As AI for Science continues to grow, Physics-informed neural networks (PINNs) have emerged as a transformative approach within the realm of scientific computing and deep learning, offering a robust and flexible framework for solving partial differential equations (PDEs) and other complex physical systems. By embedding physical laws directly into the architecture of neural networks, PINNs enable the integration of domain-specific knowledge, ensuring that the models adhere to known physics while fitting available data. In this paper, we provide a comprehensive overview of the state-of-the-art advancements and applications of PINNs across a broad spectrum of PDE problems. In particular, focus is given on the PINN architectures, data resampling methods for PINN, loss and activation functions, feature embedding methods and so on. What’s more, the potential future directions and the anticipated evolution of PINNs are also discussed. We aim to provide valuable insights into PINNs for PDE problems, with hope to encourage further exploration and research in this promising area.

A compact millimeter-wave (MMW) sensor has been developed for remote monitoring of human vital signs (heart and respiration rate). The low-power homodyne transceiver operating at 94 GHz was assembled by using solid-state active and passive block-type components and can be battery operated. A description of the MMW system front end and the back-end acquisition hardware and software is presented. Representative test case results on the application of various signal processing and data analysis algorithms developed to extract faint physiological signals of interest in presence of strong background interference are provided. Although the laboratory experiments so far have been limited to standoff distances of up to 15 m, the upper limit of the detection range is expected to be higher. In comparison with its microwave counterparts, the MMW system described here provides higher directivity, increased sensitivity, and longer detection range for measuring subtle mechanical displacements associated with heart and respiration functions. The system may be adapted for use in a wide range of standoff sensing applications including for patient health care, structural health monitoring, nondestructive testing, biometric sensing, and remote vibrometry in general.

Wireless inductive sensors have been deployed in the position and displacement sensing for a wide variety of applications ranging from manufacturing processes, medical systems, automotive and aerospace industries, to civil infrastructures. Here, we propose and experimentally demonstrate an ultrasensitive wireless displacement sensing technique based on the concept of parity-time (PT)-symmetry or space-time reflection symmetry, first explored in quantum mechanics and later extended to wave physics. This PT-symmetric telemetric sensing system comprises an active –RLC tank (stationary reader) and a passive RLC tank (movable tag), which are linked in a wireless manner via inductive coupling. Specifically, such a non-Hermitian electronic system obeying the PT-symmetry, when operated around the exceptional point (EP), can achieve drastic frequency responses and high sensitivity, well beyond the limit of conventional fully-passive wireless displacement sensors. The proposed telemetric sensing system shows great potential for contactless, high-precision measurement of displacement, lift-off distance, position, and vibration, particularly suitable for emerging industrial and healthcare internet-of-things (IoTs).

Passive millimeter-wave (PMMW) imagers using a single radiometer, called single pixel imagers, employ raster scanning to produce images. A serious drawback of such a single pixel imaging system is the long acquisition time needed to produce a high-fidelity image, arising from two factors: (a) the time to scan the whole scene pixel by pixel and (b) the integration time for each pixel to achieve adequate signal to noise ratio. Recently, compressive sensing (CS) has been developed for single-pixel optical cameras to significantly reduce the imaging time and at the same time produce high-fidelity images by exploiting the sparsity of the data in some transform domain. While the efficacy of CS has been established for single-pixel optical systems, its application to PMMW imaging is not straightforward due to its (a) longer wavelength by three to four orders of magnitude that suffers high diffraction losses at finite size spatial waveform modulators and (b) weaker radiation intensity, for example, by eight orders of magnitude less than that of infrared. We present the development and implementation of a CS technique for PMMW imagers and shows a factor-of-ten increase in imaging speed.

This paper analyzes heart rate (HR) information from physiological tracings collected with a remote millimeter wave (mmW) I-Q sensor for biometric monitoring applications. A parameter optimization method based on the nonlinear Levenberg-Marquardt algorithm is used. The mmW sensor works at 94 GHz and can detect the vital signs of a human subject from a few to tens of meters away. The reflected mmW signal is typically affected by respiration, body movement, background noise, and electronic system noise. Processing of the mmW radar signal is, thus, necessary to obtain the true HR. The down-converted received signal in this case consists of both the real part (I-branch) and the imaginary part (Q-branch), which can be considered as the cosine and sine of the received phase of the HR signal. Instead of fitting the converted phase angle signal, the method directly fits the real and imaginary parts of the HR signal, which circumvents the need for phase unwrapping. This is particularly useful when the SNR is low. Also, the method identifies both beat-to-beat HR and individual heartbeat magnitude, which is valuable for some medical diagnosis applications. The mean HR here is compared to that obtained using the discrete Fourier transform.