Bayesian Physics-Informed Extreme Learning Machine for Forward and Inverse PDE Problems with Noisy Data

Physics-informed extreme learning machine (PIELM) has recently received significant attention as a rapid version of physics-informed neural network (PINN) for solving partial differential equations (PDEs). The key characteristic is to fix the input layer weights with random values and use Moore-Penrose generalized inverse for the output layer weights. The framework is effective, but it easily suffers from overfitting noisy data and lacks uncertainty quantification for the solution under noise scenarios.To this end, we develop the Bayesian physics-informed extreme learning machine (BPIELM) to solve both forward and inverse linear PDE problems with noisy data in a unified framework. In our framework, a prior probability distribution is introduced in the output layer for extreme learning machine with physic laws and the Bayesian method is used to estimate the posterior of parameters. Besides, for inverse PDE problems, problem parameters considered as new output layer weights are unified in a framework with forward PDE problems. Finally, we demonstrate BPIELM considering both forward problems, including Poisson, advection, and diffusion equations, as well as inverse problems, where unknown problem parameters are estimated. The results show that, compared with PIELM, BPIELM quantifies uncertainty arising from noisy data and provides more accurate predictions. In addition, BPIELM is considerably cheaper than PINN in terms of the computational cost

Strange stars with different quark mass scalings

We investigate the stability of strange quark matter and the properties of the corresponding strange stars, within a wide range of quark mass scaling. The calculation shows that the resulting maximum mass always lies between 1.5 solor mass and 1.8 solor mass for all the scalings chosen here. Strange star sequences with a linear scaling would support less gravitational mass, and a change (increase or decrease) of the scaling around the linear scaling would lead to a larger maximum mass. Radii invariably decrease with the mass scaling. Then the larger the scaling, the faster the star might spin. In addition, the variation of the scaling would cause an order of magnitude change of the strong electric field on quark surface, which is essential to support possible crusts of strange stars against gravity and may then have some astrophysical implications.Comment: 5 pages, 6 figures, 1 table. accepted by M

Deciphering Charging Status, Absolute Quantum Efficiency, and Absorption Cross Section of MultiCarrier States in Single Colloidal Quantum Dot

Upon photo- or electrical-excitation, colloidal quantum dots (QDs) are often found in multi-carrier states due to multi-photon absorption and photo-charging of the QDs. While many of these multi-carrier states are observed in single-dot spectroscopy, their properties are not well studied due to random charging/discharging, emission intensity intermittency, and uncontrolled surface defects of single QD. Here we report in-situ deciphering the charging status, and precisely assessing the absorption cross section, and determining the absolute emission quantum yield of mono-exciton and biexciton states for neutral, positively-charged, and negatively-charged single core/shell CdSe/CdS QD. We uncover very different photon statistics of the three charge states in single QD and unambiguously identify their charge sign together with the information of their photoluminescence decay dynamics. We then show their distinct photoluminescence saturation behaviors and evaluated the absolute values of absorption cross sections and quantum efficiencies of monoexcitons and biexcitons. We demonstrate that addition of an extra hole or electron in a QD changes not only its emission properties but also varies its absorption cross section

Experimental verification on applying indirect inverse substructuring analysis to identify coupling dynamic stiffness of mechanical assembly via planar surface

To broaden the engineering application of inverse substructuring analysis, the mechanical assembly via planar surface is experimentally studied. Specifically, the first and the second schemes of indirect inverse substructuring analysis are applied to identify the coupling dynamic stiffness of the assembly. The experimental model of the assembly is designed, and the surface is then discretized equivalently into point-to-point connections for testing the frequency response functions (FRFs) involved in the schemes. Experimental results show that, applying both of the schemes are feasible for the identification, and the identified stiffnesses approach to be stable as the number of discretized points increases