English
Related papers

Related papers: Gaussian process learning of nonlinear dynamics

200 papers

One's ability to learn a generative model of the world without supervision depends on the extent to which one can construct abstract knowledge representations that generalize across experiences. To this end, capturing an accurate…

Machine Learning · Computer Science 2021-10-28 Zahra Sheikhbahaee , Dongshu Luo , Blake VanBerlo , S. Alex Yun , Adam Safron , Jesse Hoey

Stationary points embedded in the derivatives are often critical for a model to be interpretable and may be considered as key features of interest in many applications. We propose a semiparametric Bayesian model to efficiently infer the…

Methodology · Statistics 2024-06-11 Cheng-Han Yu , Meng Li , Colin Noe , Simon Fischer-Baum , Marina Vannucci

Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent…

Quantitative Methods · Quantitative Biology 2023-01-06 Nathaniel J. Linden , Boris Kramer , Padmini Rangamani

Mathematical models of cognition are often memoryless and ignore potential fluctuations of their parameters. However, human cognition is inherently dynamic. Thus, we propose to augment mechanistic cognitive models with a temporal dimension…

Data-driven control of nonlinear systems with rigorous guarantees is a challenging problem as it usually calls for nonconvex optimization and requires often knowledge of the true basis functions of the system dynamics. To tackle these…

Optimization and Control · Mathematics 2023-03-27 Tim Martin , Thomas B. Schön , Frank Allgöwer

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…

Systems and Control · Computer Science 2019-03-01 Ibrahim Ayed , Emmanuel de Bézenac , Arthur Pajot , Julien Brajard , Patrick Gallinari

While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In…

Artificial Intelligence · Computer Science 2018-01-17 Maziar Raissi , George Em Karniadakis

This paper considers a stochastic control framework, in which the residual model uncertainty of the dynamical system is learned using a Gaussian Process (GP). In the proposed formulation, the residual model uncertainty consists of a…

Systems and Control · Electrical Eng. & Systems 2023-05-26 Marcel Menner , Karl Berntorp

We propose a robust parameter estimation method for dynamical systems based on Statistical Learning techniques which aims to estimate a set of parameters that well fit the dynamics in order to obtain robust evidences about the qualitative…

Methodology · Statistics 2021-02-26 Diego Marcondes

A linear Gaussian state-space smoothing algorithm is presented for estimation of derivatives from a sequence of noisy measurements. The algorithm uses numerically stable square-root formulas, can handle simultaneous independent measurements…

Methodology · Statistics 2016-10-17 Robert Piche

In this paper we extend the work of Smith and Papamichail (1999) and present fast approximate Bayesian algorithms for learning in complex scenarios where at any time frame, the relationships between explanatory state space variables can be…

Machine Learning · Computer Science 2013-01-30 Raffaella Settimi , Jim Q. Smith , A. S. Gargoum

We propose a novel Bayesian approach to modelling nonlinear alignments of time series based on latent shared information. We apply the method to the real-world problem of finding common structure in the sensor data of wind turbines…

Machine Learning · Statistics 2018-05-24 Markus Kaiser , Clemens Otte , Thomas Runkler , Carl Henrik Ek

Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…

Computation · Statistics 2018-12-12 Sara Pérez-Vieites , Inés P. Mariño , Joaquín Míguez

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…

Machine Learning · Statistics 2025-08-22 Björn Volkmann , Jan-Hendrik Ewering , Michael Meindl , Simon F. G. Ehlers , Thomas Seel

Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…

Data Analysis, Statistics and Probability · Physics 2007-05-23 J. C. Lemm

Latent dynamics discovery is challenging in extracting complex dynamics from high-dimensional noisy neural data. Many dimensionality reduction methods have been widely adopted to extract low-dimensional, smooth and time-evolving latent…

Machine Learning · Computer Science 2019-07-02 Qi She , Anqi Wu

Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape…

Dynamical Systems · Mathematics 2013-06-04 Ting Gao , Jinqiao Duan

Gaussian processes are Bayesian non-parametric models used in many areas. In this work, we propose a Non-stationary Heteroscedastic Gaussian process model which can be learned with gradient-based techniques. We demonstrate the…

Machine Learning · Computer Science 2022-12-26 Zeel B Patel , Nipun Batra , Kevin Murphy

We propose a machine learning framework for parameter estimation of single mode Gaussian quantum states. Under a Bayesian framework, our approach estimates parameters of suitable prior distributions from measured data. For phase-space…

Quantum Physics · Physics 2021-08-16 Neel Kanth Kundu , Matthew R. McKay , Ranjan K. Mallik

Data-driven, model-free analytics are natural choices for discovery and forecasting of complex, nonlinear systems. Methods that operate in the system state-space require either an explicit multidimensional state-space, or, one approximated…

Machine Learning · Statistics 2021-03-15 Joseph Park , Gerald M Pao , Erik Stabenau , George Sugihara , Thomas Lorimer