A Spiking Neural Network (SNN) (Maass, 1997; Gerstner and Kistler, 2002b; Pfeiffer and Pfeil, 2018) is a neuro-inspired machine learning (ML) model that mimics the spike-based operation of the human brain (Bi and Poo, 1998). The Spike Time Dependent Plasticity (STDP) is a policy for unsupervised learning in rate-encoded SNNs (Bell et al., 1997; Magee and Johnston, 1997; Gerstner and Kistler, 2002a). The STDP relates the expected change in synaptic weights to the timing difference between postsynaptic spikes and presynaptic spikes (Feldman, 2012). Recent works using STDP trained SNNs have demonstrated promising results as an unsupervised learning paradigm for various tasks such as object classification and recognition (She et al., 2021; Diehl and Cook, 2015; Kheradpisheh et al., 2018). The generalizability is a measure of how well an ML model performs on test data that lies outside of the distribution of the training samples (Kawaguchi et al., 2017; Neyshabur et al., 2017). The generalization properties of Stochastic Gradient Descent (SGD) based training for deep neural network (DNN) have received significant attention in recent years (Poggio et al., 2019; Allen-Zhu et al., 2018; Allen-Zhu and Li, 2019). The dynamics of SGD have been studied via models of stochastic gradient Langevin dynamics with an assumption that gradient noise is Gaussian (Simsekli et al., 2020b). Here SGD is considered to be driven by a Brownian motion. Chen et al. showed that SGD dynamics commonly exhibit highly anisotropic and dynamic-changing properties (Chen et al., 2020), suggesting the presence of

Data-driven discovery of partial differential equations (PDEs) has achieved considerable development in recent years. Several aspects of problems have been resolved by sparse regression-based and neural network-based methods. However, the performances of existing methods lack stability when dealing with complex situations, including sparse data with high noise, high-order derivatives and shock waves, which bring obstacles to calculating derivatives accurately. Therefore, a robust PDE discovery framework, called the robust deep learning-genetic algorithm (R-DLGA), that incorporates the physics-informed neural network (PINN), is proposed in this work. In the framework, a preliminary result of potential terms provided by the deep learning-genetic algorithm is added into the loss function of the PINN as physical constraints to improve the accuracy of derivative calculation. It assists to optimize the preliminary result and obtain the ultimately discovered PDE by eliminating the error compensation terms. The stability and accuracy of the proposed R-DLGA in several complex situations are examined for proof-and-concept, and the results prove that the proposed framework is able to calculate derivatives accurately with the optimization of PINN and possesses surprising robustness to complex situations, including sparse data with high noise, high-order derivatives, and shock waves.

Although deep-learning has been successfully applied in a variety of science and engineering problems owing to its strong high-dimensional nonlinear mapping capability, it is of limited use in scientific knowledge discovery. In this work, we propose a deep-learning based framework to discover the macroscopic governing equation of viscous gravity current based on high-resolution microscopic simulation data without the need for prior knowledge of underlying terms. For two typical scenarios with different viscosity ratios, the deep-learning based equations exactly capture the same dominated terms as the theoretically derived equations for describing long-term asymptotic behaviors, which validates the proposed framework. Unknown macroscopic equations are then obtained for describing short-term behaviors, and hidden mechanisms are eventually discovered with deep-learned explainable compensation terms and corresponding coefficients. Consequently, the presented deep-learning framework shows considerable potential for discovering unrevealed intrinsic laws in scientific semantic space from raw experimental or simulation results in data space.

In this paper, we investigate a new multi-armed bandit (MAB) online learning model that considers real-world phenomena in many recommender systems: (i) the learning agent cannot pull the arms by itself and thus has to offer rewards to users to incentivize arm-pulling indirectly; and (ii) if users with specific arm preferences are well rewarded, they induce a "self-reinforcing" effect in the sense that they will attract more users of similar arm preferences. Besides addressing the tradeoff of exploration and exploitation, another key feature of this new MAB model is to balance reward and incentivizing payment. The goal of the agent is to maximize the total reward over a fixed time horizon $T$ with a low total payment. Our contributions in this paper are two-fold: (i) We propose a new MAB model with random arm selection that considers the relationship of users' self-reinforcing preferences and incentives; and (ii) We leverage the properties of a multi-color Polya urn with nonlinear feedback model to propose two MAB policies termed "At-Least-$n$ Explore-Then-Commit" and "UCB-List". We prove that both policies achieve $O(log T)$ expected regret with $O(log T)$ expected payment over a time horizon $T$. We conduct numerical simulations to demonstrate and verify the performances of these two policies and study their robustness under various settings.

