Related papers: Learning Stochastic Dynamical System via Flow Map …

We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…

A stochastic Machine-Learning approach is developed for data-driven Reynolds-Averaged Navier-Stokes (RANS) predictions of turbulent flows, with quantified model uncertainty. This is done by combining a Bayesian symbolic identification…

We propose new limiting dynamics for stochastic gradient descent in the small learning rate regime called stochastic modified flows. These SDEs are driven by a cylindrical Brownian motion and improve the so-called stochastic modified…

Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful tool to complement traditional scientific computing,…

In this paper, we propose a generalized framework for developing learning-rate-free momentum stochastic gradient descent (SGD) methods in the minimization of nonsmooth nonconvex functions, especially in training nonsmooth neural networks.…

Leveraging advances in variational inference, we propose to enhance recurrent neural networks with latent variables, resulting in Stochastic Recurrent Networks (STORNs). The model i) can be trained with stochastic gradient methods, ii)…

Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…

Optimization-based meta-learning typically assumes tasks are sampled from a single distribution - an assumption oversimplifies and limits the diversity of tasks that meta-learning can model. Handling tasks from multiple different…

This paper proposes a novel deep learning approach for learning operators in semigroup, with applications to modeling unknown autonomous dynamical systems using time series data collected at varied time lags. It is a sequel to the previous…

Learning continuous-time stochastic dynamics is a fundamental and essential problem in modeling sporadic time series, whose observations are irregular and sparse in both time and dimension. For a given system whose latent states and…

Language models based on discrete diffusion have attracted widespread interest for their potential to provide faster generation than autoregressive models. Despite their promise, these models typically produce samples whose quality sharply…

The reconstruction and inference of stochastic dynamical systems from data is a fundamental task in inverse problems and statistical learning. While surrogate modeling advances computational methods to approximate these dynamics, standard…

Forecasting conditional stochastic nonlinear dynamical systems is a fundamental challenge repeatedly encountered across the biological and physical sciences. While flow-based models can impressively predict the temporal evolution of…

Modeling transformations between arbitrary data distributions is a fundamental scientific challenge, arising in applications like drug discovery and evolutionary simulation. While flow matching offers a natural framework for this task, its…

Understanding the world around us and making decisions about the future is a critical component to human intelligence. As autonomous systems continue to develop, their ability to reason about the future will be the key to their success.…

Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with observation on stationary probability distributions. We develop a…

Stochastic binary hidden units in a multi-layer perceptron (MLP) network give at least three potential benefits when compared to deterministic MLP networks. (1) They allow to learn one-to-many type of mappings. (2) They can be used in…

Unraveling the connections between microscopic structure, emergent physical properties, and slow dynamics has long been a challenge when studying the glass transition. The absence of clear visible structural order in amorphous…

Available methods for identification of stochastic dynamical systems from input-output data generally impose restricting structural assumptions on either the noise structure in the data-generating system or the possible state probability…

In this chapter we take a look at the universal approximation question for stochastic feedforward neural networks. In contrast to deterministic networks, which represent mappings from a set of inputs to a set of outputs, stochastic networks…