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This paper focuses on the Partitioned-Solution Approach (PSA) employed for the Time-Domain Simulation (TDS) of dynamic power system models. In PSA, differential equations are solved at each step of the TDS for state variables, whereas algebraic equations are solved separately. The goal of this paper is to propose a novel, matrix-pencil based technique to study numerical stability and accuracy of PSA in a unified way. The proposed technique quantifies the numerical deformation that PSA-based methods introduce to the dynamics of the power system model, and allows estimating useful upper time step bounds that achieve prescribed simulation accuracy criteria. The family of Predictor-Corrector (PC) methods, which is commonly applied in practical implementations of PSA, is utilized to illustrate the proposed technique. Simulations are carried out on the IEEE 39-bus system, as well as on a 1479-bus model of the All-Island Irish Transmission System (AIITS).

The first globally convergent numerical method for a Coefficient Inverse Problem (CIP) for the Riemannian Radiative Transfer Equation (RRTE) is constructed. This is a version of the so-called \textquotedblleft convexification" method, which has been pursued by this research group for a number of years for some other CIPs for PDEs. Those PDEs are significantly different from the RRTE. The presence of the Carleman Weight Function (CWF) in the numerical scheme is the key element which insures the global convergence. Convergence analysis is presented along with the results of numerical experiments, which confirm the theory. RRTE governs the propagation of photons in the diffuse medium in the case when they propagate along geodesic lines between their collisions. Geodesic lines are generated by the spatially variable dielectric constant of the medium.

Recent advances in deep learning have accelerated its use in various applications, such as cellular image analysis and molecular discovery. In molecular discovery, a generative adversarial network (GAN), which comprises a discriminator to distinguish generated molecules from existing molecules and a generator to generate new molecules, is one of the premier technologies due to its ability to learn from a large molecular data set efficiently and generate novel molecules that preserve similar properties. However, different pharmaceutical companies may be unwilling or unable to share their local data sets due to the geo-distributed and sensitive nature of molecular data sets, making it impossible to train GANs in a centralized manner. In this paper, we propose a Graph convolutional network in Generative Adversarial Networks via Federated learning (GraphGANFed) framework, which integrates graph convolutional neural Network (GCN), GAN, and federated learning (FL) as a whole system to generate novel molecules without sharing local data sets. In GraphGANFed, the discriminator is implemented as a GCN to better capture features from molecules represented as molecular graphs, and FL is used to train both the discriminator and generator in a distributive manner to preserve data privacy. Extensive simulations are conducted based on the three bench-mark data sets to demonstrate the feasibility and effectiveness of GraphGANFed. The molecules generated by GraphGANFed can achieve high novelty (=100) and diversity (> 0.9). The simulation results also indicate that 1) a lower complexity discriminator model can better avoid mode collapse for a smaller data set, 2) there is a tradeoff among different evaluation metrics, and 3) having the right dropout ratio of the generator and discriminator can avoid mode collapse.

We present angle-uniform parallel coordinates, a data-independent technique that deforms the image plane of parallel coordinates so that the angles of linear relationships between two variables are linearly mapped along the horizontal axis of the parallel coordinates plot. Despite being a common method for visualizing multidimensional data, parallel coordinates are ineffective for revealing positive correlations since the associated parallel coordinates points of such structures may be located at infinity in the image plane and the asymmetric encoding of negative and positive correlations may lead to unreliable estimations. To address this issue, we introduce a transformation that bounds all points horizontally using an angle-uniform mapping and shrinks them vertically in a structure-preserving fashion; polygonal lines become smooth curves and a symmetric representation of data correlations is achieved. We further propose a combined subsampling and density visualization approach to reduce visual clutter caused by overdrawing. Our method enables accurate visual pattern interpretation of data correlations, and its data-independent nature makes it applicable to all multidimensional datasets. The usefulness of our method is demonstrated using examples of synthetic and real-world datasets.

