Search

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.

This paper studies the learning-to-control problem under process and sensing uncertainties for dynamical systems. In our previous work, we developed a data-based generalization of the iterative linear quadratic regulator (iLQR) to design closed-loop feedback control for high-dimensional dynamical systems with partial state observation. This method required perfect simulation rollouts which are not realistic in real applications. In this work, we briefly introduce this method and explore its efficacy under process and sensing uncertainties. We prove that in the fully observed case where the system dynamics are corrupted with noise but the measurements are perfect, it still converges to the global minimum. However, in the partially observed case where both process and measurement noise exist in the system, this method converges to a biased "optimum". Thus multiple rollouts need to be averaged to retrieve the true optimum. The analysis is verified in two nonlinear robotic examples simulated in the above cases.

In this paper, we study the use of state-of-the-art nonlinear system identification techniques for the optimal control of nonlinear systems. We show that the nonlinear systems identification problem is equivalent to estimating the generalized moments of an underlying sampling distribution and is bound to suffer from ill-conditioning and variance when approximating a system to high order, requiring samples combinatorial-exponential in the order of the approximation, i.e., the global nature of the approximation. We show that the iterative identification of "local" linear time varying (LTV) models around the current estimate of the optimal trajectory, coupled with a suitable optimal control algorithm such as iterative LQR (ILQR), is necessary as well as sufficient, to accurately solve the underlying optimal control problem., Comment: 8 pages, 11 figures

As the packing density of resistive random access memory (RRAM) devices increases, the effect of thermal cross-talk across the devices in a crossbar array arrangement influences their overall operation significantly. The electro-thermal effects in a densely packed RRAM crossbar can accelerate the retention and endurance degradation; hence poses a serious reliability threat. This paper systematically investigates the electro-thermal effects in passive RRAM crossbar arrays using COMSOL multi-physics simulations. Furthermore, we propose a methodology to model the thermal cross-talk effect and incorporate it in a SPICE-compatible physics-based RRAM compact model. Finally, we demonstrate the impact of thermal coupling on RRAM crossbar array operation in terms of vector-matrix multiplication using calibrated SPICE simulations.

In this paper, we consider the infinite horizon optimal control problem for nonlinear systems. Under the conditions of controllability of the linearized system around the origin, and nonlinear controllability of the system to a terminal set containing the origin, we establish an approximate regularized solution approach consisting of a ``finite free final time" optimal transfer problem to the terminal set, and an infinite horizon linear regulation problem within the terminal set, that is shown to render the origin globally asymptotically stable. Further, we show that the approximations converge to the true optimal cost function as the size of the terminal set decreases to zero. The approach is empirically evaluated on the pendulum and cart-pole swing-up problems to show that the finite time transfer is far shorter than the effective horizon required to solve the infinite horizon problem without the proposed regularization.

This paper considers the problem of system identification for linear time varying systems. We propose a new system realization approach that uses an "information-state" as the state vector, where the "information-state" is composed of a finite number of past inputs and outputs. The system identification algorithm uses input-output data to fit an autoregressive moving average model (ARMA) to represent the current output in terms of finite past inputs and outputs. This information-state-based approach allows us to directly realize a state-space model using the estimated time varying ARMA paramters linear time varying (LTV) systems. The paper develops the theoretical foundation for using ARMA parameters-based system representation using only the concept of linear observability, details the reasoning for exact output modeling using only the finite history, and shows that there is no need to separate the free and the forced response for identification. The paper also discusses the implications of using the information-state system for optimal output feedback control and shows that the solution obtained using a suitably posed information state problem is optimal for the original problem. The proposed approach is tested on various different systems, and the performance is compared with state-of-the-art LTV system identification techniques.

In this paper, we consider the optimal control of material micro-structures. Such material micro-structures are modeled by the so-called phase field model. We study the underlying physical structure of the model and propose a data based approach for its optimal control, along with a comparison to the control using a state of the art Reinforcement Learning (RL) algorithm. Simulation results show the feasibility of optimally controlling such micro-structures to attain desired material properties and complex target micro-structures.

In our self-similar, analytical, magneto-hydrodynamic (MHD) accretion-ejection solution, the density at the base of the outflow is explicitly dependent on the disk accretion rate - a unique property of this class of solutions. We had earlier found that the ejection index $p >\sim 0.1 (\dot{M}_{acc} \propto r^p ) $ is a key MHD parameter that decides if the flow can cause absorption lines in the high resolution X-ray spectra of black hole binaries. Here we choose 3 dense warm solutions with $p = 0.1, 0.3, 0.45$ and carefully develop a methodology to generate spectra which are convolved with the Athena and XRISM response functions to predict what they will observe seeing through such MHD outflows. In this paper two other external parameters were varied - extent of the disk, $\rm{r_o|_{max}} = 10^5, \, 10^6 \,\, \rm{r_G}$, and the angle of the line of sight, $i \sim 10 - 25^{\circ}$. Resultant absorption lines (H and He-like Fe, Ca, Ar) change in strength and their profiles manifest varying degrees of asymmetry. We checked if a) the lines and ii) the line asymmetries are detected, in our suit of synthetic Athena and XRISM spectra. Our analysis shows that Athena should detect the lines and their asymmetries for a standard 100 ksec observation of a 100 mCrab source - lines with equivalent width as low as a few eV should be detected if the 6-8 keV counts are larger than $10^4 - 10^5$ even for the least favourable simulated cases., Comment: 18 pages, 13 figures in the main body and 3 figures in the appendix. Accepted for publication in MNRAS