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Climate change has exacerbated water stress and water‐related disasters, necessitating more precise streamflow simulations. However, in the majority of global regions, a deficiency of streamflow data constitutes a significant constraint on modeling endeavors. Traditional distributed hydrological models and regionalization approaches have shown suboptimal performance. While current deep learning (DL)‐related models trained on large data sets excel in spatial generalization, the direct applicability of these models in certain regions with unique hydrological processes can be challenging due to the limited representativeness within the training data set. Furthermore, transfer learning DL models pre‐trained on large data sets still necessitate local data for retraining, thereby constraining their applicability. To address these challenges, we present a physics‐informed DL model based on a distributed framework. It involves spatial discretization and the establishment of differentiable hydrological models for discrete sub‐basins, coupled with a differentiable Muskingum method for channel routing. By introducing upstream‐downstream relationships, model errors in sub‐basins propagate through the river network to the watershed outlet, enabling the optimization using limited downstream streamflow data, thereby achieving spatial simulation of ungauged internal sub‐basins. The model, when trained solely on the downstream‐most station, outperforms the distributed hydrological model in streamflow simulation at both the training station and upstream held‐out stations. Additionally, in comparison to transfer learning models, our model requires fewer gauge stations for training, but achieves higher precision in simulating streamflow on spatially held‐out stations, indicating better spatial generalization ability. Consequently, this model offers a novel approach to hydrological simulation in data‐scarce regions, especially those with poor hydrological representativeness. Plain Language Summary Climate change leads to more water shortages and disasters, requiring better streamflow predictions. Yet, a big hurdle in dealing with this issue is the lack of streamflow data across many parts of the world. Traditional physics‐based distributed hydrological models and current deep learning (DL) models have their limitations, especially for regions with unique hydrological processes and limited observations. To address these challenges, we developed a new tool combining physics‐informed DL and a traditional river routing model based on the distributed framework. The model divides the region into sub‐basins, where a physics‐informed DL rainfall‐runoff model calculates runoff generation, and a physics‐informed DL routing model computes the movement of water within each subunit toward the river. Model errors propagate downstream through the river network, thus requiring only a small amount of downstream data to optimize all sub‐basin models and effectively simulate internal unmonitored sub‐basins. When solely using the downstream‐most discharge stations for training, our model outperforms the traditional physics‐based distributed hydrological model. In addition, our approach requires less training data than transfer learning, while achieving higher spatial generalization accuracy. In summary, our model provides a new way to simulate streamflow in data‐scarce regions with unique processes. Key Points A distributed physics‐informed deep learning hydrological model was proposed for data‐scarce regions The new model outperforms the traditional distributed hydrologic model in simulating streamflow in upstream held‐out stations Our model requires less data for training but performs better than the transfer learning model in spatial generalization

Simulation-based engineering has been a major protagonist of the technology of the last century. However, models based on well established physics fail sometimes to describe the observed reality. They often exhibit noticeable differences between physics-based model predictions and measurements. This difference is due to several reasons: practical (uncertainty and variability of the parameters involved in the models) and epistemic (the models themselves are in many cases a crude approximation of a rich reality). On the other side, approaching the reality from experimental data represents a valuable approach because of its generality. However, this approach embraces many difficulties: model and experimental variability; the need of a large number of measurements to accurately represent rich solutions (extremely nonlinear or fluctuating), the associate cost and technical difficulties to perform them; and finally, the difficulty to explain and certify, both constituting key aspects in most engineering applications. This work overviews some of the most remarkable progress in the field in recent years.

Recently, rainfall‐runoff simulations in small headwater basins have been improved by methodological advances such as deep neural networks (NNs) and hybrid physics‐NN models—particularly, a genre called differentiable modeling that intermingles NNs with physics to learn relationships between variables. However, hydrologic routing simulations, necessary for simulating floods in stem rivers downstream of large heterogeneous basins, had not yet benefited from these advances and it was unclear if the routing process could be improved via coupled NNs. We present a novel differentiable routing method (δMC‐Juniata‐hydroDL2) that mimics the classical Muskingum‐Cunge routing model over a river network but embeds an NN to infer parameterizations for Manning's roughness (n) and channel geometries from raw reach‐scale attributes like catchment areas and sinuosity. The NN was trained solely on downstream hydrographs. Synthetic experiments show that while the channel geometry parameter was unidentifiable, n can be identified with moderate precision. With real‐world data, the trained differentiable routing model produced more accurate long‐term routing results for both the training gage and untrained inner gages for larger subbasins (>2,000 km2) than either a machine learning model assuming homogeneity, or simply using the sum of runoff from subbasins. The n parameterization trained on short periods gave high performance in other periods, despite significant errors in runoff inputs. The learned n pattern was consistent with literature expectations, demonstrating the framework's potential for knowledge discovery, but the absolute values can vary depending on training periods. The trained n parameterization can be coupled with traditional models to improve national‐scale hydrologic flood simulations. Key Points A novel differentiable routing model can learn effective river routing parameterization, recovering channel roughness in synthetic runs With short periods of real training data, we can improve streamflow in large rivers compared to models not considering routing For basins >2,000 km2, our framework outperformed deep learning models that assume homogeneity, despite bias in the runoff forcings

