English
Related papers

Related papers: Learning solutions of parameterized stiff ODEs usi…

200 papers

Gaussian Processes (GPs) can be used as flexible, non-parametric function priors. Inspired by the growing body of work on Normalizing Flows, we enlarge this class of priors through a parametric invertible transformation that can be made…

Machine Learning · Computer Science 2021-02-26 Juan Maroñas , Oliver Hamelijnck , Jeremias Knoblauch , Theodoros Damoulas

In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…

Methodology · Statistics 2020-10-02 Hossein Mohammadi , Peter Challenor , Marc Goodfellow , Daniel Williamson

Fitting a theoretical model to experimental data in a Bayesian manner using Markov chain Monte Carlo typically requires one to evaluate the model thousands (or millions) of times. When the model is a slow-to-compute physics simulation,…

Machine Learning · Statistics 2022-08-25 Steven Stetzler , Michael Grosskopf , Earl Lawrence

Gaussian Processes (GPs) have been widely used in machine learning to model distributions over functions, with applications including multi-modal regression, time-series prediction, and few-shot learning. GPs are particularly useful in the…

Numerous engineering problems of interest to the industry are often characterized by expensive black-box objective experiments or computer simulations. Obtaining insight into the problem or performing subsequent optimizations requires…

Machine Learning · Statistics 2019-07-29 Piyush Pandita , Jesper Kristensen , Liping Wang

We introduce a scalable Gaussian process (GP) framework with deep product kernels for data-driven learning of parametrized spatio-temporal fields over fixed or parameter-dependent domains. The proposed framework learns a continuous…

Machine Learning · Computer Science 2026-03-03 Srinath Dama , Prasanth B. Nair

Gaussian processes are a flexible Bayesian nonparametric modelling approach that has been widely applied but poses computational challenges. To address the poor scaling of exact inference methods, approximation methods based on sparse…

Machine Learning · Statistics 2021-06-01 Rui Meng , Herbert Lee , Soper Braden , Priyadip Ray

Gaussian processes (GPs) are canonical as surrogates for computer experiments because they enjoy a degree of analytic tractability. But that breaks when the response surface is constrained, say to be monotonic. Here, we provide a mono-GP…

Computation · Statistics 2026-01-28 Steven D. Barnett , Lauren J. Beesley , Annie S. Booth , Robert B. Gramacy , Dave Osthus

Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article…

Optimization and Control · Mathematics 2015-11-06 Anna Fiedler , Fabian J. Theis , Jan Hasenauer

Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…

Methodology · Statistics 2011-06-29 Anjishnu Banerjee , David Dunson , Surya Tokdar

Many real-world systems are modelled using complex ordinary differential equations (ODEs). However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like Proper Orthogonal…

Computational Engineering, Finance, and Science · Computer Science 2025-02-26 Abhishek Ajayakumar , Soumyendu Raha

The focus of this work is on local stability of a class of nonlinear ordinary differential equations (ODE) that describe limits of empirical measures associated with finite-state weakly interacting N-particle systems. Local Lyapunov…

Probability · Mathematics 2015-02-16 Amarjit Budhiraja , Paul Dupuis , Markus Fischer , Kavita Ramanan

Parametric shape optimization aims at minimizing an objective function f(x) where x are CAD parameters. This task is difficult when f is the output of an expensive-to-evaluate numerical simulator and the number of CAD parameters is large.…

Machine Learning · Statistics 2021-05-06 David Gaudrie , Rodolphe Le Riche , Victor Picheny , Benoit Enaux , Vincent Herbert

Some scenarios require the computation of a predictive distribution of a new value evaluated on an objective function conditioned on previous observations. We are interested on using a model that makes valid assumptions on the objective…

Machine Learning · Computer Science 2021-01-21 Lucia Asencio-Martín , Eduardo C. Garrido-Merchán

Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…

Machine Learning · Computer Science 2024-02-28 Prakhar Verma , Vincent Adam , Arno Solin

Diverse domains of science and engineering use parameterised mechanistic models. Engineers and scientists can often hypothesise several rival models to explain a specific process or phenomenon. Consider a model discrimination setting where…

Machine Learning · Computer Science 2021-11-02 Simon Olofsson , Eduardo S. Schultz , Adel Mhamdi , Alexander Mitsos , Marc Peter Deisenroth , Ruth Misener

Gaussian processes (GPs) are powerful and widely used probabilistic regression models, but their effectiveness in practice is often limited by the choice of kernel function. This kernel function is typically handcrafted from a small set of…

Machine Learning · Computer Science 2026-02-13 Jihao Andreas Lin , Sebastian Ament , Louis C. Tiao , David Eriksson , Maximilian Balandat , Eytan Bakshy

We consider the problem of inferring latent stochastic differential equations (SDEs) with a time and memory cost that scales independently with the amount of data, the total length of the time series, and the stiffness of the approximate…

Machine Learning · Computer Science 2023-12-19 Kevin Course , Prasanth B. Nair

Gaussian process (GP) predictors are an important component of many Bayesian approaches to machine learning. However, even a straightforward implementation of Gaussian process regression (GPR) requires O(n^2) space and O(n^3) time for a…

Machine Learning · Statistics 2012-11-06 Krzysztof Chalupka , Christopher K. I. Williams , Iain Murray

Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…

Quantum Physics · Physics 2019-05-29 Zhikuan Zhao , Jack K. Fitzsimons , Joseph F. Fitzsimons