Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems

Yang, Yibo; Perdikaris, Paris

doi:10.1007/s00466-019-01718-y

Cited by 54 publications

(21 citation statements)

References 63 publications

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“…PINNs have been extended to convolutional [340] and graph neural network [270] backbones. They have been used in many scientific applications, including fluid mechanics modeling [243], cardiac activation mapping [263], stochastic systems modeling [323], and discovery of differential equations [241,240].…”

Section: Machine Learning Models That Incorporate Physics and Other Generative Or Causal Constraintsmentioning

confidence: 99%

Interpretable machine learning: Fundamental principles and 10 grand challenges

Rudin¹,

Chen²,

Chen³

et al. 2022

Statist. Surv.

438

202

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Interpretability in machine learning (ML) is crucial for high stakes decisions and troubleshooting. In this work, we provide fundamental principles for interpretable ML, and dispel common misunderstandings that dilute the importance of this crucial topic. We also identify 10 technical challenge areas in interpretable machine learning and provide history and background on each problem. Some of these problems are classically important, and some are recent problems that have arisen in the last few years. These problems are: (1) Optimizing sparse logical models such as decision trees;(2) Optimization of scoring systems; (3) Placing constraints into generalized additive models to encourage sparsity and better interpretability; (4) Modern case-based reasoning, including neural networks and matching for causal inference; (5) Complete supervised disentanglement of neural networks; (6) Complete or even partial unsupervised disentanglement of neural networks; (7) Dimensionality reduction for data visualization; (8) Machine learning models that can incorporate physics and other generative or causal constraints; (9) Characterization of the "Rashomon set" of good models; and (10) Interpretable reinforcement learning. This survey is suitable as a starting point for statisticians and computer scientists interested in working in interpretable machine learning.

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Section: Machine Learning Models That Incorporate Physics and Other Generative Or Causal Constraintsmentioning

confidence: 99%

Interpretable machine learning: Fundamental principles and 10 grand challenges

Rudin¹,

Chen²,

Chen³

et al. 2022

Statist. Surv.

438

202

View full text Add to dashboard Cite

show abstract

“…Here, we build two different ML models, namely Gaussian Processes (GP) Rasmussen and Williams [2006] and a probabilistic conditional generative approach Yang and Perdikaris [2019b]. We train both in a supervised learning fashion using data produced with expensive MD simulations.…”

Section: Methodology: Building Machine Learning Models To Describe Ph...mentioning

confidence: 99%

Prediction of liquid fuel properties using machine learning models with Gaussian processes and probabilistic conditional generative learning

Freitas,

Lima,

Chen

et al. 2021

Preprint

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Accurate determination of fuel properties of complex mixtures over a wide range of pressure and temperature conditions is essential to utilizing alternative fuels. The present work aims to construct cheap-to-compute machine learning (ML) models to act as closure equations for predicting the physical properties of alternative fuels. Those models can be trained using the database from MD simulations and/or experimental measurements in a data-fusion-fidelity approach. Here, Gaussian Process (GP) and probabilistic generative models are adopted. GP is a popular nonparametric Bayesian approach to build surrogate models mainly due to its capacity to handle the aleatory and epistemic uncertainties. Generative models have shown the ability of deep neural networks employed with the same intent. In this work, ML analysis is focused on a particular property, the fuel density, but it can also be extended to other physicochemical properties. This study explores the versatility of the ML models to handle multi-fidelity data. The results show that ML models can predict accurately the fuel properties of a wide range of pressure and temperature conditions. * The research leading to these results had received funding from the Brazilian National Agency for Petroleum, Natural Gas and Biofuels (ANP) through Programa de Recursos Humanos (PRH) under the PRH 8 -Mechanical Engineering for the Efficient Use of Biofuels, grant agreement numbers F0A5.EDDE.B5C0.3BCB and 2B61.4F5C.A83B.A713.

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“…Machine learning methods and data-driven modelling techniques have already proven their utility in solving high-dimensional problems in computer vision [10], natural language processing [11], etc. Owing to their capability of extracting features from high-dimensional and multi-fidelity noisy data [12,13], these methods are also gaining attraction in modelling and simulating physical and biological systems. The evolution of such systems can be typically characterized by differential equations, and several techniques have been developed to construct predictive algorithms that can synergistically combine data and mechanistic prior knowledge.…”

Section: Introductionmentioning

confidence: 99%

Bayesian differential programming for robust systems identification under uncertainty

2020

Self Cite

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This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling. This allows an efficient inference of the posterior distributions over plausible models with quantified uncertainty, while the use of sparsity-promoting priors enables the discovery of interpretable and parsimonious representations for the underlying latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed methods, including nonlinear oscillators, predator–prey systems and examples from systems biology. Taken together, our findings put forth a flexible and robust workflow for data-driven model discovery under uncertainty. All codes and data accompanying this article are available at https://bit.ly/34FOJMj .

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Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems

Cited by 54 publications

References 63 publications

Interpretable machine learning: Fundamental principles and 10 grand challenges

Interpretable machine learning: Fundamental principles and 10 grand challenges

Prediction of liquid fuel properties using machine learning models with Gaussian processes and probabilistic conditional generative learning

Bayesian differential programming for robust systems identification under uncertainty

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