We consider end-to-end learning approaches for inverse problems of gravimetry. Due to ill-posedness of the inverse gravimetry, the reliability of learning approaches is questionable. To deal with this problem, we propose the strategy of learning on the correct class. The well-posedness theorems are employed when designing the neural-network architecture and constructing the training set. Given the density-contrast function as a priori information, the domain of mass can be uniquely determined under certain constrains, and the domain inverse problem is a correct class of the inverse gravimetry. Under this correct class, we design the neural network for learning by mimicking the level-set formulation for the inverse gravimetry. Numerical examples illustrate that the method is able to recover mass models with non-constant density contrast.
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Given a dataset of expert demonstrations, inverse reinforcement learning (IRL) aims to recover a reward for which the expert is optimal. This work proposes a model-free algorithm to solve entropy-regularized IRL problem. In particular, we employ a stochastic gradient descent update for the reward and a stochastic soft policy iteration update for the policy. Assuming access to a generative model, we prove that our algorithm is guaranteed to recover a reward for which the expert is $\varepsilon$-optimal using $\mathcal{O}(1/\varepsilon^{2})$ samples of the Markov decision process (MDP). Furthermore, with $\mathcal{O}(1/\varepsilon^{4})$ samples we prove that the optimal policy corresponding to the recovered reward is $\varepsilon$-close to the expert policy in total variation distance.
Despite the widespread applications of machine learning force field (MLFF) on solids and small molecules, there is a notable gap in applying MLFF to complex liquid electrolytes. In this work, we introduce BAMBOO (ByteDance AI Molecular Simulation Booster), a novel framework for molecular dynamics (MD) simulations, with a demonstration of its capabilities in the context of liquid electrolytes for lithium batteries. We design a physics-inspired graph equivariant transformer architecture as the backbone of BAMBOO to learn from quantum mechanical simulations. Additionally, we pioneer an ensemble knowledge distillation approach and apply it on MLFFs to improve the stability of MD simulations. Finally, we propose the density alignment algorithm to align BAMBOO with experimental measurements. BAMBOO demonstrates state-of-the-art accuracy in predicting key electrolyte properties such as density, viscosity, and ionic conductivity across various solvents and salt combinations. Our current model, trained on more than 15 chemical species, achieves the average density error of 0.01 g/cm$^3$ on various compositions compared with experimental data. Moreover, our model demonstrates transferability to molecules not included in the quantum mechanical dataset. We envision this work as paving the way to a "universal MLFF" capable of simulating properties of common organic liquids.
In the present contribution we propose a novel conforming Finite Element scheme for the time-dependent Navier-Stokes equation, which is proven to be both convection quasi-robust and pressure robust. The method is built combining a "divergence-free" velocity/pressure couple (such as the Scott-Vogelius element), a Discontinuous Galerkin in time approximation, and a suitable SUPG-curl stabilization. A set of numerical tests, in accordance with the theoretical results, is included.
Cross-validation is usually employed to evaluate the performance of a given statistical methodology. When such a methodology depends on a number of tuning parameters, cross-validation proves to be helpful to select the parameters that optimize the estimated performance. In this paper, however, a very different and nonstandard use of cross-validation is investigated. Instead of focusing on the cross-validated parameters, the main interest is switched to the estimated value of the error criterion at optimal performance. It is shown that this approach is able to provide consistent and efficient estimates of some density functionals, with the noteworthy feature that these estimates do not rely on the choice of any further tuning parameter, so that, in that sense, they can be considered to be purely empirical. Here, a base case of application of this new paradigm is developed in full detail, while many other possible extensions are hinted as well.
This work presents a new algorithm to compute the matrix exponential within a given tolerance. Combined with the scaling and squaring procedure, the algorithm incorporates Taylor, partitioned and classical Pad\'e methods shown to be superior in performance to the approximants used in state-of-the-art software. The algorithm computes matrix--matrix products and also matrix inverses, but it can be implemented to avoid the computation of inverses, making it convenient for some problems. If the matrix A belongs to a Lie algebra, then exp(A) belongs to its associated Lie group, being a property which is preserved by diagonal Pad\'e approximants, and the algorithm has another option to use only these. Numerical experiments show the superior performance with respect to state-of-the-art implementations.
