Discovering governing partial differential equations from noisy data

Article Multidisciplinary Sciences

Neural ordinary differential equations with irregular and noisy data

Pawan Goyal et al.

Summary: Measurement noise is a crucial factor in data collection for physical processes. This study introduces a methodology that combines deep neural networks with neural ordinary differential equations to learn differential equations from noisy and irregularly sampled measurements. The proposed framework effectively models vector fields under noisy measurements and can handle scenarios with unavailable dependent variables on the same temporal grid. The method is demonstrated to be effective for learning models from data obtained from various differential equations and performs better than the neural ordinary differential equation method without special treatment to noise. An ensemble approach is also discussed to further improve the performance of the proposed method.

ROYAL SOCIETY OPEN SCIENCE (2023)

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Review Engineering, Chemical

Integration of machine learning and first principles models

Lokesh Rajulapati et al.

Summary: This article discusses the applications of model building and parameter estimation in various industries, and the development of first principles models, machine learning models, and hybrid models. The advantages of hybrid models and the latest research progress in the field of hybrid modeling are highlighted.

AICHE JOURNAL (2022)

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Article Computer Science, Interdisciplinary Applications

A hybrid modelling approach to model process dynamics by the discovery of a system of partial differential equations

Kiran Raviprakash et al.

Summary: This paper proposes a hybrid modeling approach that integrates partial knowledge of the system into data-driven modeling to improve the accuracy and reliability of the models.

COMPUTERS & CHEMICAL ENGINEERING (2022)

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Article Computer Science, Interdisciplinary Applications

DeepMoD: Deep learning for model discovery in noisy data

Gert-Jan Both et al.

Summary: DeepMoD is a deep learning based model discovery algorithm that uses sparse regression to discover the underlying partial differential equation in a library of possible functions and their derivatives. It is robust to noise, applicable to small data sets, and does not require a training set. The algorithm has shown promising results in benchmark tests on physical problems and successfully discovered the advection-diffusion equation in noisy experimental time-series data.

JOURNAL OF COMPUTATIONAL PHYSICS (2021)

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Review Computer Science, Interdisciplinary Applications

Recent trends on hybrid modeling for Industry 4.0

Joel Sansana et al.

Summary: This article discusses the chemical processing industry's reliance on modeling techniques and the impact of emerging data-driven frameworks on knowledge extraction, emphasizing the importance of integrating traditional mechanistic models with data-driven frameworks, and pointing out the need to incorporate process and phenomenological knowledge into big data and machine learning frameworks.

COMPUTERS & CHEMICAL ENGINEERING (2021)

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Article Multidisciplinary Sciences