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Conclusions: certain data-driven models do implicitly what physics simulations do explicitly; theoretical underpinnings in Koopman theory, delay-coordinate embeddings, and Mori-Zwanzig formalism; best approach for given system with finite data an open question; physics-informed machine learning (PIML) emerging framework for combining explicit and implicit modeling.
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This paper considers the problem of recovering missing entries in a partially observed matrix from relatively few measurements (i.e., the so-called matrix completion problem) with the aim of increasing the presently limited observability of low-voltage distribution grids. To this end, the partially observed matrix is formed using scarce voltage magnitude measurements while accounting for their spatial information. Voltage readings are assumed to be collected from distribution utility sensors and/or geographically-distributed cable television network sensors located in immediate proximity to distribution grid nodes. A matrix completion approach built on the parameter-less singular value shrinkage technique is used to estimate voltage magnitudes at otherwise non-observable low-voltage nodes using a small number of single- or multiple-snapshot data. The effectiveness of the proposed approach is demonstrated using a U.S.-style distribution test system from the synthetic SMART- DS data set under very low- to moderate-observability conditions.
We consider a high-dimensional nonlinear computational model of a dynamical system, parameterized by a vector-valued control parameter, in the presence of uncertainties represented by an uncontrolled parameter modeled by a vector-valued random variable, and possibly with stochastic excitation. The objective is to construct a statistical surrogate model where the input is any deterministic value of the control parameter, and the output is a vector-valued observation of the computational model, which is a random vector whose probability measure is updated using a target dataset. To construct this statistical surrogate model, the stochastic response of the computational model must be built, which is a vector-valued time-discretized stochastic process in high dimension, depending on the control parameter. It is assumed that the computational cost of a single evaluation of the deterministic model is high. For the probabilistic updating, we consider a subset of the components of the observation of the computational model, defined as the “identification observation” of the computational model, for which a small target dataset is available. Therefore, the target dataset is associated with partial observability, corresponding to an incomplete data case. Given a prior probability model of the random control and uncontrolled parameters, a training dataset is constructed, consisting of realizations of the random triplet composed of the stochastic response, the random identification observation, and the random control parameter. Since the computational cost of a single evaluation of the deterministic model is assumed to be large, the training dataset is also of small size. The main challenges in this problem are the high dimensionality, partial observability leading to incomplete data in the target dataset for the identification observation of the computational model (which is not sufficient to identify the computational stochastic responses), and the availability of a small training dataset. To address these challenges, we propose a methodology based on statistical methods for constructing necessary reduced representations, direct probabilistic learning under constraints using probabilistic learning on manifolds (PLoM) constrained by the target dataset, and the use of a weak formulation of the Fourier transform of probability measures. Statistical conditioning is also employed to explore the learned dataset. The constructed predictive statistical surrogate model can be implemented in the context of online computation. Here, we apply this approach to a problem of nonlinear stochastic dynamics in high dimensions within the framework of deformable solids mechanics.
Most problems within and beyond the scientific domain can be framed into one of the following three levels of complexity of function approximation. Type 1: Approximate an unknown function given input/output data. Type 2: Consider a collection of variables and functions, some of which are unknown, indexed by the nodes and hyperedges of a hypergraph (a generalized graph where edges can connect more than two vertices). Given partial observations of the variables of the hypergraph (satisfying the functional dependencies imposed by its structure), approximate all the unobserved variables and unknown functions. Type 3: Expanding on Type 2, if the hypergraph structure itself is unknown, use partial observations of the variables of the hypergraph to discover its structure and approximate its unknown functions. These hypergraphs offer a natural platform for organizing, communicating, and processing computational knowledge. While most scientific problems can be framed as the data-driven discovery of unknown functions in a computational hypergraph whose structure is known (Type 2), many require the data-driven discovery of the structure (connectivity) of the hypergraph itself (Type 3). We introduce an interpretable Gaussian Process (GP) framework for such (Type 3) problems that does not require randomization of the data, access to or control over its sampling, or sparsity of the unknown functions in a known or learned basis. Its polynomial complexity, which contrasts sharply with the super-exponential complexity of causal inference methods, is enabled by the nonlinear ANOVA capabilities of GPs used as a sensing mechanism.
