Logical Constraint Regularization Algorithms For Physics-Informed Deep Learning
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This article highlights various methods for physics-informed neural networks, including constraint regularization, multi-objective optimization, and the use of adaptive weighting mechanisms. It describes many approaches to physics-informed neural networks, such as constraint regularization, multi-objective optimization, and adaptive weighting mechanisms.Abstract
The physics-informed neural network (PINN) paradigm has been developed to add domain knowledge into deep learning models to tackle partial differential equations (PDEs) and inverse problems. Setting these physical parameters during training, however, is still a major challenge and often results in suboptimal convergence and less accurate solutions to the complex nonlinear systems. In this paper, research propose a new family of Logical Constraint Regularization (LCR) algorithms that incorporate physics-based regularization terms in an adaptive, systematic manner. The proposed approach is formulated as a multi-objective optimization problem, and it uses hierarchical constraint ordering to enhance convergence rate and solution quality. The results are presented with experimental validation for canonical problems such as Burger’s equation, Navier-Stokes equations and inverse problems, showing great improvements in prediction accuracy (up to 87.3% relative error reduction) and computational efficiency (40% reduction in convergence time). The method yields a mean absolute percentage error (MAPE) of 2.14% on test datasets, which is significantly better than the baseline PINN implementation. The results show that logical constraint regularization is a general regularization framework which can be applied to a wide range of physical systems and it is a useful addition to scientific machine learning.
