A Grey-Box Modeling Approach for the Reduction of Nonlinear Systems

Romijn, Reinout; Özkan, Leyla; Weiland, S.; Ludlage, Jobert; Marquardt, Wolfgang

doi:10.3182/20070606-3-mx-2915.00158

Cited by 4 publications

(2 citation statements)

References 8 publications

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“…In the following sections, each of these categories is explained through examples, wherever possible. It should be noted that most of the problems of real-world are a combination of one or more of these categories, as can be seen in the literature survey and summarized in Table 1 below Lumped parameter models (LPMs) [12], [16], [51], [52], [53], [54], [55], [43], [56], [57], [58], [59], [60], [22], [61], [62], [63], [64], [65], [66], [67], [64], [68], [69], [59], [60], [70], [68], [71], [66], [72], [73], [74], [75], [76] Residual modeling (RM) [30], [18], [20], [77], [78], [79], [34], [35], [33], [80], [81], …”

Section: Cstr Modelingmentioning

confidence: 99%

Integration of machine learning and first principles models

et al. 2022

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Model building and parameter estimation are traditional concepts widely used in chemical, biological, metallurgical, and manufacturing industries. Early modeling methodologies focused on mathematically capturing the process knowledge and domain expertise of the modeler. The models thus developed are termed first principles models (or white‐box models). Over time, computational power became cheaper, and massive amounts of data became available for modeling. This led to the development of cutting edge machine learning models (black‐box models) and artificial intelligence (AI) techniques. Hybrid models (gray‐box models) are a combination of first principles and machine learning models. The development of hybrid models has captured the attention of researchers as this combines the best of both modeling paradigms. Recent attention to this field stems from the interest in explainable AI (XAI), a critical requirement as AI systems become more pervasive. This work aims at identifying and categorizing various hybrid models available in the literature that integrate machine‐learning models with different forms of domain knowledge. Benefits such as enhanced predictive power, extrapolation capabilities, and other advantages of combining the two approaches are summarized. The goal of this article is to consolidate the published corpus in the area of hybrid modeling and develop a comprehensive framework to understand the various techniques presented. This framework can further be used as the foundation to explore rational associations between several models.

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Section: Cstr Modelingmentioning

confidence: 99%

Integration of machine learning and first principles models

et al. 2022

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“…Commonly used model structures include multivariate linear or polynomial models, neural networks, or vector machines among others (Hastie et al, 2003). This way, a certain type of hybrid (or grey-box) model (Psichogios and Ungar, 1992;Agarwal , 1997;Olivera, 2004) arises in a natural way by combining first principles models fixed on previous decision levels with an empirical model on the current decision level (Kahrs, Marquardt , 2008;Romijn et al, 2008;Kahrs et al, 2009).…”

Section: Model Bmentioning

confidence: 99%

Models, Simulations, and the Reduction of Complexity

Gähde¹,

Hartmann²,

Wolf³

2013

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Upon which foundation should one build a model for the Universe as a whole?The idea that such a model should exist seems bold itself. Can we really believe that we might be able to construct a physical model for a unique object that we cannot experiment with, that we are part of and of which we can only see a very small section? The goal of this article is to explain that this does indeed seem possible, that mathematical simplicity is used as a guiding principle in this construction, and that the resulting world model is remarkably consistent with a wealth of observations.Let us begin with a detour through the foundation of laws of nature in physics. It is important to realise that laws of nature do not describe nature herself, but human concepts of nature. Otherwise it would not be possible to replace established laws by other, more general ones, as it has happened several times in the history of physics. Theories in physics are based on axioms chosen by physicists, and these axioms can be altered.Newton's axioms underlie classical mechanics. They distinguish four entities; bodies, forces, space and time, and formulate how bodies move in time through space under the influence of forces. Field theory, initiated by Faraday, attaches forces to space and gives force fields their own dynamics. Special Relativity realises that space and time have no independent existence and thereby connects forces, space and time. General Relativity explains how the presence of bodies and energy affects the structure of space-time. Thus, in a general-relativistic field theory, the four initially separate entities of Newtonian physics are all linked together.The dynamics of physical entities, i.e. their change in time, is described by differential equations. They themselves are not postulated, but derived from a more general concept overarching physics, namely that of an extremal principle . The best-known example is perhaps Fermat's principle, which states that light rays connect the source and the receiver in such a way that the light travel time is extremal along them. The extremal principle underlying essentially all of the established theories in physics is the so-called principle of least action , or Hamilton 's principle. The action itself is an abstract quantity that can be constructed under very general rules. It must be independent of any observer's state of motion,

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