This paper presents a novel physics‐informed neural network (PINN) approach for developing pedotransfer functions (PTFs) to predict continuous soil water retention curves (SWRCs) based on soil textural fractions, organic carbon content, and bulk density. In contrast to conventional parametric PTFs developed for specific SWRC models, the PINN learns a non‐specific form of the SWRC from both measurements and physical constraints imposed during the training process. This approach allows the estimated SWRC to maintain its physical integrity from saturation to oven‐dry conditions, even in scenarios with sparse data. The new approach is particularly effective for tackling the challenges encountered in developing PTFs on large SWRC data sets, which often have an imbalance toward the wet‐end (pF≤4.2$pF\\mathit{\\le }4.2$ ) and include numerous samples with limited and unevenly distributed measurements, many of which do not meet the requirements to fit traditional SWRC models. We compared the performance of the PINN with that of a conventional physics‐agnostic neural network using a data set of 4,200 soil samples. While both networks performed similarly at the wet‐end where data are abundant, with RMSE values of around 0.041 m3 m−3, the PINN excelled at the dry‐end (pF>4.2$pF > 4.2$ ) where data are sparse and unevenly distributed, achieving a normalized RMSE of 0.172 (RMSE = 0.0045 m3 m−3) compared to a normalized RMSE of 0.522 (RMSE = 0.0136 m3 m−3) for the conventional neural network. The SWRC derived from the PINN is differentiable with respect to matric potential, making it well‐suited for integration into models of water flow in the unsaturated zone. Key Points A novel physics‐informed machine learning method for developing continuous soil pedotransfer functions is introduced The method is suitable for data sets of SWRC with imbalanced and incomplete wet and dry measurements The SWRC derived from PINN is differentiable with respect to matric potential and can be integrated into numerical algorithms

Recently, a hybrid framework combining machine learning (ML) and process‐based equations, termed differentiable modeling, has shown comparable accuracy to pure ML models while offering enhanced interpretability and spatial generalizability. However, it remained unclear how well hybrid models generalize to extreme floods outside of the range of training data, and whether optimizing models for extreme events jeopardizes spatial generalizability and the physical significance of internal variables. Here we evaluated multiple versions of a differentiable model (δHBV1.0 and δHBV1.1p) for predicting unseen extreme events, and benchmarked them against a widely‐applied long short‐term memory (LSTM) network on the CAMELS data set. We found that both δHBV and LSTM models performed well, with δHBV1.1p outperforming LSTM for events with a return period of 5 years or more. This advantage was more pronounced as the return period increased (0.06 higher median Nash‐Sutcliffe efficiency and lower peak flow errors for 80% of the 50‐year or rarer events). Loss function choice had a larger impact on δHBV1.1p than on LSTM, and we showed the proper loss led to δHBV models that further surpassed LSTM in different performance aspects. Furthermore, allowing more dynamic parameters improved the extreme metrics, had no negative impact on spatial generalization, and exerted a minimal influence on the untrained variables. We hypothesize that δHBV's mass balance and first‐order exchange terms help constrain and inform its responses to mitigate the underestimation of peaks compared to LSTM. We conclude that adopting interpretable structural priors can improve generalizability to unseen cases and thus increase model reliability to better inform stakeholder preparedness.

Elastography is a medical imaging technique used to measure the elasticity of tissues by comparing ultrasound signals before and after a light compression. The lateral resolution of ultrasound is much inferior to the axial resolution. Current elastography methods generally require both axial and lateral displacement components, making them less effective for clinical applications. Additionally, these methods often rely on the assumption of material incompressibility, which can lead to inaccurate elasticity reconstruction as no materials are truly incompressible. To address these challenges, a new physics‐informed deep‐learning method for elastography is proposed. This new method integrates a displacement network and an elasticity network to reconstruct the Young's modulus field of a heterogeneous object based on only a measured axial displacement field. It also allows for the removal of the assumption of material incompressibility, enabling the reconstruction of both Young's modulus and Poisson's ratio fields simultaneously. The authors demonstrate that using multiple measurements can mitigate the potential error introduced by the “eggshell” effect, in which the presence of stiff material prevents the generation of strain in soft material. These improvements make this new method a valuable tool for a wide range of applications in medical imaging, materials characterization, and beyond. ElastNet learns the Young's modulus field of a heterogeneous object based on a measured displacement field. The predicted stress tensor is calculated by the encoded elastic constitutive relation based on the strain and Young's modulus. The training procedure minimizes the unbalanced forces with a physical constraint and updates the predicted Young's modulus using backpropagation.

