Deep Learning based Model-free Robust Load Restoration to Enhance Bulk System Resilience with Wind Power Penetration

This paper proposes a new deep learning (DL) based model-free robust method for bulk system on-line load restoration with high penetration of wind power. Inspired by the iterative calculation of the two-stage robust load restoration model, the deep neural network (DNN) and deep convolutional neural network (CNN) are respectively designed to find the worst-case system condition of a load pickup decision and evaluate the corresponding security. In order to find the optimal result within a limited number of checks, a load pickup checklist generation (LPCG) algorithm is developed to ensure the optimality. Then, the fast robust load restoration strategy acquisition is achieved based on the designed one-line strategy generation (OSG) algorithm. The proposed method finds the optimal result in a model-free way, holds the robustness to handle uncertainties, and provides real-time computation. It can completely replace conventional robust optimization and supports on-line robust load restoration which better satisfies the changeable restoration process. The effectiveness of the proposed method is validated using the IEEE 30-bus system and the IEEE 118-bus system, showing high computational efficiency and considerable accuracy.

GALOPP: Multi-Agent Deep Reinforcement Learning For Persistent Monitoring With Localization Constraints

Persistently monitoring a region under localization and communication constraints is a challenging problem. In this paper, we consider a heterogenous robotic system consisting of two types of agents -- anchor agents that have accurate localization capability, and auxiliary agents that have low localization accuracy. The auxiliary agents must be within the communication range of an {anchor}, directly or indirectly to localize itself. The objective of the robotic team is to minimize the uncertainty in the environment through persistent monitoring. We propose a multi-agent deep reinforcement learning (MADRL) based architecture with graph attention called Graph Localized Proximal Policy Optimization (GALLOP), which incorporates the localization and communication constraints of the agents along with persistent monitoring objective to determine motion policies for each agent. We evaluate the performance of GALLOP on three different custom-built environments. The results show the agents are able to learn a stable policy and outperform greedy and random search baseline approaches.

Risk-Adjusted Valuation for Real Option Decisions

We model investor heterogeneity using different required returns on an investment and evaluate the impact on the valuation of an investment. By assuming no disagreement on the cash flows, we emphasize how risk preferences in particular, but also the costs of capital, influence a subjective evaluation of the decision to invest now or retain the option to invest in future. We propose a risk-adjusted valuation model to facilitate investors subjective decision making, in response to the market valuation of an investment opportunity. The investors subjective assessment arises from their perceived misvaluation of the investment by the market, so projected cash flows are discounted using two different rates representing the investors and the markets view. This liberates our model from perfect or imperfect hedging assumptions and instead, we are able to illustrate the hedging effect on the real option value when perceptions of risk premia diverge. During crises periods, delaying an investment becomes more valuable as the idiosyncratic risk of future cash flows increases, but the decision-maker may rush to invest too quickly when the risk level is exceptionally high. Our model verifies features established by classical real-option valuation models and provides many new insights about the importance of modelling divergences in decision-makers risk premia, especially during crisis periods. It also has many practical advantages because it requires no more parameter inputs than basic discounted cash flow approaches, such as the marketed asset disclaimer method, but the outputs are much richer. They allow for complex interactions between cost and revenue uncertainties as well as an easy exploration of the effects of hedgeable and un-hedgeable risks on the real option value. Furthermore, we provide fully-adjustable Python code in which all parameter values can be chosen by the user.

Differential Privacy in Personalized Pricing with Nonparametric Demand Models

In the recent decades, the advance of information technology and abundant personal data facilitate the application of algorithmic personalized pricing. However, this leads to the growing concern of potential violation of privacy due to adversarial attack. To address the privacy issue, this paper studies a dynamic personalized pricing problem with textit{unknown} nonparametric demand models under data privacy protection. Two concepts of data privacy, which have been widely applied in practices, are introduced: textit{central differential privacy (CDP)} and textit{local differential privacy (LDP)}, which is proved to be stronger than CDP in many cases. We develop two algorithms which make pricing decisions and learn the unknown demand on the fly, while satisfying the CDP and LDP gurantees respectively. In particular, for the algorithm with CDP guarantee, the regret is proved to be at most $tilde O(T^{(d+2)/(d+4)}+varepsilon^{-1}T^{d/(d+4)})$. Here, the parameter $T$ denotes the length of the time horizon, $d$ is the dimension of the personalized information vector, and the key parameter $varepsilon>0$ measures the strength of privacy (smaller $varepsilon$ indicates a stronger privacy protection). On the other hand, for the algorithm with LDP guarantee, its regret is proved to be at most $tilde O(varepsilon^{-2/(d+2)}T^{(d+1)/(d+2)})$, which is near-optimal as we prove a lower bound of $Omega(varepsilon^{-2/(d+2)}T^{(d+1)/(d+2)})$ for any algorithm with LDP guarantee.