While computer modeling and simulation are crucial for understanding scientometrics, their practical use in literature remains somewhat limited. In this study, we establish a joint coauthorship and citation network using preferential attachment. As papers get published, we update the coauthorship network based on each paper's author list, representing the collaborative team behind it. This team is formed considering the number of collaborations each author has, and we introduce new authors at a fixed probability, expanding the coauthorship network. Simultaneously, as each paper cites a specific number of references, we add an equivalent number of citations to the citation network upon publication. The likelihood of a paper being cited depends on its existing citations, fitness value, and age. Then we calculate the journal impact factor and h-index, using them as examples of scientific impact indicators. After thorough validation, we conduct case studies to analyze the impact of different parameters on the journal impact factor and h-index. The findings reveal that increasing the reference number N or reducing the paper's lifetime {\theta} significantly boosts the journal impact factor and average h-index. On the other hand, enlarging the team size m without introducing new authors or decreasing the probability of newcomers p notably increases the average h-index. In conclusion, it is evident that various parameters influence scientific impact indicators, and their interpretation can be manipulated by authors. Thus, exploring the impact of these parameters and continually refining scientific impact indicators are essential. The modeling and simulation method serves as a powerful tool in this ongoing process, and the model can be easily extended to include other scientific impact indicators and scenarios.
In this study, our main objective is to address the challenge of solving elliptic equations with quasiperiodic coefficients. To achieve accurate and efficient computation, we introduce the projection method, which enables the embedding of quasiperiodic systems into higher-dimensional periodic systems. To enhance the computational efficiency, we propose a compressed storage strategy for the stiffness matrix by its multi-level block circulant structure, reducing memory requirements while preserving accuracy. Furthermore, we design a diagonal preconditioner to efficiently solve the resulting high-dimensional linear system by reducing the condition number of the stiffness matrix. These techniques collectively contribute to the computational effectiveness of our proposed approach. We demonstrate the effectiveness and accuracy of our approach through a series of numerical examples. Moreover, we apply our method to achieve a highly accurate computation of the homogenized coefficients for a quasiperiodic multiscale elliptic equation.
We hypothesize that due to the greedy nature of learning in multi-modal deep neural networks, these models tend to rely on just one modality while under-fitting the other modalities. Such behavior is counter-intuitive and hurts the models' generalization, as we observe empirically. To estimate the model's dependence on each modality, we compute the gain on the accuracy when the model has access to it in addition to another modality. We refer to this gain as the conditional utilization rate. In the experiments, we consistently observe an imbalance in conditional utilization rates between modalities, across multiple tasks and architectures. Since conditional utilization rate cannot be computed efficiently during training, we introduce a proxy for it based on the pace at which the model learns from each modality, which we refer to as the conditional learning speed. We propose an algorithm to balance the conditional learning speeds between modalities during training and demonstrate that it indeed addresses the issue of greedy learning. The proposed algorithm improves the model's generalization on three datasets: Colored MNIST, Princeton ModelNet40, and NVIDIA Dynamic Hand Gesture.
We derive information-theoretic generalization bounds for supervised learning algorithms based on the information contained in predictions rather than in the output of the training algorithm. These bounds improve over the existing information-theoretic bounds, are applicable to a wider range of algorithms, and solve two key challenges: (a) they give meaningful results for deterministic algorithms and (b) they are significantly easier to estimate. We show experimentally that the proposed bounds closely follow the generalization gap in practical scenarios for deep learning.
When and why can a neural network be successfully trained? This article provides an overview of optimization algorithms and theory for training neural networks. First, we discuss the issue of gradient explosion/vanishing and the more general issue of undesirable spectrum, and then discuss practical solutions including careful initialization and normalization methods. Second, we review generic optimization methods used in training neural networks, such as SGD, adaptive gradient methods and distributed methods, and theoretical results for these algorithms. Third, we review existing research on the global issues of neural network training, including results on bad local minima, mode connectivity, lottery ticket hypothesis and infinite-width analysis.
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