dynamics simulations, a Markovian Langevin model is constructed that aims to reproduce the time evolution of the underlying process. While at equilibrium the free energy landscape is sampled,…
The stochastic motions of a diffusing particle contain information concerning the particle's interactions with binding partners and with its local environment. However, accurate determination of the underlying diffusive properties, beyond…
In this contribution, we propose a generic online (also sometimes called adaptive or recursive) version of the Expectation-Maximisation (EM) algorithm applicable to latent variable models of independent observations. Compared to the…
Pervasive across diverse domains, stochastic systems exhibit fluctuations in processes ranging from molecular dynamics to climate phenomena. The Langevin equation has served as a common mathematical model for studying such systems, enabling…
The mean-field Langevin dynamics (MFLD) minimizes an entropy-regularized nonlinear convex functional on the Wasserstein space over $\mathbb{R}^d$, and has gained attention recently as a model for the gradient descent dynamics of interacting…