Operator Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations Characterized by Sharp Solutions

Physics-informed Neural Networks (PINNs) have been shown as a promising approach for solving both forward and inverse problems of partial differential equations (PDEs). Meanwhile, the neural operator approach, including methods such as Deep Operator Network (DeepONet) and Fourier neural operator (FNO), has been introduced and extensively employed in approximating solution of PDEs. Nevertheless, to solve problems consisting of sharp solutions poses a significant challenge when employing these two approaches. To address this issue, we propose in this work a novel framework termed Operator Learning Enhanced Physics-informed Neural Networks (OL-PINN). Initially, we utilize DeepONet to learn the solution operator for a set of smooth problems relevant to the PDEs characterized by sharp solutions. Subsequently, we integrate the pre-trained DeepONet with PINN to resolve the target sharp solution problem. We showcase the efficacy of OL-PINN by successfully addressing various problems, such as the nonlinear diffusion-reaction equation, the Burgers equation and the incompressible Navier-Stokes equation at high Reynolds number. Compared with the vanilla PINN, the proposed method requires only a small number of residual points to achieve a strong generalization capability. Moreover, it substantially enhances accuracy, while also ensuring a robust training process. Furthermore, OL-PINN inherits the advantage of PINN for solving inverse problems. To this end, we apply the OL-PINN approach for solving problems with only partial boundary conditions, which usually cannot be solved by the classical numerical methods, showing its capacity in solving ill-posed problems and consequently more complex inverse problems.Comment: Preprint submitted to Elsevie

Neutron powder diffraction study on the iron-based nitride superconductor ThFeAsN

We report neutron diffraction and transport results on the newly discovered superconducting nitride ThFeAsN with $T_c=$ 30 K. No magnetic transition, but a weak structural distortion around 160 K, is observed cooling from 300 K to 6 K. Analysis on the resistivity, Hall transport and crystal structure suggests this material behaves as an electron optimally doped pnictide superconductors due to extra electrons from nitrogen deficiency or oxygen occupancy at the nitrogen site, which together with the low arsenic height may enhance the electron itinerancy and reduce the electron correlations, thus suppress the static magnetic order.Comment: 4 pages, 4 figures, Accepted by EP

Corporate sustainability policies and corporate investment efficiency: Evidence from the quasi-natural experiment in China

This paper studies the impact of green disclosure on firm investment efficiency, leveraging a policy experiment in China. Since 2012, the Chinese government has begun to implement the Ambient Air Quality Standards (AQS), which have strengthened the requirements for green disclosure throughout the country. We exploit the rollout of the AQS and find that tightening the green disclosure requirements significantly increases corporate investment efficiency. This increase is primarily driven by a reduction in underinvestment among non-state-owned firms and firms with low institutional ownership. Further analysis suggests that the alleviation of agency problems and the reduction of financial constraints are the two main mechanisms through which green disclosure influences firm investment efficiency. Our findings provide valuable policy implications, indicating that strengthening green disclosure standards can have a substantial positive impact on firm investment outcomes

Mechanism for Selective Binding of Aromatic Compounds on Oxygen-Rich Graphene Nanosheets Based on Molecule Size/Polarity Matching

Selective binding of organic compounds is the cornerstone of many important industrial and pharmaceutical applications. Here, we achieved highly selective binding of aromatic compounds in aqueous solution and gas phase by oxygen-enriched graphene oxide (GO) nanosheets via a previously unknown mechanism based on size matching and polarity matching. Oxygen-containing functional groups (predominately epoxies and hydroxyls) on the nongraphitized aliphatic carbons of the basal plane of GO formed highly polar regions that encompass graphitic regions slightly larger than the benzene ring. This facilitated size match–based interactions between small apolar compounds and the isolated aromatic region of GO, resulting in high binding selectivity relative to larger apolar compounds. The interactions between the functional group(s) of polar aromatics and the epoxy/hydroxyl groups around the isolated aromatic region of GO enhanced binding selectivity relative to similar-sized apolar aromatics. These findings provide opportunities for precision separations and molecular recognition enabled by size/polarity match–based selectivity

Integrating optical imaging techniques for a novel approach to evaluate Siberian wild rye seed maturity

