Deep learning

Transfer of learning

Operator (biology)

Multi-task learning

Mathematics

Reproducing kernel Hilbert space

Transcription factor

Partial differential equation

Gene

Statistics

Machine learning

Mathematical analysis

Artificial intelligence

Management

Repressor

Economics

Chemistry

Computer science

Conditional probability distribution

Task (project management)

Embedding

Biochemistry

Hilbert space

Nature Machine Intelligence

Transfer learning enables the transfer of knowledge gained while learning to perform one task (source) to a related but different task (target), hence addressing the expense of data acquisition and labelling, potential computational power limitations and dataset distribution mismatches. We propose a new transfer learning framework for task-specific learning (functional regression in partial differential equations) under conditional shift based on the deep operator network (DeepONet). Task-specific operator learning is accomplished by fine-tuning task-specific layers of the target DeepONet using a hybrid loss function that allows for the matching of individual target samples while also preserving the global properties of the conditional distribution of the target data. Inspired by conditional embedding operator theory, we minimize the statistical distance between labelled target data and the surrogate prediction on unlabelled target data by embedding conditional distributions onto a reproducing kernel Hilbert space. We demonstrate the advantages of our approach for various transfer learning scenarios involving nonlinear partial differential equations under diverse conditions due to shifts in the geometric domain and model dynamics. Our transfer learning framework enables fast and efficient learning of heterogeneous tasks despite considerable differences between the source and target domains. A promising area for deep learning is in modelling complex physical processes described by partial differential equations (PDEs), which is computationally expensive for conventional approaches. An operator learning approach called DeepONet was recently introduced to tackle PDE-related problems, and in new work, this approach is extended with transfer learning, which transfers knowledge obtained from learning to perform one task to a related but different task.

Deep transfer operator learning for partial differential equations under conditional shift