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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…
Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…
It is well-known from the work of Sch\"onbucher (2005) that the marginal laws of a loss process can be matched by a unit increasing time inhomogeneous Markov process, whose deterministic jump intensity is called local intensity. The…
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…
Automatic machine learning of empirical models from experimental data has recently become possible as a result of increased availability of computational power and dedicated algorithms. Despite the successes of non-parametric inference and…
We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…
We show that the bias of the approximate maximum-likelihood estimation (MLE) objective of a persistent chain energy-based model (EBM) is precisely equal to the thermodynamic excess work of an overdamped Langevin dynamical system. We then…
Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…
I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…
Empirical Bayes provides a powerful approach to learning and adapting to latent structure in data. Theory and algorithms for empirical Bayes have a rich literature for sequence models, but are less understood in settings where latent…
Machine learning methods have been lately used to solve partial differential equations (PDEs) and dynamical systems. These approaches have been developed into a novel research field known as scientific machine learning in which techniques…
A core problem in machine learning is to learn expressive latent variables for model prediction on complex data that involves multiple sub-components in a flexible and interpretable fashion. Here, we develop an approach that improves…
This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the Multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and…
We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally…
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,…
Systems of interacting continuous-time Markov chains are a powerful model class, but inference is typically intractable in high dimensional settings. Auxiliary information, such as noisy observations, is typically only available at discrete…
In order to learn the complex features of large spatio-temporal data, models with large parameter sets are often required. However, estimating a large number of parameters is often infeasible due to the computational and memory costs of…
This paper studies the fundamental problem of learning deep generative models that consist of multiple layers of latent variables organized in top-down architectures. Such models have high expressivity and allow for learning hierarchical…
We propose a number of new algorithms for learning deep energy models and demonstrate their properties. We show that our SteinCD performs well in term of test likelihood, while SteinGAN performs well in terms of generating realistic looking…
In this work, we explore modeling change points in time-series data using neural stochastic differential equations (neural SDEs). We propose a novel model formulation and training procedure based on the variational autoencoder (VAE)…