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A multi-fidelity (MF) active learning method is presented for design optimization problems characterized by noisy evaluations of the performance metrics. Namely, a generalized MF surrogate model is used for design-space exploration,…

Optimization and Control · Mathematics 2022-07-12 Riccardo Pellegrini , Jeroen Wackers , Riccardo Broglia , Andrea Serani , Michel Visonneau , Matteo Diez

From the nano-scale to the macro-scale, biological tissue is spatially heterogeneous. Even when tissue behavior is well understood, the exact subject specific spatial distribution of material properties is often unknown. And, when…

Tissues and Organs · Quantitative Biology 2020-11-02 Emma Lejeune , Bill Zhao

High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated for modeling a given…

Machine Learning · Computer Science 2023-09-04 Paolo Conti , Mengwu Guo , Andrea Manzoni , Attilio Frangi , Steven L. Brunton , J. Nathan Kutz

This paper introduces the notion of stochastic simulation-gap function, which formally quantifies the gap between an approximate mathematical model and a high-fidelity stochastic simulator. Since controllers designed for the mathematical…

Systems and Control · Electrical Eng. & Systems 2026-03-24 P Sangeerth , Abolfazl Lavaei , Pushpak Jagtap

Neural posterior estimation has emerged as a powerful tool for amortized inference, with growing adoption across scientific and applied domains. In many of these applications, the conditioning variable is a set of observations whose…

Machine Learning · Computer Science 2026-05-11 Antoine Wehenkel , Michael Kagan , Lukas Heinrich , Chris Pollard

We present a new Subset Simulation approach using Hamiltonian neural network-based Monte Carlo sampling for reliability analysis. The proposed strategy combines the superior sampling of the Hamiltonian Monte Carlo method with…

Machine Learning · Statistics 2024-01-11 Denny Thaler , Somayajulu L. N. Dhulipala , Franz Bamer , Bernd Markert , Michael D. Shields

In this paper, we present an adaptive algorithm to construct response surface approximations of high-fidelity models using a hierarchy of lower fidelity models. Our algorithm is based on multi-index stochastic collocation and automatically…

Numerical Analysis · Mathematics 2021-05-04 John D. Jakeman , Michael Eldred , Gianluca Geraci , Alex Gorodetsky

This paper explores learning emulators for parameter estimation with uncertainty estimation of high-dimensional dynamical systems. We assume access to a computationally complex simulator that inputs a candidate parameter and outputs a…

Machine Learning · Computer Science 2022-11-04 Ruoxi Jiang , Rebecca Willett

Stochastic simulation models are generative models that mimic complex systems to help with decision-making. The reliability of these models heavily depends on well-calibrated input model parameters. However, in many practical scenarios,…

Methodology · Statistics 2024-11-11 Ziwei Su , Diego Klabjan

Simulation models often have parameters as input and return outputs to understand the behavior of complex systems. Calibration is the process of estimating the values of the parameters in a simulation model in light of observed data from…

Methodology · Statistics 2024-11-15 Özge Sürer

There has been increasing interest in characterising the error behaviour of systems which contain deep learning models before deploying them into any safety-critical scenario. However, characterising such behaviour usually requires…

Machine Learning · Computer Science 2021-11-08 Jonathan Sadeghi , Blaine Rogers , James Gunn , Thomas Saunders , Sina Samangooei , Puneet Kumar Dokania , John Redford

Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit…

Machine Learning · Statistics 2024-02-09 Stefan T. Radev , Ulf K. Mertens , Andreas Voss , Lynton Ardizzone , Ullrich Köthe

The objective of this work is to quantify the uncertainty in probability of failure estimates resulting from incomplete knowledge of the probability distributions for the input random variables. We propose a framework that couples the…

Methodology · Statistics 2021-10-26 Dimitris G. Giovanis , Michael Shields

Efficiently performing predictive studies of irradiated particle-laden turbulent flows has the potential of providing significant contributions towards better understanding and optimizing, for example, concentrated solar power systems. As…

Computational Physics · Physics 2018-08-20 Hillary R. Fairbanks , Lluis Jofre , Gianluca Geraci , Gianluca Iaccarino , Alireza Doostan

We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost…

Computation · Statistics 2021-05-04 Alex A. Gorodetsky , Gianluca Geraci , Mike Eldred , John D. Jakeman

Complex simulator-based models are now routinely used to perform inference across the sciences and engineering, but existing inference methods are often unable to account for outliers and other extreme values in data which occur due to…

Machine Learning · Statistics 2026-02-18 Ayush Bharti , Charita Dellaporta , Yuga Hikida , François-Xavier Briol

Simulation is a useful tool in situations where training data for machine learning models is costly to annotate or even hard to acquire. In this work, we propose a reinforcement learning-based method for automatically adjusting the…

Machine Learning · Computer Science 2019-05-15 Nataniel Ruiz , Samuel Schulter , Manmohan Chandraker

How can one perform Bayesian inference on stochastic simulators with intractable likelihoods? A recent approach is to learn the posterior from adaptively proposed simulations using neural network-based conditional density estimators.…

Machine Learning · Computer Science 2019-05-21 David S. Greenberg , Marcel Nonnenmacher , Jakob H. Macke

Multi-fidelity modelling arises in many situations in computational science and engineering world. It enables accurate inference even when only a small set of accurate data is available. Those data often come from a high-fidelity model,…

Machine Learning · Statistics 2022-04-12 Jiahao Zhang , Shiqi Zhang , Guang Lin

Learning from demonstrations (LfD) is an efficient paradigm to train AI agents. But major issues arise when there are differences between (a) the demonstrator's own sensory input, (b) our sensors that observe the demonstrator and (c) the…

Artificial Intelligence · Computer Science 2020-03-03 Jalal Etesami , Philipp Geiger