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The discoveries in this paper show that Intelligence Processing Units (IPUs) offer a viable accelerator alternative to GPUs for machine learning (ML) applications within the fields of materials science and battery research. We investigate the process of migrating a model from GPU to IPU and explore several optimization techniques, including pipelining and gradient accumulation, aimed at enhancing the performance of IPU-based models. Furthermore, we have effectively migrated a specialized model to the IPU platform. This model is employed for predicting effective conductivity, a parameter crucial in ion transport processes, which govern the performance of multiple charge and discharge cycles of batteries. The model utilizes a Convolutional Neural Network (CNN) architecture to perform prediction tasks for effective conductivity. The performance of this model on the IPU is found to be comparable to its execution on GPUs. We also analyze the utilization and performance of Graphcore's Bow IPU. Through benchmark tests, we observe significantly improved performance with the Bow IPU when compared to its predecessor, the Colossus IPU., Comment: arXiv admin note: This version has been removed by arXiv administrators as the submitter did not have the right to agree to the license at the time of submission

This paper investigates the central role played by the Hamiltonian in continuous-time nonlinear optimal control problems. We show that the strict convexity of the Hamiltonian in the control variable is a sufficient condition for the existence of a unique optimal trajectory, and the nonlinearity/non-convexity of the dynamics and the cost are immaterial. The analysis is extended to discrete-time problems, revealing that discretization destroys the convex Hamiltonian structure, leading to multiple spurious optima, unless the time discretization is sufficiently small. We present simulated results comparing the "indirect" Iterative Linear Quadratic Regulator (iLQR) and the "direct" Sequential Quadratic Programming (SQP) approach for solving the optimal control problem for the cartpole and pendulum models to validate the theoretical analysis. Results show that the ILQR always converges to the "globally" optimum solution while the SQP approach gets stuck in spurious minima given multiple random initial guesses for a time discretization that is insufficiently small, while both converge to the same unique solution if the discretization is sufficiently small.

This paper considers the infinite horizon optimal control problem for nonlinear systems. Under the condition of nonlinear controllability of the system to any terminal set containing the origin and forward invariance of the terminal set, we establish a regularized solution approach consisting of a ``finite free final time" optimal transfer problem to the terminal set which renders the set globally asymptotically stable. Further, we show that the approximations converge to the optimal infinite horizon cost as the size of the terminal set decreases to zero. We also perform the analysis for the discounted problem and show that the terminal set is asymptotically stable only for a subset of the state space and not globally. The theory is empirically evaluated on various nonholonomic robotic systems to show that the cost of our approximate problem converges and the transfer time into the terminal set is dependent on the initial state of the system, necessitating the free final time formulation.

Observation of blue-shifted X-ray absorption lines indicates the presence of wind from the accretion disk in X-ray binaries. Magnetohydrodynamic (MHD) driving is one of the possible wind launching mechanisms. Recent theoretical development makes magnetic accretion-ejection self-similar solutions much more generalized, and wind can be launched even at much lower magnetization compared to equipartition value, which was the only possibility beforehand. Here, we model the transmitted spectra through MHD driven photoionized wind - models which have different values of magnetizations. We investigate the possibility of detecting absorption lines by the upcoming instruments XRISM and Athena. Attempts are made to find the robustness of the method of fitting asymmetric line profiles by multiple Gaussians. We use photoionization code XSTAR to simulate the transmitted model spectra. Fake observed spectra are finally produced by convolving model spectra with instruments' responses. Since the line asymmetries are apparent in the convolved spectra as well, this can be used as an observable diagnostic to fit for, in future XRISM and Athena spectra. We demonstrate some amount of rigor in assessing the equivalent widths of the major absorption lines, including the Fe XXVI Ly$\alpha$ doublets which can be clearly distinguished in the superior quality, future high resolution spectra. Disk magnetization becomes another crucial MHD variable that can significantly alter the absorption line profiles. Low magnetization pure MHD outflow models are dense enough to be observed by the existing or upcoming instruments. Thus these models become simpler alternatives to MHD-thermal models. Fitting with multiple Gaussians is a promising method to handle asymmetric line profiles, as well as the Fe XXVI Ly$\alpha$ doublets., Comment: 17 pages (including 4 pages of Appendix), 13 figures, Accepted for publication in A&A

This paper discusses the predictive capability of Dynamic Mode Decomposition (DMD) in the context of orbital mechanics. The focus is specifically on the Hankel variant of DMD which uses a stacked set of time-delayed observations for system identification and subsequent prediction. A theory on the minimum number of time delays required for accurate reconstruction of periodic trajectories of nonlinear systems is presented and corroborated using experimental analysis. In addition, the window size for training and prediction regions, respectively, is presented. The need for a meticulous approach while using DMD is emphasized by drawing comparisons between its performance on two candidate satellites, the ISS and MOLNIYA-3-50.