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What are the goals of this tutorial? Introduce novices to major topics within Artificial Intelligence (AI); Introduce expert non-specialists to an AI subarea; Introduce expert non-specialists to the use of readily deployed AI tools (e.g. machine learning models) in various areas of AI research; Motivate and explain a topic of emerging importance for AI; Provide instruction in established but specialised AI methodologies.
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What knowledge will be conveyed? Foundational understanding of differential equations and numerical methods, and their role in modelling real-world systems. Introduction and hands-on of two foundational architectures, Physics-Informed Neural Networks and Neural Ordinary Differential Equations and their respective official libraries. Clarification of the common misconception that Physics-Informed Neural Networks and Neural Ordinary Differential Equations are two architectures that achieve the same goal.
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What techniques/methods, concepts and modelling frameworks will be conveyed? Basic theory of differential equations and numerical methods; Physics-Informed Neural Networks, DeepXDE library, Neural Ordinary Differential Equations, Torchdiffeq library, When to use Physics-Informed Neural Networks and Neural Ordinary Differential Equations.
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Why is this topic relevant? The integration of differential equations with Neural Networks represents an innovative and highly relevant frontier in the field of artificial intelligence. This tutorial addresses a critical need in scientific and engineering disciplines by introducing the concepts of Physics-Informed Neural Networks and Neural Ordinary Differential Equations. These methodologies bridge the gap between traditional mathematical modelling and contemporary AI applications, offering powerful tools for understanding and predicting complex systems. By exploring novel architectures and fostering interdisciplinary collaboration, this tutorial ensures participants are at the forefront of a rapidly evolving field, poised to make significant contributions to the intersection of differential equations and neural network methodologies. Furthermore, it is a common misconception in the AI community that Physics-Informed Neural Networks and Neural Ordinary Differential Equations achieve the same goal and the difference between adjusting a differential equation to data (Neural Ordinary Differential Equations) and adjusting a differential equation’s solution to data (Physics-Informed Neural Networks) is not clear.
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In which scenarios can these architectures be applied? Engineering and science problems such as fluid mechanics, chemistry, physics and population growth dynamics.