Abstract: Remaining Useful Life (RUL) of battery is an important parameter to know the battery's remaining life and need for recharge. The goal of this research project is to develop machine learning-based models for the battery RUL dataset. Different ML models are developed to classify the RUL of the vehicle, and the IoT (Internet of Things) concept is simulated for automating the charging system and managing any faults aligning. The graphs plotted depict the relationship between various vehicle parameters using the Blynk IoT platform. Results show that the catboost, Multi-Layer Perceptron (MLP), Gated Recurrent Unit (GRU), and hybrid model developed could classify RUL into three classes with 99% more accuracy. The data is fed using the tkinter GUI for simulating artificial intelligence (AI)-based charging, and with a pyserial backend, data can be entered into the Esp-32 microcontroller for making charge discharge possible with the model's predictions. Also, with an IoT system, the charging can be disconnected, monitored, and analyzed for automation. The results show that an accuracy of 99% can be obtained on models MLP, catboost model and similar accuracy on GRU model can be obtained, and finally relay-based triggering can be made by prediction through the model used for automating the charging and energy-saving mechanism. Keywords: RUL, power management, Internet of Things, catboost, cross-validation 1. Introduction A battery's ability to store and release energy steadily diminishes with use as a result of a number of variables, including temperature changes, chemical deterioration, and charge-discharge cycles. An estimate of how long the battery should continue to function dependably is given by the RUL.

Ensuring safety is a key aspect in sequential decision making problems, such as robotics or process control. The complexity of the underlying systems often makes finding the optimal decision challenging, especially when the safety-critical system is time-varying. Overcoming the problem of optimizing an unknown time-varying reward subject to unknown time-varying safety constraints, we propose TVSafeOpt, a new algorithm built on Bayesian optimization with a spatio-temporal kernel. The algorithm is capable of safely tracking a time-varying safe region without the need for explicit change detection. Optimality guarantees are also provided for the algorithm when the optimization problem becomes stationary. We show that TVSafeOpt compares favorably against SafeOpt on synthetic data, both regarding safety and optimality. Evaluation on a realistic case study with gas compressors confirms that TVSafeOpt ensures safety when solving time-varying optimization problems with unknown reward and safety functions.

Simulating fluid flow around arbitrary shapes is key to solving various engineering problems. However, simulating flow physics across complex geometries remains numerically challenging and computationally resource-intensive, particularly when using conventional PDE solvers. Machine learning methods offer attractive opportunities to create fast and adaptable PDE solvers. However, benchmark datasets to measure the performance of such methods are scarce, especially for flow physics across complex geometries. We introduce FlowBench, a dataset for neural simulators with over 10K samples, which is currently larger than any publicly available flow physics dataset. FlowBench contains flow simulation data across complex geometries (\textit{parametric vs. non-parametric}), spanning a range of flow conditions (\textit{Reynolds number and Grashoff number}), capturing a diverse array of flow phenomena (\textit{steady vs. transient; forced vs. free convection}), and for both 2D and 3D. FlowBench contains over 10K data samples, with each sample the outcome of a fully resolved, direct numerical simulation using a well-validated simulator framework designed for modeling transport phenomena in complex geometries. For each sample, we include velocity, pressure, and temperature field data at 3 different resolutions and several summary statistics features of engineering relevance (such as coefficients of lift and drag, and Nusselt numbers). %Additionally, we include masks and signed distance fields for each shape. We envision that FlowBench will enable evaluating the interplay between complex geometry, coupled flow phenomena, and data sufficiency on the performance of current, and future, neural PDE solvers. We enumerate several evaluation metrics to help rank order the performance of neural PDE solvers. We benchmark the performance of several baseline methods including FNO, CNO, WNO, and DeepONet.

Option pricing models, essential in financial mathematics and risk management, have been extensively studied and recently advanced by AI methodologies. However, American option pricing remains challenging due to the complexity of determining optimal exercise times and modeling non-linear payoffs resulting from stochastic paths. Moreover, the prevalent use of the Black-Scholes formula in hybrid models fails to accurately capture the discontinuity in the price process, limiting model performance, especially under scarce data conditions. To address these issues, this study presents a comprehensive framework for American option pricing consisting of six interrelated modules, which combine nonlinear optimization algorithms, analytical and numerical models, and neural networks to improve pricing performance. Additionally, to handle the scarce data challenge, this framework integrates the transfer learning through numerical data augmentation and a physically constrained, jump diffusion process-informed neural network to capture the leptokurtosis of the log return distribution. To increase training efficiency, a warm-up period using Bayesian optimization is designed to provide optimal data loss and physical loss coefficients. Experimental results of six case studies demonstrate the accuracy, convergence, physical effectiveness, and generalization of the framework. Moreover, the proposed model shows superior performance in pricing deep out-of-the-money options. Introduction Options are fundamental financial derivatives widely employed for risk management. The movement of option prices follows a stochastic process influenced by various factors such as the price process of the underlying assets ( S t), the strike price (K), the time-to-maturity ( T), the option type (American or European; Put ( P) or Call ( C) options), and numerous macroeconomic and market factors.

The recent promises of Model Predictive Control in robotics have motivated the development of tailored second-order methods to solve optimal control problems efficiently. While those methods benefit from strong convergence properties, tailored efficient implementations are challenging to derive. In this work, we study the potential effectiveness of first-order methods and show on a torque controlled manipulator that they can equal the performances of second-order methods.