PDE-constrained inverse problems are some of the most challenging and computationally demanding problems in computational science today. Fine meshes that are required to accurately compute the PDE solution introduce an enormous number of parameters and require large scale computing resources such as more processors and more memory to solve such systems in a reasonable time. For inverse problems constrained by time dependent PDEs, the adjoint method that is often employed to efficiently compute gradients and higher order derivatives requires solving a time-reversed, so-called adjoint PDE that depends on the forward PDE solution at each timestep. This necessitates the storage of a high dimensional forward solution vector at every timestep. Such a procedure quickly exhausts the available memory resources. Several approaches that trade additional computation for reduced memory footprint have been proposed to mitigate the memory bottleneck, including checkpointing and compression strategies. In this work, we propose a close-to-ideal scalable compression approach using autoencoders to eliminate the need for checkpointing and substantial memory storage, thereby reducing both the time-to-solution and memory requirements. We compare our approach with checkpointing and an off-the-shelf compression approach on an earth-scale ill-posed seismic inverse problem. The results verify the expected close-to-ideal speedup for both the gradient and Hessian-vector product using the proposed autoencoder compression approach. To highlight the usefulness of the proposed approach, we combine the autoencoder compression with the data-informed active subspace (DIAS) prior to show how the DIAS method can be affordably extended to large scale problems without the need of checkpointing and large memory.

The atomic cluster expansion (ACE) (Drautz, 2019) yields a highly efficient and intepretable parameterisation of symmetric polynomials that has achieved great success in modelling properties of many-particle systems. In the present work we extend the practical applicability of the ACE framework to the computation of many-electron wave functions. To that end, we develop a customized variational Monte-Carlo algorithm that exploits the sparsity and hierarchical properties of ACE wave functions. We demonstrate the feasibility on a range of proof-of-concept applications to one-dimensional systems.

We study vulnerability of a uniformly distributed random graph to an attack by an adversary who aims for a global change of the distribution while being able to make only a local change in the graph. We call a graph property $A$ anti-stochastic if the probability that a random graph $G$ satisfies $A$ is small but, with high probability, there is a small perturbation transforming $G$ into a graph satisfying $A$. While for labeled graphs such properties are easy to obtain from binary covering codes, the existence of anti-stochastic properties for unlabeled graphs is not so evident. If an admissible perturbation is either the addition or the deletion of one edge, we exhibit an anti-stochastic property that is satisfied by a random unlabeled graph of order $n$ with probability $(2+o(1))/n^2$, which is as small as possible. We also express another anti-stochastic property in terms of the degree sequence of a graph. This property has probability $(2+o(1))/(n\ln n)$, which is optimal up to factor of 2.

A relational dataset is often analyzed by optimally assigning a label to each element through clustering or ordering. While similar characterizations of a dataset would be achieved by both clustering and ordering methods, the former has been studied much more actively than the latter, particularly for the data represented as graphs. This study fills this gap by investigating methodological relationships between several clustering and ordering methods, focusing on spectral techniques. Furthermore, we evaluate the resulting performance of the clustering and ordering methods. To this end, we propose a measure called the label continuity error, which generically quantifies the degree of consistency between a sequence and partition for a set of elements. Based on synthetic and real-world datasets, we evaluate the extents to which an ordering method identifies a module structure and a clustering method identifies a banded structure.

Underwater imagery often exhibits distorted coloration as a result of light-water interactions, which complicates the study of benthic environments in marine biology and geography. In this research, we propose an algorithm to restore the true color (albedo) in underwater imagery by jointly learning the effects of the medium and neural scene representations. Our approach models water effects as a combination of light attenuation with distance and backscattered light. The proposed neural scene representation is based on a neural reflectance field model, which learns albedos, normals, and volume densities of the underwater environment. We introduce a logistic regression model to separate water from the scene and apply distinct light physics during training. Our method avoids the need to estimate complex backscatter effects in water by employing several approximations, enhancing sampling efficiency and numerical stability during training. The proposed technique integrates underwater light effects into a volume rendering framework with end-to-end differentiability. Experimental results on both synthetic and real-world data demonstrate that our method effectively restores true color from underwater imagery, outperforming existing approaches in terms of color consistency.

Coupled cluster theory is considered to be the ``gold standard'' ansatz of molecular quantum chemistry. The finite-size error of the correlation energy in periodic coupled cluster calculations for three-dimensional insulating systems has been observed to satisfy the inverse volume scaling, even in the absence of any correction schemes. This is surprising, as simpler theories that utilize only a subset of the coupled cluster diagrams exhibit much slower decay of the finite-size error, which scales inversely with the length of the system. In this study, we present a rigorous numerical analysis that explains the underlying mechanisms behind this phenomenon in the context of coupled cluster doubles (CCD) calculations, and reconciles a few seemingly paradoxical statements with respect to the finite-size scaling. Our findings also have implications on how to effectively address finite-size errors in practical quantum chemistry calculations for periodic systems.