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Accurate predictions of water temperature are the foundation for many decisions and regulations, with direct impacts on water quality, fishery yields, and power production. Building accurate broad-scale models for lake temperature prediction remains challenging in practice due to the variability in the data distribution across different lake systems monitored by static and time-series data. In this paper, to tackle the above challenges, we propose a novel machine learning based approach for integrating static and time-series data in deep recurrent models, which we call Invertibility-Aware-Long Short-Term Memory(IA-LSTM), and demonstrate its effectiveness in predicting lake temperature. Our proposed method integrates components of the Invertible Network and LSTM to better predict temperature profiles (forward modeling) and infer the static features (i.e., inverse modeling) that can eventually enhance the prediction when static variables are missing. We evaluate our method on predicting the temperature profile of 450 lakes in the Midwestern U.S. and report a relative improvement of 4\% to capture data heterogeneity and simultaneously outperform baseline predictions by 12\% when static features are unavailable. 

This paper proposes a physics-guided machine learning approach that combines machine learning models and physics-based models to improve the prediction of water flow and temperature in river networks. We first build a recurrent graph network model to capture the interactions among multiple segments in the river network. Then we transfer knowledge from physics-based models to guide the learning of the machine learning model. We also propose a new loss function that balances the performance over different river segments. We demonstrate the effectiveness of the proposed method in predicting temperature and streamflow in a subset of the Delaware River Basin. In particular, the proposed method has brought a 33%/14% accuracy improvement over the state-of-the-art physics-based model and 24%/14% over traditional machine learning models (e.g., LSTM) in temperature/streamflow prediction using very sparse (0.1%) training data. The proposed method has also been shown to produce better performance when generalized to different seasons or river segments with different streamflow ranges. 

We construct a notion of teleparallelization for Newton–Cartan theory, and show that the teleparallel equivalent of this theory is Newtonian gravity; furthermore, we show that this result is consistent with teleparallelization in general relativity, and can be obtained by null-reducing the teleparallel equivalent of a five-dimensional gravitational wave solution. This work thus strengthens substantially the connections between four theories: Newton–Cartan theory, Newtonian gravitation theory, general relativity, and teleparallel gravity. 

This paper proposes a physics-guided recurrent neural network model (PGRNN) that combines RNNs and physics-based models to leverage their complementary strengths and improve the modeling of physical processes. Specifically, we show that a PGRNN can improve prediction accuracy over that of physical models, while generating outputs consistent with physical laws, and achieving good generalizability. Standard RNNs, even when producing superior prediction accuracy, often produce physically inconsistent results and lack generalizability. We further enhance this approach by using a pre-training method that leverages the simulated data from a physics-based model to address the scarcity of observed data. Although we present and evaluate this methodology in the context of modeling the dynamics of temperature in lakes, it is applicable more widely to a range of scientific and engineering disciplines where mechanistic (also known as process-based) models are used, e.g., power engineering, climate science, materials science, computational chemistry, and biomedicine. 

Abstract Rotating nonaxisymmetric neutron stars (NSs) are promising sources for continuous gravitational waves (CWs). CWs may, if detected, inform us about the internal structure and equation of state of NSs. Here, we present a narrowband search for CWs from known pulsars, for which a matched-filter search can be applied. Narrowband searches are robust to mismatches between electromagnetic (EM) and gravitational emissions, in contrast to fully targeted searches where they are assumed to be phase-locked. In this work, we search for the CW counterparts emitted by 34 pulsars using data from the first and second parts of the fourth LIGO–Virgo–KAGRA observing run. We use the 5n-vector narrowband pipeline, which applies frequency-domain matched filtering. In previous searches, it covered a narrow range in the frequency—frequency time derivative (f— $\dot{f}$ ) space. Here, we also explore a range in the second time derivative of the frequency $\ddot{f}$ around the EM observations. Additionally, for the first time, we target sources in a binary system with this kind of search. We find no evidence for CWs and therefore set upper limits on the strain amplitude emitted by each pulsar. For 20 analyses, we report an upper limit below the theoretical spin-down limit. The tightest constraint is for pulsar PSR J0534+2200 (the Crab pulsar), for which our strain upper limit on the CW amplitude corresponds to ≤0.04% of the spin-down power being radiated in the CW channel.