The precise knowledge regarding the state of the power grid is important in order to ensure optimal and reliable grid operation. Specifically, knowing the state of the distribution grid becomes increasingly important as more renewable energy sources are connected directly into the distribution network, increasing the fluctuations of the injected power. In this paper, we consider the case when the distribution grid becomes partially observable, due to for example cyber attacks, and the state estimation problem is under-determined. We present a new methodology that leverages a deep neural network (DNN) to estimate the grid state. The standard DNN training method is modified to explicitly incorporate the physical information of the grid topology and line/shunt admittance. We show that our method leads to a superior accuracy of the estimation when compared to the case when no physical information is provided. Finally, we compare the performance of our method to the standard state estimation approach, which is based on the weighted least squares with pseudo-measurements, and show that our method performs significantly better with respect to the estimation accuracy.
Nuclear research articles can provide information about early nuclear proliferation indicators such as influential research entities and technology capability levels of a country, but detection of nuclear activities typically occurs after they have started. We investigate the extent to which nuclear research articles can be used to infer whether a research entity will acquire or develop a nuclear technology before it happens. Early detection of nuclear proliferation or technology development indicators from data is challenging due to partial observability, sparse and unlabeled information, and confounding signals from multiple concurrent activities. This paper presents the early detection problem as a sequential decision-making, goal inference problem, where the objective is to characterize and predict an individual’s, organization’s, or a country’s intent (unobserved goal-directed behavior) towards developing a nuclear capability from partially observed sequences of their research publications, using inverse reinforcement learning and Bayesian goal inference methods. A computational framework is presented, and its application demonstrated using 29,196 Scopus records for a case study related to a civil nuclear capability. The case study results serve as a proof-of-concept demonstration for inference of technology-directed research activity of authors who publish in the nuclear domain. The inference method, combined with advanced computing, may be used to assess and monitor activities pertaining to early developmental stages of a nuclear technology or capability, which in turn can help to identify and prioritize activities with nuclear proliferation potential for further investigation.
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Efficient outage location is critical to enhancing the resilience of power distribution systems. However, accurate outage location requires combining massive evidence received from diverse data sources, including smart meter (SM) last gasp signals, customer trouble calls, social media messages, weather data, vegetation information, and physical parameters of the network. This is a computationally complex task due to the high dimensionality of data in distribution grids. In this paper, we propose a multi-source data fusion approach to locate outage events in partially observable distribution systems using Bayesian networks (BNs). A novel aspect of the proposed approach is that it takes multi-source evidence and the complex structure of distribution systems into account using a probabilistic graphical method. Our method can radically reduce the computational complexity of outage location inference in high-dimensional spaces. The graphical structure of the proposed BN is established based on the network’s topology and the causal relationship between random variables, such as the states of branches/customers and evidence. Utilizing this graphical model, accurate outage locations are obtained by leveraging a Gibbs sampling (GS) method, to infer the probabilities of de-energization for all branches. Compared with commonly-used exact inference methods that have exponential complexity in the size of the BN, GS quantifies the target conditional probability distributions in a timely manner. As a result, a case study of several real-world distribution systems is presented to validate the proposed method.
Electronic health records (EHR) are not designed for population‐based research, but they provide easy and quick access to longitudinal health information for a large number of individuals. Many statistical methods have been proposed to account for selection bias, missing data, phenotyping errors, or other problems that arise in EHR data analysis. However, addressing multiple sources of bias simultaneously is challenging. We developed a methodological framework (R package, SAMBA ) for jointly handling both selection bias and phenotype misclassification in the EHR setting that leverages external data sources. These methods assume factors related to selection and misclassification are fully observed, but these factors may be poorly understood and partially observed in practice. As a follow‐up to the methodological work, we demonstrate how to apply these methods for two real‐world case studies, and we evaluate their performance. In both examples, we use individual patient‐level data collected through the University of Michigan Health System and various external population‐based data sources. In case study (a), we explore the impact of these methods on estimated associations between gender and cancer diagnosis. In case study (b), we compare corrected associations between previously identified genetic loci and age‐related macular degeneration with gold standard external summary estimates. These case studies illustrate how to utilize diverse auxiliary information to achieve less biased inference in EHR‐based research.
