Surface water sodium (Na+) concentration prediction using hybrid weighted exponential regression model with gradient-based optimization

Undeniably, there is a link between water resources and people's lives and, consequently, economic development, which makes them vital in health and the environment. Proper water quality forecasting time series has a crucial role in giving on-time warnings for water pollution and supporting the decision-making of water resource management. The principal aim of this study is to develop a novel and cutting-edge ensemble data intelligence model named the weighted exponential regression and hybridized by gradient-based optimization (WER-GBO). Indeed, this is to reach more meticulous sodium (Na⁺) prediction monthly at Maroon River in the southwest of Iran. This developed model has advantages over other previous methodologies thanks to the following merits: (i) it can improve the performance and ability by mixing the outputs of four distinct data intelligence (DI) models, i.e., adaptive neuro-fuzzy inference system (ANFIS), least square support vector regression (LSSVM), Bayesian linear regression (BLR), and response surface regression (RSR); (ii) the proposed model can employ a Cauchy weighted function combined with an exponential-based regression model being optimized by GBO algorithm. To evaluate the performance of these models, diverse statistical indices and graphical assessment including error distributions, box plots, scatter-plots with confidence bounds and Taylor diagrams were conducted. According to obtained statistical metrics and verified validation procedures, the proposed WER-GBO resulted in promising accuracy compared to other models. Furthermore, the outcomes revealed the WER-GBO (R = 0.9712, RMSE = 0.639, and KGE = 0.948) reached more accurate and reliable results than other methods such as the ANFIS, LSSVM, BLR, and RSR for Na prediction in this study. Hence, the WER-GBO model can be considered a constructive technique to forecast the water quality parameters.

Multiparameter optimization of nonuniform passive diffusion properties for creating coarse-grained equivalent models of cardiac propagation

The arrhythmogenic role of discrete cardiac propagation may be assessed by comparing discrete (fine-grained) and equivalent continuous (coarse-grained) models. We aim to develop an optimization algorithm for estimating the smooth conductivity field that best reproduces the diffusion properties of a given discrete model. Our algorithm iteratively adjusts local conductivity of the coarse-grained continuous model by simulating passive diffusion from white noise initial conditions during 3-10 ms and computing the root mean square error with respect to the discrete model. The coarse-grained conductivity field was interpolated from up to 300 evenly spaced control points. We derived an approximate formula for the gradient of the cost function that required (in two dimensions) only two additional simulations per iteration regardless of the number of estimated parameters. Conjugate gradient solver facilitated simultaneous optimization of multiple conductivity parameters. The method was tested in rectangular anisotropic tissues with uniform and nonuniform conductivity (slow regions with sinusoidal profile) and random diffuse fibrosis, as well as in a monolayer interconnected cable model of the left atrium with spatially-varying fibrosis density. Comparison of activation maps served as validation. The results showed that after convergence the errors in activation time were < 1 ms for rectangular geometries and 1-3 ms in the atrial model. Our approach based on the comparison of passive properties (<10 ms simulation) avoids performing active propagation simulations (>100 ms) at each iteration while reproducing activation maps, with possible applications to investigating the impact of microstructure on arrhythmias.

Enhanced sensitivity shaping by data-based tuning of disturbance observer with non-binomial filter

This work presents a new method of sensitivity shaping for motion control systems with disturbance observer (DOB). Although the traditional DOB design has been proved to be an effective means of rejecting disturbances in many applications, shaping of the closed-loop sensitivity is constrained since the Q-filter in DOB is usually restricted to a standard Butterworth or binomial form, where the cutoff frequency is the only tunable parameter. To overcome this limitation and achieve better performance for more demanding motion systems, a general form of the Q-filter is employed in this work. An data-based iteratively tuning procedure is subsequently developed according to a pre-defined cost function, so that the disturbance rejection in the low-frequency band is improved while the high-frequency noise attenuation and robust stability are not compromised. This method is data-based in the sense that the sensitivity shaping process is conducted based on the input-output data collected from the operating motion system, instead of relying on the identified system model. Simulation and experimental results are presented to show the advantage of this data-based sensitivity shaping approach.

Fine-tuning property domain weighting factors and the objective function in force-field parameter optimization

Force field (FF) based molecular modeling is an often used method to investigate and study structural and dynamic properties of (bio-)chemical substances and systems. When such a system is modeled or refined, the force-field parameters need to be adjusted. This force-field parameter optimization can be a tedious task and is always a trade-off in terms of errors regarding the targeted properties. To better control the balance of various properties' errors, in this study we introduce weighting factors for the optimization objectives. Different weighting strategies are compared to fine-tune the balance between bulk-phase density and relative conformational energies (RCE), using n-octane as a representative system. Additionally, a non-linear projection of the individual property-specific parts of the optimized loss function is deployed to further improve the balance between them. The results show that the combined error for the reproduction of the properties targeted in this optimization is reduced. Furthermore, the transferability of the force field parameters (FFParams) to chemically similar systems is increased. One interesting outcome is a large variety in the resulting optimized FFParams and corresponding errors, suggesting that the optimization landscape is multi-modal and very dependent on the weighting factor setup. We conclude that adjusting the weighting factors can be a very important feature to lower the overall error in the FF optimization procedure, giving researchers the possibility to fine-tune their FFs.

Automatic, dynamic, and nearly optimal learning rate specification via local quadratic approximation

In deep learning tasks, the update step size determined by the learning rate at each iteration plays a critical role in gradient-based optimization. However, determining the appropriate learning rate in practice typically relies on subjective judgment. In this work, we propose a novel optimization method based on local quadratic approximation (LQA). In each update step, we locally approximate the loss function along the gradient direction by using a standard quadratic function of the learning rate. Subsequently, we propose an approximation step to obtain a nearly optimal learning rate in a computationally efficient manner. The proposed LQA method has three important features. First, the learning rate is automatically determined in each update step. Second, it is dynamically adjusted according to the current loss function value and parameter estimates. Third, with the gradient direction fixed, the proposed method attains a nearly maximum reduction in the loss function. Extensive experiments were conducted to prove the effectiveness of the proposed LQA method.