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What knowledge will be conveyed? Foundational understanding of DEs and numerical methods, and their role in modelling real-world systems. Introduction and hands-on of two foundational architectures, PINNs, Neural Operators and Neural ODEs and their respective official libraries. Clarification of the common misconception that PINNs (and Neural Operators) and Neural ODEs are two architectures that achieve the same goal.
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What techniques/methods, concepts, or modelling frameworks will be conveyed? Basic theory of DEs and numerical methods; PINNs, Neural Operators, DeepXDE and Neural Operators library, Neural ODEs, Torchdiffeq library, When to use PINNs, Neural Operators and Neural ODEs.
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Why is the topic innovative/relevant? The integration of DEs with NNs 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 PINNs, Neural Operators and Neural ODEs. 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 PINNs, Neural Operators and Neural ODEs achieve the same goal and the difference between adjusting a DE to data (Neural ODEs) and adjusting a DE’s solution to data (PINNs, Neural Operators) 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.