Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China (Dated: September 26, 2023) We developed a deep generative model-based variational free energy approach to the equations of state of dense hydrogen. We employ a normalizing flow network to model the proton Boltzmann distribution and a fermionic neural network to model the electron wave function at given proton positions. By jointly optimizing the two neural networks we reached a comparable variational free energy to the previous coupled electron-ion Monte Carlo calculation. The predicted equation of state of dense hydrogen under planetary conditions is denser than the findings of ab initio molecular dynamics calculation and empirical chemical model. Moreover, direct access to the entropy and free energy of dense hydrogen opens new opportunities in planetary modeling and high-pressure physics research. Hydrogen is the most abundant element in the visible universe.

While exogenous variables have a major impact on performance improvement in time series analysis, inter-series correlation and time dependence among them are rarely considered in the present continuous methods. The dynamical systems of multivariate time series could be modelled with complex unknown partial differential equations (PDEs) which play a prominent role in many disciplines of science and engineering. In this paper, we propose a continuous-time model for arbitrary-step prediction to learn an unknown PDE system in multivariate time series whose governing equations are parameterised by self-attention and gated recurrent neural networks. The proposed model, \underline{E}xogenous-\underline{g}uided \underline{P}artial \underline{D}ifferential \underline{E}quation Network (EgPDE-Net), takes account of the relationships among the exogenous variables and their effects on the target series. Importantly, the model can be reduced into a regularised ordinary differential equation (ODE) problem with special designed regularisation guidance, which makes the PDE problem tractable to obtain numerical solutions and feasible to predict multiple future values of the target series at arbitrary time points. Extensive experiments demonstrate that our proposed model could achieve competitive accuracy over strong baselines: on average, it outperforms the best baseline by reducing $9.85\%$ on RMSE and $13.98\%$ on MAE for arbitrary-step prediction.

It is widely acknowledged that trained convolutional neural networks (CNNs) have different levels of sensitivity to signals of different frequency. In particular, a number of empirical studies have documented CNNs sensitivity to low-frequency signals. In this work we show with theory and experiments that this observed sensitivity is a consequence of the frequency distribution of natural images, which is known to have most of its power concentrated in low-to-mid frequencies. Our theoretical analysis relies on representations of the layers of a CNN in frequency space, an idea that has previously been used to accelerate computations and study implicit bias of network training algorithms, but to the best of our knowledge has not been applied in the domain of model robustness.

We introduce a fully 3D, deep learning-based approach for the joint inversion of time-lapse surface gravity and seismic data for reconstructing subsurface density and velocity models. The target application of this proposed inversion approach is the prediction of subsurface CO2 plumes as a complementary tool for monitoring CO2 sequestration deployments. Our joint inversion technique outperforms deep learning-based gravity-only and seismic-only inversion models, achieving improved density and velocity reconstruction, accurate segmentation, and higher R-squared coefficients. These results indicate that deep learning-based joint inversion is an effective tool for CO$_2$ storage monitoring. Future work will focus on validating our approach with larger datasets, simulations with other geological storage sites, and ultimately field data.

Offline reinforcement learning (RL) methods strike a balance between exploration and exploitation by conservative value estimation -- penalizing values of unseen states and actions. Model-free methods penalize values at all unseen actions, while model-based methods are able to further exploit unseen states via model rollouts. However, such methods are handicapped in their ability to find unseen states far away from the available offline data due to two factors -- (a) very short rollout horizons in models due to cascading model errors, and (b) model rollouts originating solely from states observed in offline data. We relax the second assumption and present a novel unseen state augmentation strategy to allow exploitation of unseen states where the learned model and value estimates generalize. Our strategy finds unseen states by value-informed perturbations of seen states followed by filtering out states with epistemic uncertainty estimates too high (high error) or too low (too similar to seen data). We observe improved performance in several offline RL tasks and find that our augmentation strategy consistently leads to overall lower average dataset Q-value estimates i.e. more conservative Q-value estimates than a baseline.