Accurate streamflow predictions are essential for water resources management. Recent studies have examined the use of hybrid models that integrate machine learning models with process‐based (PB) hydrologic models to improve streamflow predictions. Yet, there are many open questions regarding optimal hybrid model construction, especially in Mediterranean‐climate watersheds that experience pronounced wet and dry seasons. In this study, we performed model benchmarking to (a) compare hybrid model performance to PB and machine learning models and (b) examine the sensitivity of hybrid model performance to PB model parameter calibration, structural complexity, and variable selection. Hybrid models were generated by post‐processing process‐based models using Long Short‐Term Memory neural networks. Models were benchmarked within two northern California watersheds that are managed for both municipal water supplies and aquatic habitat. Though model performance varied substantially by watershed and error metric, calibrated hybrid models frequently outperformed both the machine learning model (for 72% of watershed‐model‐metric combinations) and the calibrated process‐based models (for 79% of combinations). Furthermore, hybrid models were relatively insensitive to PB model calibration and structural complexity, but sensitive to PB model variable selection. Our results demonstrate that hybrid models can improve streamflow prediction in Mediterranean‐climate watersheds. Additionally, hybrid model insensitivity to PB model parameter calibration and structural complexity suggests that uncalibrated or less complex PB models could be used in hybrid models without any loss of streamflow prediction accuracy, improving model construction efficiency. Moreover, hybrid model sensitivity to the selection of PB model variables suggests a strategy for diagnosing poorly performing PB model components. Key Points Hybrid streamflow prediction models frequently outperformed both machine learning and process‐based (PB) models Hybrid models were relatively insensitive to PB model calibration and structural complexity, but sensitive to PB model variable selection Hybrid models can improve streamflow prediction accuracy, efficiency, and diagnostics in Mediterranean‐climate watersheds

The integration of artificial intelligence chatbots/technologies into teaching-learning process improves students’ learning outcome and reduces teachers’ pedagogical stress in classroom. The present study focused on the In and Pre-service physics teachers’ willingness to integrate AI Chatbots in teaching and learning of physics. 45 In-service and 55 Pre-service physics teachers were engaged in the study. Attitude towards AI and Technology Readiness Index’ components were correlated with their willingness to integrate AI Chatbots in teaching. Three research instruments were adapted and used to elicit information from the respondents. Partial Least Square of Structural Equation Model (PLS-SEM) was employed and the data collected were analyzed using SmartPLS software version 4.0.9.2. The multi-group analysis of the In and Pre-service physics teachers were run separately and together to determine the difference in the willingness to integrate AI Chatbots in teaching-learning process. The findings of the study revealed that the affective, behavioural and cognitive components of the attitude towards AI significantly correlated with the respondents’ willingness to integrate AI Chatbots in teaching-learning process. The study concluded that attitude towards AI influences their willingness to integrate AI Chatbots to teaching-learning process.

The pretrained large language models have been widely tested for their performance on some challenging tasks including arithmetic, commonsense, and symbolic reasoning. Recently how to combine LLMs with prompting techniques has attracted lots of researchers to propose their models to automatically solve math word problems. However, most research works focus on solving math problems at the elementary school level and few works aim to solve problems in science disciplines, e.g., Physics. In this exploratory study, we discussed the potential pedagogical benefits of using ChatGPT in physics and demonstrated how to prompt ChatGPT in solving physics problems. The results suggest that ChatGPT is able to solve some physics calculation problems, explain solutions, and generate new exercises at a human level.

The study aims to find out first, whether there is a difference between the learning model of Assurance, Relevance, Interest, Assessment, and Satisfaction (ARIAS) and Problem Based Learning (PBL) on the concept mastery of temperature and heat. Second, it also aims to investigate the effectiveness of ARIAS and PBL learning model on the concept mastery of temperature and heat. The study uses Quasi-Experiment method with Nonequivalent Control Group Design, and sample selection with Cluster Random Sampling technique. This technique consists of two classes, i.e., experimental class I applying ARIAS learning model and experimental class II applying PBL model. The technique of data collection uses test instruments (pretest and posttest). The result of t test with 5% significant level indicates that t calculate = 2.03 > t table = 1.99, thus, it is concluded that (1) there is a difference using the learning model of ARIAS and PBL on concept mastery. The result of Effect Size test is a score of 0.45 with the medium category. Based on the result, it can be concluded that (2) using the learning model of ARIAS is more effective than PBL on the concept mastery of temperature and heat in high school students.