Related papers: Learning Partially Known Stochastic Dynamics with …
Real-world data contains aleatoric uncertainty - irreducible noise arising from imperfect measurements or from incomplete knowledge about the data generation process. Mean-variance estimation networks can learn this type of uncertainty but…
Accuracy and generalization capabilities are key objectives when learning dynamical system models. To obtain such models from limited data, current works exploit prior knowledge and assumptions about the system. However, the fusion of…
In this article, we employ a collection of stochastic differential equations with drift and diffusion coefficients approximated by neural networks to predict the trend of chaotic time series which has big jump properties. Our contributions…
We propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central…
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…
Stochastic and conditional simulation methods have been effective towards producing realistic realizations and simulations of spatial numerical models that share equal probability of occurrence. Application of these methods are valuable…
We consider a nonlinear state-space model with the state transition and observation functions expressed as basis function expansions. The coefficients in the basis function expansions are learned from data. Using a connection to Gaussian…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
In real-world applications, the distribution of the data, and our goals, evolve over time. The prevailing theoretical framework for studying machine learning, namely probably approximately correct (PAC) learning, largely ignores time. As a…
Complex dynamical systems, from macromolecules to ecosystems, are often modeled by stochastic differential equations. To learn such models from data, a common approach involves sparse selection among a large function library. However, we…
We propose a novel framework for discovering Stochastic Partial Differential Equations (SPDEs) from data. The proposed approach combines the concepts of stochastic calculus, variational Bayes theory, and sparse learning. We propose the…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…
We develop a stochastic parametrization, based on a `simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike…
Uncertainty quantification is crucial for building reliable and trustable machine learning systems. We propose to estimate uncertainty in recurrent neural networks (RNNs) via stochastic discrete state transitions over recurrent timesteps.…
Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…
Stochastic differential equations (SDEs) are one of the most important representations of dynamical systems. They are notable for the ability to include a deterministic component of the system and a stochastic one to represent random…
We present novel monotone comparative statics results for steady-state behavior in a dynamic optimization environment with misspecified Bayesian learning. Building on \cite{ep21a}, we analyze a Bayesian learner whose prior is over…
Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…
Making the most of multispectral image time-series is a promising but still relatively under-explored research direction because of the complexity of jointly analyzing spatial, spectral and temporal information. Capturing and characterizing…