Advances in optical imaging technology using rapid and non-destructive methods have led to improvements in the efficiency of seed quality detection. Accurately timing the harvest is crucial for maximizing the yield of higher-quality Siberian wild rye seeds by minimizing excessive shattering during harvesting. This research applied integrated optical imaging techniques and machine learning algorithms to develop different models for classifying Siberian wild rye seeds based on different maturity stages and grain positions. The multi-source fusion of morphological, multispectral, and autofluorescence data provided more comprehensive information but also increases the performance requirements of the equipment. Therefore, we employed three filtering algorithms, namely minimal joint mutual information maximization (JMIM), information gain, and Gini impurity, and set up two control methods (feature union and no-filtering) to assess the impact of retaining only 20% of the features on the model performance. Both JMIM and information gain revealed autofluorescence and morphological features (CIELab A, CIELab B, hue and saturation), with these two filtering algorithms showing shorter run times. Furthermore, a strong correlation was observed between shoot length and morphological and autofluorescence spectral features. Machine learning models based on linear discriminant analysis (LDA), random forests (RF) and support vector machines (SVM) showed high performance (>0.78 accuracies) in classifying seeds at different maturity stages. Furthermore, it was found that there was considerable variation in the different grain positions at the maturity stage, and the K-means approach was used to improve the model performance by 5.8%-9.24%. In conclusion, our study demonstrated that feature filtering algorithms combined with machine learning algorithms offer high performance and low cost in identifying seed maturity stages and that the application of k-means techniques for inconsistent maturity improves classification accuracy. Therefore, this technique could be employed classification of seed maturity and superior physiological quality for Siberian wild rye seeds

Observation of nonrelativistic plaid-like spin splitting in a noncoplanar antiferromagnet

Spatial, momentum and energy separation of electronic spins in condensed matter systems guides the development of novel devices where spin-polarized current is generated and manipulated. Recent attention on a set of previously overlooked symmetry operations in magnetic materials leads to the emergence of a new type of spin splitting besides the well-studied Zeeman, Rashba and Dresselhaus effects, enabling giant and momentum dependent spin polarization of energy bands on selected antiferromagnets independent of relativistic spin-orbit interaction. Despite the ever-growing theoretical predictions, the direct spectroscopic proof of such spin splitting is still lacking. Here, we provide solid spectroscopic and computational evidence for the existence of such materials. In the noncoplanar antiferromagnet MnTe$_2$, the in-plane components of spin are found to be antisymmetric about the high-symmetry planes of the Brillouin zone, comprising a plaid-like spin texture in the antiferromagnetic ground state. Such an unconventional spin pattern, further found to diminish at the high-temperature paramagnetic state, stems from the intrinsic antiferromagnetic order instead of the relativistic spin-orbit coupling. Our finding demonstrates a new type of spin-momentum locking with a nonrelativistic origin, placing antiferromagnetic spintronics on a firm basis and paving the way for studying exotic quantum phenomena in related materials.Comment: Version 2, 30 pages, 4 main figures and 8 supporting figure

Transient obscuration event captured in NGC~3227 II. Warm absorbers and obscuration events in archival XMM-Newton and NuSTAR observations

© The European Southern Observatory (ESO). This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1051/0004-6361/202141599The relationship between warm absorber (WA) outflows of active galactic nuclei and nuclear obscuration activities caused by optically thick clouds (obscurers) crossing the line of sight is still unclear. NGC 3227 is a suitable target for studying the properties of both WAs and obscurers because it matches the following selection criteria: WAs in both ultraviolet (UV) and X-rays, suitably variable, bright in UV and X-rays, and adequate archival spectra for making comparisons with the obscured spectra. In the aim of investigating WAs and obscurers of NGC 3227 in detail, we used a broadband spectral-energy-distribution model that is built in findings of the first paper in our series together with the photoionization code of SPEX software to fit the archival observational data taken by XMM-Newton and NuSTAR in 2006 and 2016. Using unobscured observations, we find four WA components with different ionization states (loga ζ [erg cm s -1] ∼-1.0, 2.0, 2.5, 3.0). The highest-ionization WA component has a much higher hydrogen column density (∼10 22 cm -2) than the other three components (∼10 21 cm -2). The outflow velocities of these WAs range from 100 to 1300 km s -1, and show a positive correlation with the ionization parameter. These WA components are estimated to be distributed from the outer region of the broad line region (BLR) to the narrow line region. It is worth noting that we find an X-ray obscuration event in the beginning of the 2006 observation, which was missed by previous studies. We find that it can be explained by a single obscurer component. We also study the previously published obscuration event captured in one observation in 2016, which needs two obscurer components to fit the spectrum. A high-ionization obscurer component (loga ζa ∼a 2.80; covering factor C f a ∼a 30%) only appears in the 2016 observation, which has a high column density (∼10 23 cm -2). A low-ionization obscurer component (loga ζa ∼a 1.0a -a 1.9; C f a ∼a 20%-50%) exists in both 2006 and 2016 observations, which has a lower column density (∼10 22 cm -2). These obscurer components are estimated to reside within the BLR by their crossing time of transverse motions. The obscurers of NGC 3227 are closer to the center and have larger number densities than the WAs, which indicate that the WAs and obscurers might have different origins.Peer reviewe