From Theory to Practice: Neural Operators Transforming Acoustics

18 Jul 24 08:00 UTC

AI techniques are fundamentally transforming the field of simulation by combining physics-based modeling with data-driven machine learning.

Jakob is a Junior AI Researcher at TransferLab and a student of computational science and engineering at the Technical University of Munich (TUM). With a foundation in mechanical engineering from his undergraduate studies, Jakob has evolved into a computational scientist and engineer, driven by his passion for computer and data-driven approaches, especially physics-informed machine learning. Currently, Jakob is finishing his studies and submitted his thesis on “Physics-Informed Neural Operators with Applications to Sonic Crystals” at TUM in collaboration with the appliedAI Institute for Europe. His goal is to make research in this field accessible and practical for both researches and industry professionals, ensuring that cutting-edge advancements can be effectively utilized in real-world applications.

Jakob Wagner, Junior AI Researcher at the appliedAI Institute for Europe, will talk about the topic of his Master’s thesis, conducted in collaboration with TUM, on applying neural operators to real-world acoustic problems.

Abstract

This seminar deals with the application of neural operators to real-world problems. We will explore the broad field of neural operators (integrating past seminars into a broader picture), showcase the Continuiti framework for fast and elegant implementation of neural operators, and explore how these techniques can be applied in acoustics. In acoustics, solving inverse problems or optimizing meta-materials are tasks often too expensive using conventional approaches. Two examples, a pulsating sphere and so-called sonic crystals will be examined to showcase their capabilities in this area of research.

continuiti: Learning Function Operators with Neural Networks

continuiti is a Python package for machine learning on function operators. It implements various neural operator architectures (e.g., DeepONets), physics-informed loss functions, and a collection of examples and benchmarks.

References

[Kov23N]

Neural Operator: Learning Maps Between Function Spaces With Applications to PDEs, Nikola Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar.

2023

The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks to learn operators, termed neural operators, that map between infinite dimensional function spaces. We formulate the neural operator as a composition of linear integral operators and nonlinear activation …

[Lu21L]

Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators, Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, George Em Karniadakis.

Mar 2021

It is widely known that neural networks (NNs) are universal approximators of continuous functions. However, a less known but powerful result is that a NN with a single hidden layer can accurately approximate any nonlinear continuous operator. This universal approximation theorem of operators is suggestive of the structure and potential of deep neural networks (DNNs) in learning continuous …

[Elf11M]

Matryoshka locally resonant sonic crystal, Daniel P. Elford, Luke Chalmers, Feodor V. Kusmartsev, Gerry M. Swallowe.

Nov 2011

The results of numerical modeling of sonic crystals with resonant array elements are reported. The investigated resonant elements include plain slotted cylinders as well as their various combinations, in particular, Russian doll or Matryoshka configurations. The acoustic band structure and transmission characteristics of such systems have been computed with the use of finite element methods. The …

Publication

Abstract

continuiti is a Python package for machine learning on function operators. It implements various neural operator architectures (e.g., DeepONets), physics-informed loss functions, and a collection of examples and benchmarks.

References

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