Constructing Physics-Informed Neural Networks with Architecture Based on Analytical Modification of Numerical Methods by Solving the Problem of Modelling Processes in a Chemical Reactor.

A novel type of neural network with an architecture based on physics is proposed. The network structure builds on a body of analytical modifications of classical numerical methods. A feature of the constructed neural networks is defining parameters of the governing equations as trainable parameters. Constructing the network is carried out in three stages. In the first step, a neural network solution to an equation corresponding to a numerical scheme is constructed. It allows for forming an initial low-fidelity neural network solution to the original problem. At the second stage, the network with physics-based architecture (PBA) is further trained to solve the differential equation by minimising the loss function, as is typical in works devoted to physics-informed neural networks (PINNs). In the third stage, the physics-informed neural network with architecture based on physics (PBA-PINN) is trained on high-fidelity sensor data, parameters are identified, or another task of interest is solved. This approach makes it possible to solve insufficiently studied PINN problems: selecting neural network architecture and successfully initialising network weights corresponding to the problem being solved that ensure rapid convergence to the loss function minimum. It is advisable to use the devised PBA-PINNs in the problems of surrogate modelling and modelling real objects with multi-fidelity data. The effectiveness of the approach proposed is demonstrated using the problem of modelling processes in a chemical reactor. Experiments show that subsequent retraining of the initial low-fidelity PBA model based on a few high-accuracy data leads to the achievement of relatively high accuracy.

Intelligent LED Certification System in Mass Production.

It is impossible to effectively use light-emitting diodes (LEDs) in medicine and telecommunication systems without knowing their main characteristics, the most important of them being efficiency. Reliable measurement of LED efficiency holds particular significance for mass production automation. The method for measuring LED efficiency consists in comparing two cooling curves of the LED crystal obtained after exposure to short current pulses of positive and negative polarities. The measurement results are adversely affected by noise in the electrical measuring circuit. The widely used instrumental noise suppression filters, as well as classical digital infinite impulse response (IIR), finite impulse response (FIR) filters, and adaptive filters fail to yield satisfactory results. Unlike adaptive filters, blind methods do not require a special reference signal, which makes them more promising for removing noise and reconstructing the waveform when measuring the efficiency of LEDs. The article suggests a method for sequential blind signal extraction based on a cascading neural network. Statistical analysis of signal and noise values has revealed that the signal and the noise have different forms of the probability density function (PDF). Therefore, it is preferable to use high-order statistical moments characterizing the shape of the PDF for signal extraction. Generalized statistical moments were used as an objective function for optimization of neural network parameters, namely, generalized skewness and generalized kurtosis. The order of the generalized moments was chosen according to the criterion of the maximum Mahalanobis distance. The proposed method has made it possible to implement a multi-temporal comparison of the crystal cooling curves for measuring LED efficiency.