Physics-informed ConvNet: Learning Physical Field from a Shallow Neural Network
This addresses the problem of improving generalization in physics-informed machine learning for researchers and engineers dealing with noisy, scarce data in physical systems, though it appears incremental as a shallow alternative to existing deep PINN methods.
The paper tackles the challenge of modeling multi-physical systems with data scarcity by proposing a shallow physics-informed convolutional network (PICN) that generates physical fields using a deconvolution layer and single convolution layer. The method demonstrates effectiveness in solving nonlinear physical operator equations and recovering information from noisy observations, showing potential for approximating multi-frequency physical fields.
Big-data-based artificial intelligence (AI) supports profound evolution in almost all of science and technology. However, modeling and forecasting multi-physical systems remain a challenge due to unavoidable data scarcity and noise. Improving the generalization ability of neural networks by "teaching" domain knowledge and developing a new generation of models combined with the physical laws have become promising areas of machine learning research. Different from "deep" fully-connected neural networks embedded with physical information (PINN), a novel shallow framework named physics-informed convolutional network (PICN) is recommended from a CNN perspective, in which the physical field is generated by a deconvolution layer and a single convolution layer. The difference fields forming the physical operator are constructed using the pre-trained shallow convolution layer. An efficient linear interpolation network calculates the loss function involving boundary conditions and the physical constraints in irregular geometry domains. The effectiveness of the current development is illustrated through some numerical cases involving the solving (and estimation) of nonlinear physical operator equations and recovering physical information from noisy observations. Its potential advantage in approximating physical fields with multi-frequency components indicates that PICN may become an alternative neural network solver in physics-informed machine learning.