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The leveraging of Artificial Intelligence (AI) for model discovery in dynamical systems is cross-fertilizing and revolutionizing both disciplines, heralding a new era of data-driven science. This book is placed at the forefront of this endeavor, taking model discovery to the next level. Dealing with Artificial Intelligence, this book delineates AI’s role in model discovery for dynamical systems. With the implementation of topological methods to construct metamodels, it engages with levels of complexity and multiscale hierarchies hitherto considered off limits for Data Science.
With the implementation of topological methods, AI-empowered metamodel discovery is able to focus on levels of system complexity and multiscale hierarchies considered off limits in current machine learning (ML) technologies. This is so because the information on time series is encoded at the maximum level of coarse-graining hence, it greatly simplifies the computations while enabling a decoding of the information generated at the level of a topological description.
The topological dynamics methodology described in the book will render tractable problems in model discovery hitherto considered off limits for AI-based approaches. Thus, ultra-complex hierarchical realities recreating cellular, biomedical, or cosmological contexts will be within reach as the topological methods are incorporated to AI-empowered metamodel discovery. These advances represent substantial contributions to dynamical systems research and have implications for a vast array of applications.
Artificial Intelligence refers to machines capable of exhibiting behavioral traits that humans regard as indicators of intelligence, such as learning and problem-solving. Within this protean and fuzzily delineated subject, machine learning refers to the ability to learn without being explicitly instructed to do so, while Deep Learning (DL) refers to an automated extraction of features, patterns, and ultimately models from arrayed data that is sequentially represented within an abstraction hierarchy organized as a multilayered neural network (NN). DL will be the aspect of AI that this book mostly focuses on as we seek to unravel mathematical models enshrined in the patterns that underlie vast arrays of dynamic data.
DL has been shown to be highly efficacious at identifying features that are in principle discoverable from the data. As in face recognition, features are hierarchically organized, so that large-scale patterns (eyes, noses, face shapes) emerge after several layers of abstraction from simpler or more rudimentary patterns (lines, curves, shades). The beauty and power of DL resides in the fact that the feature extraction process may be carried out in an unsupervised manner: the features emerge from the training of the system without human input or bias, and enable the network to make accurate inferences. In this era of big data, arising primarily in biology, biomedicince, and cosmology, we may state that time is ripe to plunge into DL and master the field.
Intended for graduate students, researchers, and practitioners interested in dynamical systems empowered by AI or Machine Learning (ML) and in their biological, engineering, and biomedical applications, this book will represent a significant educational resource for people engaged in AI-related cross-disciplinary projects