Bayesian evaluation of residual production cross sections in proton induced spallation reactions

The Bayesian neural network (BNN) method is used to construct a predictive model for fragment prediction of proton induced spallation reactions with the guidance of a simplified EPAX formula. Compared to the experimental data, it is found that the BNN + sEPAX model can reasonably extrapolate with less information compared with BNN method. The BNN + sEPAX method provides a new approach to predict the energy-dependent residual cross sections produced in proton-induced spallation reactions from tens of MeV/u up to several GeV/u.

Magnetohydrodynamic with Adaptively Embedded Particle-in-Cell model: MHD-AEPIC

Space plasma simulations have seen an increase in the use of magnetohydrodynamic (MHD) with embedded Particle-in-Cell (PIC) models. This combined MHD-EPIC algorithm simulates some regions of interest using the kinetic PIC method while employing the MHD description in the rest of the domain. The MHD models are highly efficient and their fluid descriptions are valid for most part of the computational domain, thus making large-scale global simulations feasible. However, in practical applications, the regions where the kinetic effects are critical can be changing, appearing, disappearing and moving in the computational domain. If a static PIC region is used, this requires a much larger PIC domain than actually needed, which can increase the computational cost dramatically. To address the problem, we have developed a new method that is able to dynamically change the region of the computational domain where a PIC model is applied. We have implemented this new MHD with Adaptively Embedded PIC (MHD-AEPIC) algorithm using the BATS-R-US Hall MHD and the Adaptive Mesh Particle Simulator (AMPS) as the semi-implicit PIC models. We describe the algorithm and present a test case of two merging flux ropes to demonstrate its accuracy. The implementation uses dynamic allocation/deallocation of memory and load balancing for efficient parallel execution. We evaluate the performance of MHD-AEPIC compared to MHD-EPIC and the scaling properties of the model to large number of computational cores.

Learning Nonlinear Waves in Plasmon-induced Transparency

Plasmon-induced transparency (PIT) displays complex nonlinear dynamics that find critical phenomena in areas such as nonlinear waves. However, such a nonlinear solution depends sensitively on the selection of parameters and different potentials in the Schrodinger equation. Despite this complexity, the machine learning community has developed remarkable efficiencies in predicting complicated datasets by regression. Here, we consider a recurrent neural network (RNN) approach to predict the complex propagation of nonlinear solitons in plasmon-induced transparency metamaterial systems with applied potentials bypassing the need for analytical and numerical approaches of a guiding model. We demonstrate the success of this scheme on the prediction of the propagation of the nonlinear solitons solely from a given initial condition and potential. We prove the prominent agreement of results in simulation and prediction by long short-term memory (LSTM) artificial neural networks. The framework presented in this work opens up a new perspective for the application of RNN in quantum systems and nonlinear waves using Schrodinger-type equations, for example, the nonlinear dynamics in cold-atom systems and nonlinear fiber optics.

Pruning Ternary Quantization

We propose pruning ternary quantization (PTQ), a simple, yet effective, symmetric ternary quantization method. The method significantly compresses neural network weights to a sparse ternary of [-1,0,1] and thus reduces computational, storage, and memory footprints. We show that PTQ can convert regular weights to ternary orthonormal bases by simply using pruning and L2 projection. In addition, we introduce a refined straight-through estimator to finalize and stabilize the quantized weights. Our method can provide at most 46x compression ratio on the ResNet-18 structure, with an acceptable accuracy of 65.36%, outperforming leading methods. Furthermore, PTQ can compress a ResNet-18 model from 46 MB to 955KB (~48x) and a ResNet-50 model from 99 MB to 3.3MB (~30x), while the top-1 accuracy on ImageNet drops slightly from 69.7% to 65.3% and from 76.15% to 74.47%, respectively. Our method unifies pruning and quantization and thus provides a range of size-accuracy trade-off.

Effective Scaling Approach to Frictionless Quantum Quenches in Trapped Bose Gases

We work out the effective scaling approach to frictionless quantum quenches in a one-dimensional Bose gas trapped in a harmonic trap. The effective scaling approach produces an auxiliary equation for the scaling parameter interpolating between the noninteracting and the Thomas-Fermi limits. This allows us to implement a frictionless quench by engineering inversely the smooth trap frequency, as compared to the two-jump trajectory. Our result is beneficial to design the shortcut-to-adiabaticity expansion of trapped Bose gases for arbitrary values of interaction, and can be directly extended to the three-dimensional case.

Computational Hardness of the Hylland-Zeckhauser Scheme

We study the complexity of the classic Hylland-Zeckhauser scheme [HZ79] for one-sided matching markets. We show that the problem of finding an $epsilon$-approximate equilibrium in the HZ scheme is PPAD-hard, and this holds even when $epsilon$ is polynomially small and when each agent has no more than four distinct utility values. Our hardness result, when combined with the PPAD membership result of [VY21], resolves the approximation complexity of the HZ scheme. We also show that the problem of approximating the optimal social welfare (the weight of the matching) achievable by HZ equilibria within a certain constant factor is NP-hard.