This Paper Addresses the Generalization Challenge by Proposing Neural Operators for Modeling Constitutive Laws
What challenges do traditional methods face in modeling magnetic hysteresis?
Traditional methods, such as recurrent neural networks (RNNs), long short-term memory (LSTM) networks, and gated recurrent units (GRUs), struggle to generalize to novel magnetic fields in modeling magnetic hysteresis. These methods primarily achieve accuracy only for specific excitations used during training and fail to generalize to novel magnetic fields, as they cannot model mappings between functions in continuous domains, which is crucial for accurately predicting hysteresis behavior under varying conditions.
How do neural operators differ from traditional neural networks?
Neural operators differ from traditional neural networks in that they approximate the underlying operator that maps input functions to output functions, rather than learning mappings between finite-dimensional vector spaces1. This allows neural operators to generalize to novel inputs and enables them to model mappings in continuous domains, making them suitable for tasks such as predicting hysteresis behavior in varying magnetic fields.
What specific neural operators are proposed for modeling hysteresis?
The researchers propose using neural operators, specifically the Deep Operator Network (DeepONet) and Fourier Neural Operator (FNO), to model the hysteresis relationship between magnetic fields. Additionally, a rate-independent Fourier Neural Operator (RIFNO) is introduced to predict material responses at different sampling rates.