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Neural operators have emerged as a powerful tool for learning the mapping between infinite-dimensional parameter and solution spaces of partial differential equations (PDEs). In this work, we focus on multiscale PDEs that have important applications such as reservoir modeling and turbulence prediction. We demonstrate that for such PDEs, the spectral bias towards low-frequency components presents a significant challenge for existing neural operators. To address this challenge, we propose a hierarchical attention neural operator (HANO) inspired by the hierarchical matrix approach. HANO features a scale-adaptive interaction range and self-attentions over a hierarchy of levels, enabling nested feature computation with controllable linear cost and encoding/decoding of multiscale solution space. We also incorporate an empirical H 1 loss function to enhance the learning of high-frequency components. Our numerical experiments demonstrate that HANO outperforms state-of-the-art (SOTA) methods for representative multiscale problems. [ABSTRACT FROM AUTHOR]

• An extended modal approach is proposed for OMA under the harmonic excitations. • The extended modal matrix is identified using PSDT method. • The extended modal responses (EMRs) are acquired using least squares reconstruction method. • The spurious mode can be screened according to EDF of reconstructed EMR. • The approach is validated numerically and experimentally. The existing operational modal analysis (OMA) methods for the structure subjected to white noise and harmonic combined excitations have some limitations such as easy misjudgment of true and spurious modes and slow identification speed. Through expressing the system response with the extended modal matrix (EMM) and the extended modal response (EMR) vector, a novel operational modal parameter identification approach called the extended modal approach is proposed to obtain structural true modes under the existence of multiple harmonic excitations. The EMRs consist of the true modal responses and the spurious modal responses, and each of the former is random while each of the latter is harmonic. It is also proved theoretically that the EMM can be identified using the power spectrum density transmissibility (PSDT) method. Therefore, the extended modal approach includes three steps: (1) Using the PSDT to identify the EMM; (2) Utilizing the least squares reconstruction method to obtain the EMRs from the underdetermined extended modal equation; (3) Judging each of the EMRs to be true or spurious according to its empirical density function. Structural true modes can be ultimately obtained by removing all spurious modes from the identified results. The new approach is numerically verified through the OMA of two multiple-degree-of-freedom systems and then experimentally verified through the OMA of a test beam. The results in numerical simulation and experiments all show that the extended modal approach can identify accurately and quickly structural true modes under multiple harmonic excitations. Besides, the approach has good robustness against noise contamination. [ABSTRACT FROM AUTHOR]

Body measurement is an important link in monitoring the growth of livestock in breeding management. Conventional measurements are notoriously difficult, unstable, stressful and time-consuming. 3D Computer vision technology has demonstrated its superiority in body size measurement and live body weight estimation because it has advantages of being both non-contact and effective. The objective of this paper was validating the use of single-frame surface point clouds to measure the body size, and develop a model to estimate the pig weight. With a limit bar not applied, a Kinect camera was fixed above the drinking area allowed multiple images of pigs to be captured at one time in a group-house. Body size parameters were extracted from back surface point clouds, and subsequently used as independent variables to build the three regression analysis models: i) stepwise regression analysis, ii) ridge regression analysis, and iii) partial least squares regression analysis. An experiment was conducted on fifty pigs in a group-house, half of which were Landrace gilts, half were Yorkshire shoats. The result of size measurement showed the mean relative absolute errors of body length, height, shoulder width were 0.7%, 1.8%, and 3.3%, respectively. Final ridge regression equation was developed with an R 2 of 0.958 and a MAE of 2.961 kg. It was concluded that the proposed methods based on Kinect v2 was shown to be accurate and reliable for body size measurement and live body mass estimation. • Novel body size measurement method based on single view Kinect without limit bar presented. • Mean relative absolute errors of body length, height, shoulder width were acceptable. • Non-contact and low-cost measurement for small-scale farms was provided. • Scheme for data collection in intelligent breeding environment provided. • Ridge regression performed well in weight estimation R 2 of 0.958 & MAE of 2.961 kg. [ABSTRACT FROM AUTHOR]

Multidimensional (coupled land use, soil properties, and topography) landscape effects on stream water nitrogen (N) are complex and scale-dependent. However, studies that identify critical buffer zones that explain large variations in riverine N, and estimate specific thresholds of multidimensional landscape patterns at the class level, result in a sudden changes in riverine N pollution, are still limited. Here, a new multidimensional landscape metric that combined land use, soil properties, and topography effects was applied to various riparian buffer zones and sub-watershed scales, and their relationships to riverine N levels were investigated. We used stream water ammonium−N, nitrate−N, and total−N concentrations datasets, from 2010 to 2017, in the nine subtropical sub-watersheds in China. The results of model selection and model averaging in ordinary least squares regressions, indicated that the riparian buffer zone with widths of 400 m, had more pronounced influence on water NH 4 –N and TN levels than at other scales. Within the 400 m buffer zone, the key landscape metrics for NH 4 –N, NO 3 –N and TN concentrations in stream water were different, and explained up to 43.35%–76.55% (adjusted R2) of the total variation in river N levels. When ENN_MN Class17 below 39–56 m, PD Class8 above 4.63–6.55 n/km2, PLAND Class27 above 23–29%, and CONTIG_MN Class42 below 0.35–0.37% within the 400 m buffer zone, riverine NH 4 –N and TN would be abruptly increased. This study provided practical ideas for regulation regarding landscape management linked to watershed structure, and identified reference thresholds for multidimensional landscape metrics, which should help reduce riverine N pollution in subtropical China. • Multidimensional landscape patterns affect riverine N at watershed outlets. • The 400 m riparian buffer zone has the strongest influence on riverine NH 4 –N and TN concentrations. • The ENN_MN Class17 , PD Class8 , PLAND Class27 , and CONTIG_MN Class42 are important metrics to characterize riverine N. • There exist change points in riverine N along a gradient of multidimensional landscape metrics. [ABSTRACT FROM AUTHOR]