Related papers: Learning Partially Known Stochastic Dynamics with …
We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of multi-dimensional non-linear stochastic differential equations, which relies upon discrete-time observations of the state. The…
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…
We present a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our basic assumption is that the governing equations for the…
Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…
Bayesian inference methods are applied within a Bayesian hierarchical modelling framework to the problems of joint state and parameter estimation, and of state forecasting. We explore and demonstrate the ideas in the context of a simple…
One of the defining properties of deep learning is that models are chosen to have many more parameters than available training data. In light of this capacity for overfitting, it is remarkable that simple algorithms like SGD reliably return…
Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…
We identify an issue in recent approaches to learning-based control that reformulate systems with uncertain dynamics using a stochastic differential equation. Specifically, we discuss the approximation that replaces a model with fixed but…
In this paper we focus on the parameter estimation of dynamic load models with stochastic terms, in particular, load models where protection settings are uncertain, such as in aggregated air conditioning units. We show how the uncertainty…
In this paper we derive a PAC-Bayesian-Like error bound for a class of stochastic dynamical systems with inputs, namely, for linear time-invariant stochastic state-space models (stochastic LTI systems for short). This class of systems is…
In this paper we derive a PAC-Bayesian error bound for autonomous stochastic LTI state-space models. The motivation for deriving such error bounds is that they will allow deriving similar error bounds for more general dynamical systems,…
We study stochastic optimization with data-adaptive sampling schemes to train pairwise learning models. Pairwise learning is ubiquitous, and it covers several popular learning tasks such as ranking, metric learning and AUC maximization. A…
Effective quantification of uncertainty is an essential and still missing step towards a greater adoption of deep-learning approaches in different applications, including mission-critical ones. In particular, investigations on the…
The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at…
Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated…
Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end,…
We introduce a novel paradigm for learning non-parametric drift and diffusion functions for stochastic differential equation (SDE). The proposed model learns to simulate path distributions that match observations with non-uniform time…
Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are…
Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…
This work introduces a neural architecture for learning forward models of stochastic environments. The task is achieved solely through learning from temporal unstructured observations in the form of images. Once trained, the model allows…