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To plan and optimize energy storage demands that account for Li-ion battery aging dynamics, techniques need to be developed to diagnose battery internal states accurately and rapidly. This study seeks to reduce the computational resources needed to determine a battery's internal states by replacing physics-based Li-ion battery models -- such as the single-particle model (SPM) and the pseudo-2D (P2D) model -- with a physics-informed neural network (PINN) surrogate. The surrogate model makes high-throughput techniques, such as Bayesian calibration, tractable to determine battery internal parameters from voltage responses. This manuscript is the first of a two-part series that introduces PINN surrogates of Li-ion battery models for parameter inference (i.e., state-of-health diagnostics). In this first part, a method is presented for constructing a PINN surrogate of the SPM. A multi-fidelity hierarchical training, where several neural nets are trained with multiple physics-loss fidelities is shown to significantly improve the surrogate accuracy when only training on the governing equation residuals. The implementation is made available in a companion repository (https://github.com/NREL/pinnstripes). The techniques used to develop a PINN surrogate of the SPM are extended in Part II for the PINN surrogate for the P2D battery model, and explore the Bayesian calibration capabilities of both surrogates.

Reservoir computing, using nonlinear dynamical systems, offers a cost-effective alternative to neural networks for complex tasks involving processing of sequential data, time series modeling, and system identification. Echo state networks (ESNs), a type of reservoir computer, mirror neural networks but simplify training. They apply fixed, random linear transformations to the internal state, followed by nonlinear changes. This process, guided by input signals and linear regression, adapts the system to match target characteristics, reducing computational demands. A potential drawback of ESNs is that the fixed reservoir may not offer the complexity needed for specific problems. While directly altering (training) the internal ESN would reintroduce the computational burden, an indirect modification can be achieved by redirecting some output as input. This feedback can influence the internal reservoir state, yielding ESNs with enhanced complexity suitable for broader challenges. In this paper, we demonstrate that by feeding some component of the reservoir state back into the network through the input, we can drastically improve upon the performance of a given ESN. We rigorously prove that, for any given ESN, feedback will almost always improve the accuracy of the output. For a set of three tasks, each representing different problem classes, we find that with feedback the average error measures are reduced by $30\%-60\%$. Remarkably, feedback provides at least an equivalent performance boost to doubling the initial number of computational nodes, a computationally expensive and technologically challenging alternative. These results demonstrate the broad applicability and substantial usefulness of this feedback scheme., Comment: 32 pages, 6 figures

This paper studies the coexistence between a downlink multiuser massive multi-input-multi-output (MIMO) communication system and MIMO radar. The performance of the massive MIMO system with maximum ratio ($\MR$), zero-forcing ($\ZF$), and protective $\ZF$ ($\PZF$) precoding designs is characterized in terms of spectral efficiency (SE) and by taking the channel estimation errors and power control into account. The idea of $\PZF$ precoding relies on the projection of the information-bearing signal onto the null space of the radar channel to protect the radar against communication signals. We further derive closed-form expressions for the detection probability of the radar system for the considered precoding designs. By leveraging the closed-form expressions for the SE and detection probability, we formulate a power control problem at the radar and base station (BS) to maximize the detection probability while satisfying the per-user SE requirements. This optimization problem can be efficiently tackled via the bisection method by solving a linear feasibility problem. Our analysis and simulations show that the $\PZF$ design has the highest detection probability performance among all designs, with intermediate SE performance compared to the other two designs. Moreover, by optimally selecting the power control coefficients at the BS and radar, the detection probability improves significantly., Comment: 10 Figures, IEEE Open Journal of the Communication society

We study the effect of acceleration and deceleration on the stability of channel flows. To do so, we derive an exact solution for laminar profiles of channel flows with arbitrary, time-varying wall motion and pressure gradient. This solution then allows us to investigate the stability of any unsteady channel flow. In particular, we restrict our investigation to the nonnormal growth of perturbations about time-varying base flows with exponentially decaying acceleration and deceleration, with comparisons to growth about a constant base flow (i.e., the time-invariant simple shear or parabolic profile). We apply this acceleration and deceleration through the velocity of the walls and through the flow rate. For accelerating base flows, perturbations never grow larger than perturbations about a constant base flow, while decelerating flows show massive amplification of perturbations - at a Reynolds number of 500, properly timed perturbations about the decelerating base flow grow $\mathscr{O}(10^5)$ times larger than perturbations grow about a constant base flow. This amplification increases as we raise the rate of deceleration and the Reynolds number. We find that this amplification arises due to a transition from spanwise perturbations leading to the largest amplification, to streamwise perturbations leading to the largest amplification that only occurs in the decelerating base flow. By evolving the optimal perturbations through the linearized equations of motion, we reveal that the decelerating base flow achieves this massive amplification through the Orr mechanism, or the down-gradient Reynolds stress mechanism, which accelerating and constant base flows cannot maintain.