We consider the non-stationary multi-armed bandit (MAB) framework and propose a Kolmogorov-Smirnov (KS) test based Thompson Sampling (TS) algorithm named TS-KS, that actively detects change points and resets the TS parameters once a change is detected. In particular, for the two-armed bandit case, we derive bounds on the number of samples of the reward distribution to detect the change once it occurs. Consequently, we show that the proposed algorithm has sub-linear regret. Contrary to existing works, our algorithm is able to detect a change when the underlying reward distribution changes even though the mean reward remains the same. Finally, to test the efficacy of the proposed algorithm, we employ it in two case-studies: i) task-offloading scenario in wireless edge-computing, and ii) portfolio optimization. Our results show that the proposed TS-KS algorithm outperforms not only the static TS algorithm but also it performs better than other bandit algorithms designed for non-stationary environments. Moreover, the performance of TS-KS is at par with the state-of-the-art forecasting algorithms such as Facebook-PROPHET and ARIMA.

The increased digitalisation and monitoring of the energy system opens up numerous opportunities % and solutions which can help to decarbonise the energy system. Applications on low voltage (LV), localised networks, such as community energy markets and smart storage will facilitate decarbonisation, but they will require advanced control and management. Reliable forecasting will be a necessary component of many of these systems to anticipate key features and uncertainties. Despite this urgent need, there has not yet been an extensive investigation into the current state-of-the-art of low voltage level forecasts, other than at the smart meter level. This paper aims to provide a comprehensive overview of the landscape, current approaches, core applications, challenges and recommendations. Another aim of this paper is to facilitate the continued improvement and advancement in this area. To this end, the paper also surveys some of the most relevant and promising trends. It establishes an open, community-driven list of the known LV level open datasets to encourage further research and development.

LKAB, Minalyze AB and Sentian say they have joined forces in a consortium to develop the latest technology for scanning drill core. In March 2020, LKAB started a test with the Minalyzer CS drill core scanner where the goal was to improve the workflow for core logging – ie how the results of exploration drilling are analysed. The test led to a permanent installation in Kiruna (Sweden) and expansion to Malmberget where data from the Minalyzer CS is used to help geological logging of the drill core. The consortium of LKAB, Minalyze and Sentian are now set to take the use of data to the next level when boreholes in LKAB's deposits are to be investigated. The new artificial intelligence application being developed by the trio will make the analysis much faster, with the time to evaluate a drill core reduced from weeks to minutes, with increased accuracy.

Plant metabolites consist of a wide range of extremely important chemicals. Many, such as the malaria drug artemisinin, have remarkable therapeutic properties, while others, like natural rubber or biofuel from tree sap, have mechanical properties. Because most plant metabolites are isolated in individual cells, the method of extracting the metabolites is also important, since the procedure affects both product purity and yield. Usually the extraction involves grinding, centrifugation, and chemical treatment using solvents. This results in considerable pollution, which contributes to the high financial and environmental processing costs.

As was mentioned earlier in this article, Type Curves that are generated using mathematical equations are very "well-behaved" (continuous, non-linear, certain shape that changes in a similar fashion from curve to curve). Figure 16 demonstrates few more examples of Type Curves that have been generated in reservoir engineering. The question is, "what is the main characteristic of a model that is capable of generating series of well-behave Type Curves?" The immediate, simple answer to this question would be: "the model that is capable of generating a series of well-behave Type Curves is a physics-based model developed by one or more mathematical equations. The well-behave Type Curves that clearly explain the behavior of the physics-based model are generated through the solutions of the mathematical equations."

So maybe you can make it more tangible. But that's the understanding I have. Where do you really see digital twins driving value in terms of day-to-day decisions for executives who really need to steer the company?