We study how meaningful physical predictions can arise in nonperturbative quantum gravity in a closed Lorentzian universe. In such settings, recent developments suggest that the quantum gravitational Hilbert space is one-dimensional and real for each α-sector, as induced by spacetime wormholes. This appears to obstruct the conventional quantum-mechanical prescription of assigning probabilities via projection onto a basis of states. While previous approaches have introduced external observers or augmented the theory to resolve this issue, we argue that quantum gravity itself contains all the necessary ingredients to make physical predictions. We demonstrate that the emergence of classical observables and probabilistic outcomes can be understood as a consequence of partial observability: physical observers access only a subsystem of the universe. Tracing out the inaccessible degrees of freedom yields reduced density matrices that encode classical information, with uncertainties exponentially suppressed by the environment’s entropy. We develop this perspective using both the Lorentzian path integral and operator formalisms and support it with a simple microscopic model. Our results show that quantum gravity in a closed universe naturally gives rise to meaningful, robust predictions without recourse to external constructs.
Biological systems function through complex interactions between various ‘omics (biomolecules), and a more complete understanding of these systems is only possible through an integrated, multi-omic perspective. This has presented the need for the development of integration approaches that are able to capture the complex, often non-linear, interactions that define these biological systems and are adapted to the challenges of combining the heterogenous data across ‘omic views. A principal challenge to multi-omic integration is missing data because all biomolecules are not measured in all samples. Due to either cost, instrument sensitivity, or other experimental factors, data for a biological sample may be missing for one or more ‘omic techologies. Recent methodological developments in artificial intelligence and statistical learning have greatly facilitated the analyses of multi-omics data, however many of these techniques assume access to completely observed data. A subset of these methods incorporate mechanisms for handling partially observed samples, and these methods are the focus of this review. We describe recently developed approaches, noting their primary use cases and highlighting each method's approach to handling missing data. We additionally provide an overview of the more traditional missing data workflows and their limitations; and we discuss potential avenues for further developments as well as how the missing data issue and its current solutions may generalize beyond the multi-omics context.
The goal of this paper is to solve a class of stochastic optimal control problems numerically, in which the state process is governed by an Itô type stochastic differential equation with control process entering both in the drift and the diffusion, and is observed partially. The optimal control of feedback form is determined based on the available observational data. In this work, we call this type of control problems the data driven feedback control. The computational framework that we introduce to solve such type of problems aims to find the best estimate for the optimal control as a conditional expectation given the observational information. To make our method feasible in providing timely feedback to the controlled system from data, we develop an efficient stochastic optimization algorithm to implement our computational framework.
The evolution of characteristic nonequilibrium features presenting in morphologically distinct regions of rapid solidification (RS) microstructures in a hypoeutectic Al—10Cu (atomic %) in response to non-isothermal annealing transients has been studied by transmission electron microscopy (TEM). The capabilities of the Movie-Mode Dynamic TEM (MM-DTEM) instrument were used to expose select regions of the RS microstructure to sequences of rapid heating and cooling transients induced by nanosecond laser pulses while permitting in-situ observation. Partial melting, microstructural scale coarsening, morphological changes of the nonequilibrium features in the multi-phase RS microstructure, and solid-state phase transformation were observed. Heterogeneous nucleation of nanoscale θ-Al 2 Cu phase involved metastable supersaturated α-Al and the θ'-Al 2 Cu phases, establishing different sets of orientation relationships for the stable θ-Al 2 Cu and α-Al phases. Replacement of banded morphology grains that formed under conditions driven farthest from equilibrium by an equiaxed nanocrystalline structure comprised of α-Al phase, the primary solidification product, and an intergranular network of Al 2 Cu crystals has been attributed to local remelting. Here the experimental approach explored, permitted discovery of mechanistic details of location-specific transformation pathways activated in the multi-phase RS microstructure of hypoeutectic Al—Cu during subsequent nonisothermal transients.