The dimension of models derived on the basis of data is commonly restricted by the number of observations, or in the context of monitored systems, sensing nodes. This is particularly true for structural systems, which are typically high-dimensional in nature. In the scope of physics-informed machine learning, this article proposes a framework—termed neural modal ordinary differential equations (Neural Modal ODEs)—to integrate physics-based modeling with deep learning for modeling the dynamics of monitored and high-dimensional engineered systems. In this initiating exploration, we restrict ourselves to linear or mildly nonlinear systems. We propose an architecture that couples a dynamic version of variational autoencoders with physics-informed neural ODEs (Pi-Neural ODEs). An encoder, as a part of the autoencoder, learns the mappings from the first few items of observational data to the initial values of the latent variables, which drive the learning of embedded dynamics via Pi-Neural ODEs, imposing a modal model structure on that latent space. The decoder of the proposed model adopts the eigenmodes derived from an eigenanalysis applied to the linearized portion of a physics-based model: a process implicitly carrying the spatial relationship between degrees-of-freedom (DOFs). The framework is validated on a numerical example, and an experimental dataset of a scaled cable-stayed bridge, where the learned hybrid model is shown to out perform a purely physics-based approach to modeling. We further show the functionality of the proposed scheme within the context of virtual sensing, that is, the recovery of generalized response quantities in unmeasured DOFs from spatially sparse data.

Metamorphic robots are a new type of unmanned vehicle that can reconfigure and morph between a car mode and a biped walking machine mode. Such a vehicle is superior in trafficability because it can drive at high speeds on its wheels on structured pavement and walk on its legs on unstructured pavement. An engineering prototype of a metamorphic robot was proposed and designed based on the characteristics of wheeled–legged hybrid motion, and reconfiguration planning of the robot was conducted. A kinematics model of the reconfiguration process was established using the screw theory for metamorphic robots. To avoid component impact during the rapid global reconfiguration and achieve smoothness of the reconfiguration process, a rotation rule for each rotating joint was designed and the kinematics model was used to simulate and validate the motion of the system’s end mechanism (front frame) and the entire robot system. Based on the kinematics model and the rotation rules of the rotating joints, a zero-moment point (ZMP) calculation model of the entire robot mechanism in the reconfiguration process was established, and the stability of the reconfiguration motions was evaluated based on the ZMP motion trajectory. The foot landing position was optimized to improve the robot’s stability during the reconfiguration. Finally, the smoothness and stability of the reconfiguration motion were further validated by testing the prototype of the metamorphic robot.

Motivated by Ahmadi-Javid (Journal of Optimization Theory Applications, 155(3), 2012, 1105–1123) and Ahmadi-Javid and Pichler (Mathematics and Financial Economics, 11, 2017, 527–550), the concept of Tsallis Value-at-Risk (TsVaR) based on Tsallis entropy is introduced in this paper. TsVaR corresponds to the tightest possible upper bound obtained from the Chernoff inequality for the Value-at-Risk. The main properties and analogous dual representation of TsVaR are investigated. These results partially generalize the Entropic Value-at-Risk by involving Tsallis entropies. Three spaces, called the primal, dual, and bidual Tsallis spaces, corresponding to TsVaR are fully studied. It is shown that these spaces equipped with the norm induced by TsVaR are Banach spaces. The Tsallis spaces are related to the $L^p$ spaces, as well as specific Orlicz hearts and Orlicz spaces. Finally, we derive explicit formula for the dual TsVaR norm.

Zhu and He [(2018). A new closed-form formula for pricing European options under a skew Brownian motion. The European Journal of Finance 24(12): 1063–1074] provided an innovative closed-form solution by replacing the standard Brownian motion in the Black–Scholes framework using a particular skew Brownian motion. Their formula involves numerically integrating the product of the Guassian density and corresponding distribution function. Being different from their pricing formula, we derive a much simpler formula that only involves the Gaussian distribution function and Owen's $T$ function.

Aerosol particles play an important role in the climate system by absorbing and scattering radiation and influencing cloud properties. They are also one of the biggest sources of uncertainty for climate modeling. Many climate models do not include aerosols in sufficient detail due to computational constraints. To represent key processes, aerosol microphysical properties and processes have to be accounted for. This is done in the ECHAM-HAM (European Center for Medium-Range Weather Forecast-Hamburg-Hamburg) global climate aerosol model using the M7 microphysics, but high computational costs make it very expensive to run with finer resolution or for a longer time. We aim to use machine learning to emulate the microphysics model at sufficient accuracy and reduce the computational cost by being fast at inference time. The original M7 model is used to generate data of input–output pairs to train a neural network (NN) on it. We are able to learn the variables’ tendencies achieving an average $ {R}^2 $ score of 77.1%. We further explore methods to inform and constrain the NN with physical knowledge to reduce mass violation and enforce mass positivity. On a Graphics processing unit (GPU), we achieve a speed-up of up to over 64 times faster when compared to the original model.

