Search for: All records

The inception of physics-constrained or physics-informed machine learning represents a paradigm shift, addressing the challenges associated with data scarcity and enhancing model interpretability. This innovative approach incorporates the fundamental laws of physics as constraints, guiding the training process of machine learning models. In this work, the physics-constrained convolutional recurrent neural network is further extended for solving spatial-temporal partial differential equations with arbitrary boundary conditions. Two notable advancements are introduced: the implementation of boundary conditions as soft constraints through finite difference-based differentiation, and the establishment of an adaptive weighting mechanism for the optimal allocation of weights to various losses. These enhancements significantly augment the network's ability to manage intricate boundary conditions and expedite the training process. The efficacy of the proposed model is validated through its application to two-dimensional phase transition, fluid dynamics, and reaction-diffusion problems, which are pivotal in materials modeling. Compared to traditional physics-constrained neural networks, the physics-constrained convolutional recurrent neural network demonstrates a tenfold increase in prediction accuracy within a similar computational budget. Moreover, the model's exceptional performance in extrapolating solutions for the Burgers' equation underscores its utility. Therefore, this research establishes the physics-constrained recurrent neural network as a viable surrogate model for sophisticated spatial-temporal PDE systems, particularly beneficial in scenarios plagued by sparse and noisy datasets. 

Compressed sensing (CS) as a new data acquisition technique has been applied to monitor manufacturing processes. With a few measurements, sparse coefficient vectors can be recovered by solving an inverse problem and original signals can be reconstructed. Dictionary learning methods have been developed and applied in combination with CS to improve the sparsity level of the recovered coefficient vectors. In this work, a physics-constrained dictionary learning approach is proposed to solve both of reconstruction and classification problems by optimizing measurement, basis, and classification matrices simultaneously with the considerations of the application-specific restrictions. It is applied in image acquisitions in selective laser melting (SLM). The proposed approach includes the optimization in two steps. In the first stage, with the basis matrix fixed, the measurement matrix is optimized by determining the pixel locations for sampling in each image. The optimized measurement matrix only includes one non-zero entry in each row. The optimization of pixel locations is solved based on a constrained FrameSense algorithm. In the second stage, with the measurement matrix fixed, the basis and classification matrices are optimized based on the K-SVD algorithm. With the optimized basis matrix, the coefficient vector can be recovered with CS. The original signal can be reconstructed by the linear combination of the basis matrix and the recovered coefficient vector. The original signal can also be classified to identify different machine states by the linear combination of the classification matrix and the coefficient vector.