We present a generative AI algorithm for addressing the challenging task of fast, accurate and robust statistical computation of three-dimensional turbulent fluid flows. Our algorithm, termed as GenCFD, is based on a conditional score-based diffusion model. Through extensive numerical experimentation with both incompressible and compressible fluid flows, we demonstrate that GenCFD provides very accurate approximation of statistical quantities of interest such as mean, variance, point pdfs, higher-order moments, while also generating high quality realistic samples of turbulent fluid flows and ensuring excellent spectral resolution. In contrast, ensembles of operator learning baselines which are trained to minimize mean (absolute) square errors regress to the mean flow. We present rigorous theoretical results uncovering the surprising mechanisms through which diffusion models accurately generate fluid flows. These mechanisms are illustrated with solvable toy models that exhibit the relevant features of turbulent fluid flows while being amenable to explicit analytical formulas.

In scientific machine learning, the task of identifying partial differential equations accurately from sparse and noisy data poses a significant challenge. Current sparse regression methods may identify inaccurate equations on sparse and noisy datasets and are not suitable for varying coefficients. To address this issue, we propose a hybrid framework that combines two alternating direction optimization phases: discovery and embedding. The discovery phase employs current well-developed sparse regression techniques to preliminarily identify governing equations from observations. The embedding phase implements a recurrent convolutional neural network (RCNN), enabling efficient processes for time-space iterations involved in discretized forms of wave equation. The RCNN model further optimizes the imperfect sparse regression results to obtain more accurate functional terms and coefficients. Through alternating update of discovery-embedding phases, essential physical equations can be robustly identified from noisy and low-resolution measurements. To assess the performance of proposed framework, numerical experiments are conducted on various scenarios involving wave equation in elastic/viscoelastic and homogeneous/inhomogeneous media. The results demonstrate that the proposed method exhibits excellent robustness and accuracy, even when faced with high levels of noise and limited data availability in both spatial and temporal domains.

Scientific machine learning (SciML) is an interdisciplinary research field that integrates machine learning, particularly deep learning, with physics theory to understand and predict complex natural phenomena. By incorporating physical knowledge, SciML reduces the dependency on observational data, which is often limited in the natural sciences. In this article, the fundamental concepts of SciML, its applications in seismology, and prospects are described. Specifically, two popular methods are mainly discussed: physics-informed neural networks (PINNs) and neural operators (NOs). PINNs can address both forward and inverse problems by incorporating governing laws into the loss functions. The use of PINNs is expanding into areas such as simultaneous solutions of differential equations, inference in underdetermined systems, and regularization based on physics. These research directions would broaden the scope of deep learning in natural sciences. NOs are models designed for operator learning, which deals with relationships between infinite-dimensional spaces. NOs show promise in modeling the time evolution of complex systems based on observational or simulation data. Since large amounts of data are often required, combining NOs with physics-informed learning holds significant potential. Finally, SciML is considered from a broader perspective beyond deep learning: statistical (or mathematical) frameworks that integrate observational data with physical principles to model natural phenomena. In seismology, mathematically rigorous Bayesian statistics has been developed over the past decades, whereas more flexible and scalable deep learning has only emerged recently. Both approaches can be considered as part of SciML in a broad sense. Theoretical and practical insights in both directions would advance SciML methodologies and thereby deepen our understanding of earthquake phenomena.

Understanding and predicting the behavior of complex physical systems is a cornerstone of scientific and engineering endeavors. In fluid mechanics, for instance, accurately simulating real operational conditions is essential for the design and optimization of pipelines, aerospace components, and various industrial processes. However, full-scale simulations of such systems are often prohibitively expensive and time-consuming due to the intricate dynamics and vast parameter spaces involved. This poses a significant challenge for researchers and engineers who seek to explore and optimize these systems efficiently. One promising approach to mitigate these challenges is the identification of scaling similarities and symmetry groups within physical systems. By uncovering the correct scaling relations, we can develop smaller, more manageable models that accurately capture the essential behavior of real-world scenarios. These scaled models not only reduce computational costs but also accelerate the design and testing processes by allowing for efficient exploration of the parameter space. Moreover, understanding these scaling laws deepens our insight into the fundamental principles governing these systems, enabling us to generalize findings from simplified models to full-scale applications with greater confidence. In recent years, the application of machine learning in fluid mechanics has been on the rise, offering innovative tools to address complex problems that are difficult to solve analytically.

Lossy compression is one of the most effective methods for reducing the size of scientific data containing multiple data fields. It reduces information density through prediction or transformation techniques to compress the data. Previous approaches use local information from a single target field when predicting target data points, limiting their potential to achieve higher compression ratios. In this paper, we identified significant cross-field correlations within scientific datasets. We propose a novel hybrid prediction model that utilizes CNN to extract cross-field information and combine it with existing local field information. Our solution enhances the prediction accuracy of lossy compressors, leading to improved compression ratios without compromising data quality. We evaluate our solution on three scientific datasets, demonstrating its ability to improve compression ratios by up to 25% under specific error bounds. Additionally, our solution preserves more data details and reduces artifacts compared to baseline approaches.