Participant selection (PS) helps to accelerate federated learning (FL) convergence, which is essential for the practical deployment of FL over mobile devices. While most existing PS approaches focus on improving training accuracy and efficiency rather than residual energy of mobile devices, which fundamentally determines whether the selected devices can participate. Meanwhile, the impacts of mobile devices' heterogeneous wireless transmission rates on PS and FL training efficiency are largely ignored. Moreover, PS causes the staleness issue. Prior research exploits isolated functions to force long-neglected devices to participate, which is decoupled from original PS designs. In this paper, we propose a residual energy and wireless aware PS design for efficient FL training over mobile devices (REWAFL). REW AFL introduces a novel PS utility function that jointly considers global FL training utilities and local energy utility, which integrates energy consumption and residual battery energy of candidate mobile devices. Under the proposed PS utility function framework, REW AFL further presents a residual energy and wireless aware local computing policy. Besides, REWAFL buries the staleness solution into its utility function and local computing policy. The experimental results show that REW AFL is effective in improving training accuracy and efficiency, while avoiding "flat battery" of mobile devices.

Empirical risk minimization (ERM) and distributionally robust optimization (DRO) are popular approaches for solving stochastic optimization problems that appear in operations management and machine learning. Existing generalization error bounds for these methods depend on either the complexity of the cost function or dimension of the random perturbations. Consequently, the performance of these methods can be poor for high-dimensional problems with complex objective functions. We propose a simple approach in which the distribution of random perturbations is approximated using a parametric family of distributions. This mitigates both sources of complexity; however, it introduces a model misspecification error. We show that this new source of error can be controlled by suitable DRO formulations. Our proposed parametric DRO approach has significantly improved generalization bounds over existing ERM and DRO methods and parametric ERM for a wide variety of settings. Our method is particularly effective under distribution shifts and works broadly in contextual optimization. We also illustrate the superior performance of our approach on both synthetic and real-data portfolio optimization and regression tasks.

It has been called the new gold rush – a rush to catch up with China in producing and refining the materials needed in everything from computers to cars: but has it come too late to save Europe's car industry? Deep inside a former East German town lies the first fruits of the EU's grand plan to "de-risk" and wean itself off dependency on imports for the green revolution. In Bitterfeld-Wolfen, 140km south-west of Berlin, an Amsterdam-listed company is scrambling to complete construction of a vast factory that will be the first in Europe to deliver battery-grade lithium. There is now a race across Europe to both mine the silver-white soft metal and manufacture its refined form, lithium hydroxide – the key ingredient in the batteries that power electric cars, robot vacuum cleaners and mobile phones. "Everybody wants to get access to lithium. This is maybe why they call it the white gold, because it is like a gold rush," says Stefan Scherer, chief executive of AMG Lithium.

Figure 1 | Schematic overview of the data regimes for which we show experimental results. These regimes are characterized by how much data from the target environment is available to the agent, and how much (potentially generalizable) experience has been collected in other environments. The experiments both demonstrate that TDMs are capable single-environment models (marked purple) and generalize across environments (marked yellow). If sufficient data from the target environment is available, we can learn a single-environment specialist model (section 5.1). If there are only small amounts of data from the target environment, but more data from other environments, a generalist model can be pre-trained and then fine-tuned on the target environment (section 5.2.1). Finally, if we are able to train a generalist model on large amounts of data from different environments, we can zero-shot apply this model to our target environment without fine-tuning (section 5.2.2). We also show an example for unsuccessful generalization (no color) in section E.

This paper studies decentralized online convex optimization in a networked multi-agent system and proposes a novel algorithm, Learning-Augmented Decentralized Online optimization (LADO), for individual agents to select actions only based on local online information. LADO leverages a baseline policy to safeguard online actions for worst-case robustness guarantees, while staying close to the machine learning (ML) policy for average performance improvement. In stark contrast with the existing learning-augmented online algorithms that focus on centralized settings, LADO achieves strong robustness guarantees in a decentralized setting. We also prove the average cost bound for LADO, revealing the tradeoff between average performance and worst-case robustness and demonstrating the advantage of training the ML policy by explicitly considering the robustness requirement.