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1. A linear hybrid model for enhanced servo error pre-compensation of feed drives with unmodeled nonlinear dynamics

   https://doi.org/https://doi.org/10.1016/j.cirp.2021.04.070  

   Chou, Cheng-Hao; Duan, Molong; Okwudire, Chinedum E. (January 2021, CIRP annals)

   null (Ed.)

   Servo error pre-compensation (SEP) is commonly used to improve the accuracy of feed drives. Existing SEP approaches often involve the use of physics-based linear models (e.g., transfer functions) to predict servo errors, but suffer from inaccuracies due to unmodeled nonlinear dynamics in feed drives. This paper proposes a linear hybrid model for SEP that combines physics-based and data-driven linear models. The proposed model is shown to approximate nonlinearities unmodeled in physics-based linear models. In experiments on a precision feed drive, the proposed hybrid model improves the accuracy of servo error prediction by up to 38% compared to a physics-based model. 

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2. Uncertainty drives deviations in normative foraging decision strategies

   https://doi.org/10.1098/rsif.2021.0337  

   Kilpatrick, Zachary P.; Davidson, Jacob D.; El Hady, Ahmed (July 2021, Journal of The Royal Society Interface)

   Nearly all animals forage to acquire energy for survival through efficient search and resource harvesting. Patch exploitation is a canonical foraging behaviour, but there is a need for more tractable and understandable mathematical models describing how foragers deal with uncertainty. To provide such a treatment, we develop a normative theory of patch foraging decisions, proposing mechanisms by which foraging behaviours emerge in the face of uncertainty. Our model foragers statistically and sequentially infer patch resource yields using Bayesian updating based on their resource encounter history. A decision to leave a patch is triggered when the certainty of the patch type or the estimated yield of the patch falls below a threshold. The time scale over which uncertainty in resource availability persists strongly impacts behavioural variables like patch residence times and decision rules determining patch departures. When patch depletion is slow, as in habitat selection, departures are characterized by a reduction of uncertainty, suggesting that the forager resides in a low-yielding patch. Uncertainty leads patch-exploiting foragers to overharvest (underharvest) patches with initially low (high) resource yields in comparison with predictions of the marginal value theorem. These results extend optimal foraging theory and motivate a variety of behavioural experiments investigating patch foraging behaviour. 

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3. Dissipative Capture of Planets into First-order Mean-motion Resonances

   https://doi.org/10.3847/2041-8213/acc015  

   Batygin, Konstantin; Petit, Antoine C (March 2023, The Astrophysical Journal Letters)

   The emergence of orbital resonances among planets is a natural consequence of the early dynamical evolution of planetary systems. While it is well established that convergent migration is necessary for mean-motion commensurabilities to emerge, recent numerical experiments have shown that the existing adiabatic theory of resonant capture provides an incomplete description of the relevant physics, leading to an erroneous mass scaling in the regime of strong dissipation. In this work, we develop a new model for resonance capture that self-consistently accounts for migration and circularization of planetary orbits, and derive an analytic criterion based upon stability analysis that describes the conditions necessary for the formation of mean-motion resonances. We subsequently test our results against numerical simulations and find satisfactory agreement. Our results elucidate the critical role played by adiabaticity and resonant stability in shaping the orbital architectures of planetary systems during the nebular epoch, and provide a valuable tool for understanding their primordial dynamical evolution. 

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4. Data-driven learning of chaotic dynamical systems using Discrete-Temporal Sobolev Networks

   Connor, Kennedy; Trace, Crowdis; Haoran, Hu; Sankaran, Vaidyanathan; H-K, Zhang (May 2024, Neural networks)

   We introduce the Discrete-Temporal Sobolev Network (DTSN), a neural network loss function that assists dynamical system forecasting by minimizing variational differences between the network output and the training data via a temporal Sobolev norm. This approach is entirely data-driven, architecture agnostic, and does not require derivative information from the estimated system. The DTSN is particularly well suited to chaotic dynamical systems as it minimizes noise in the network output which is crucial for such sensitive systems. For our test cases we consider discrete approximations of the Lorenz-63 system and the Chua circuit. For the network architectures we use the Long Short-Term Memory (LSTM) and the Transformer. The performance of the DTSN is compared with the standard MSE loss for both architectures, as well as with the Physics Informed Neural Network (PINN) loss for the LSTM. The DTSN loss is shown to substantially improve accuracy for both architectures, while requiring less information than the PINN and without noticeably increasing computational time, thereby demonstrating its potential to improve neural network forecasting of dynamical systems. 

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5. Physics-Guided Recurrent Graph Model for Predicting Flow and Temperature in River Networks

   Jia, X.; Zwart, J.; Sadler, J.: Appling; Oliver, S.; Markstrom, S.; Willard, J.; Xu, S.; Steinbach, M.; Read, J.; Kumar, V. (April 2021, Proceedings of the 2021 SIAM International Conference on Data Mining)

   Demeniconi, Carlotta; Davidson, Ian (Ed.)

   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. 

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