We introduce a diagrammatic monoidal category, the spin Brauer category, that plays the same role for the spin and pin groups as the Brauer category does for the orthogonal groups. In particular, there is a full functor from the spin Brauer category to the category of finite-dimensional modules for the spin and pin groups. This functor becomes essentially surjective after passing to the Karoubi envelope, and its kernel is the tensor ideal of negligible morphisms. In this way, the spin Brauer category can be thought of as an interpolating category for the spin and pin groups. We also define an affine version of the spin Brauer category, which acts on categories of modules for the pin and spin groups via translation functors., Comment: 46 pages. v2: Changed order of Sections 7 and 8, other improvements and corrections throughout

The moments of the real eigenvalues of real Ginibre matrices are investigated from the viewpoint of explicit formulas, differential and difference equations, and large $N$ expansions. These topics are inter-related. For example, a third order differential equation can be derived for the density of the real eigenvalues, and this can be used to deduce a second order difference equation for the general complex moments $M_{2p}^{\rm r}$. The latter are expressed in terms of the ${}_3 F_2$ hypergeometric functions, with a simplification to the ${}_2 F_1$ hypergeometric function possible for $p=0$ and $p=1$, allowing for the large $N$ expansion of these moments to be obtained. The large $N$ expansion involves both integer and half integer powers of $1/N$. The three term recurrence then provides the large $N$ expansion of the full sequence $\{ M_{2p}^{\rm r} \}_{p=0}^\infty$. Fourth and third order linear differential equations are obtained for the moment generating function and for the Stieltjes transform of the real density, respectively, and properties of the large $N$ expansion of these quantities are determined., Comment: 14 pages; v2 15 pages, accepted for publication in Ramanujan J

Safe deployment of large language models (LLMs) may benefit from a reliable method for assessing their generated content to determine when to abstain or to selectively generate. While likelihood-based metrics such as perplexity are widely employed, recent research has demonstrated the limitations of using sequence-level probability estimates given by LLMs as reliable indicators of generation quality. Conversely, LLMs have demonstrated strong calibration at the token level, particularly when it comes to choosing correct answers in multiple-choice questions or evaluating true/false statements. In this work, we reformulate open-ended generation tasks into token-level prediction tasks, and leverage LLMs' superior calibration at the token level. We instruct an LLM to self-evaluate its answers, employing either a multi-way comparison or a point-wise evaluation approach, with the option to include a ``None of the above'' option to express the model's uncertainty explicitly. We benchmark a range of scoring methods based on self-evaluation and evaluate their performance in selective generation using TruthfulQA and TL;DR. Through experiments with PaLM-2 and GPT-3, we demonstrate that self-evaluation based scores not only improve accuracy, but also correlate better with the overall quality of generated content.

Fine-tuning language models~(LMs) on human-generated data remains a prevalent practice. However, the performance of such models is often limited by the quantity and diversity of high-quality human data. In this paper, we explore whether we can go beyond human data on tasks where we have access to scalar feedback, for example, on math problems where one can verify correctness. To do so, we investigate a simple self-training method based on expectation-maximization, which we call ReST$^{EM}$, where we (1) generate samples from the model and filter them using binary feedback, (2) fine-tune the model on these samples, and (3) repeat this process a few times. Testing on advanced MATH reasoning and APPS coding benchmarks using PaLM-2 models, we find that ReST$^{EM}$ scales favorably with model size and significantly surpasses fine-tuning only on human data. Overall, our findings suggest self-training with feedback can substantially reduce dependence on human-generated data., Comment: Accepted to TMLR. Camera-ready version. First three authors contributed equally

Widespread use of artificial intelligence (AI) algorithms and machine learning (ML) models on the one hand and a number of crucial issues pertaining to them warrant the need for explainable artificial intelligence (XAI). A key explainability question is: given this decision was made, what are the input features which contributed to the decision? Although a range of XAI approaches exist to tackle this problem, most of them have significant limitations. Heuristic XAI approaches suffer from the lack of quality guarantees, and often try to approximate Shapley values, which is not the same as explaining which features contribute to a decision. A recent alternative is so-called formal feature attribution (FFA), which defines feature importance as the fraction of formal abductive explanations (AXp's) containing the given feature. This measures feature importance from the view of formally reasoning about the model's behavior. It is challenging to compute FFA using its definition because that involves counting AXp's, although one can approximate it. Based on these results, this paper makes several contributions. First, it gives compelling evidence that computing FFA is intractable, even if the set of contrastive formal explanations (CXp's) is provided, by proving that the problem is #P-hard. Second, by using the duality between AXp's and CXp's, it proposes an efficient heuristic to switch from CXp enumeration to AXp enumeration on-the-fly resulting in an adaptive explanation enumeration algorithm effectively approximating FFA in an anytime fashion. Finally, experimental results obtained on a range of widely used datasets demonstrate the effectiveness of the proposed FFA approximation approach in terms of the error of FFA approximation as well as the number of explanations computed and their diversity given a fixed time limit.

Assuming the Hasse--Weil conjecture and the generalized Riemann hypothesis for the $L$-functions of the elliptic curve, we give an upper bound of the average analytic rank of elliptic curves over the number field with a level structure such that the corresponding compactified moduli stack is representable by the projective line.

In this work we present an experimental demonstration of the Contextual Subspace Variational Quantum Eigensolver on superconducting quantum hardware. In particular, we compute the potential energy curve for molecular nitrogen, where a dominance of static correlation in the dissociation limit proves challenging for many conventional quantum chemistry techniques. Our quantum simulations retain good agreement with the full configuration interaction energy in the chosen STO-3G basis, outperforming all benchmarked single-reference wavefunction techniques in capturing the bond-breaking appropriately. Moreover, our methodology is competitive with several multiconfigurational approaches, but at a considerable saving of quantum resource, meaning larger active spaces can be treated for a fixed qubit allowance. To achieve this result we deploy an error mitigation/suppression strategy comprised of dynamical decoupling, measurement-error mitigation and zero-noise extrapolation, in addition to circuit parallelization that not only provides passive averaging of noise but improves the effective shot-yield to reduce the measurement overhead. Furthermore, we introduce a modification to previous adaptive ansatz construction algorithms that incorporates hardware-awareness into our variational circuits to minimize the transpilation cost for the target qubit topology., Comment: 22 pages, 12 figures