We prove new mixing rate estimates for the random walks on homogeneous spaces determined by a probability distribution on a finite group $G$. We introduce the switched random walk determined by a finite set of probability distributions on $G$, prove that its long-term behaviour is determined by the Fourier joint spectral radius of the distributions, and give Hermitian sum-of-squares algorithms for the effective estimation of this quantity.

We present PolicyCLOUD: a prototype for an extensible serverless cloud-based system that supports evidence-based elaboration and analysis of policies. PolicyCLOUD allows flexible exploitation and management of policy-relevant dataflows, by enabling the practitioner to register datasets and specify a sequence of transformations and/or information extraction through registered ingest functions. Once a possibly transformed dataset has been ingested, additional insights can be retrieved by further applying registered analytic functions to it. PolicyCLOUD was built as an extensible framework toward the creation of an analytic ecosystem. As of now, we have developed several essential ingest and analytic functions that are built-in within the framework. They include data cleaning, enhanced interoperability, and sentiment analysis generic functions; in addition, a trend analysis function is being created as a new built-in function. PolicyCLOUD has also the ability to tap on the analytic capabilities of external tools; we demonstrate this with a social dynamics tool implemented in conjunction with PolicyCLOUD, and describe how this stand-alone tool can be integrated with the PolicyCLOUD platform to enrich it with policy modeling, design and simulation capabilities. Furthermore, PolicyCLOUD is supported by a tailor-made legal and ethical framework derived from privacy/data protection best practices and existing standards at the EU level, which regulates the usage and dissemination of datasets and analytic functions throughout its policy-relevant dataflows. The article describes and evaluates the application of PolicyCLOUD to four families of pilots that cover a wide range of policy scenarios.

We discuss a recently proposed family of statistical network models—relational hyperevent models (RHEMs)—for analyzing team selection and team performance in scientific coauthor networks. The underlying rationale for using RHEM in studies of coauthor networks is that scientific collaboration is intrinsically polyadic, that is, it typically involves teams of any size. Consequently, RHEM specify publication rates associated with hyperedges representing groups of scientists of any size. Going beyond previous work on RHEM for meeting data, we adapt this model family to settings in which relational hyperevents have a dedicated outcome, such as a scientific paper with a measurable impact (e.g., the received number of citations). Relational outcome can on the one hand be used to specify additional explanatory variables in RHEM since the probability of coauthoring may be influenced, for instance, by prior (shared) success of scientists. On the other hand, relational outcome can also serve as a response variable in models seeking to explain the performance of scientific teams. To tackle the latter, we propose relational hyperevent outcome models that are closely related with RHEM to the point that both model families can specify the likelihood of scientific collaboration—and the expected performance, respectively—with the same set of explanatory variables allowing to assess, for instance, whether variables leading to increased collaboration also tend to increase scientific impact. For illustration, we apply RHEM to empirical coauthor networks comprising more than 350,000 published papers by scientists working in three scientific disciplines. Our models explain scientific collaboration and impact by, among others, individual activity (preferential attachment), shared activity (familiarity), triadic closure, prior individual and shared success, and prior success disparity among the members of hyperedges.

Wind turbine towers are subjected to highly varying internal loads, characterized by large uncertainty. The uncertainty stems from many factors, including what the actual wind fields experienced over time will be, modeling uncertainties given the various operational states of the turbine with and without controller interaction, the influence of aerodynamic damping, and so forth. To monitor the true experienced loading and assess the fatigue, strain sensors can be installed at fatigue-critical locations on the turbine structure. A more cost-effective and practical solution is to predict the strain response of the structure based only on a number of acceleration measurements. In this contribution, an approach is followed where the dynamic strains in an existing onshore wind turbine tower are predicted using a Gaussian process latent force model. By employing this model, both the applied dynamic loading and strain response are estimated based on the acceleration data. The predicted dynamic strains are validated using strain gauges installed near the bottom of the tower. Fatigue is subsequently assessed by comparing the damage equivalent loads calculated with the predicted as opposed to the measured strains. The results confirm the usefulness of the method for continuous tracking of fatigue life consumption in onshore wind turbine towers.

The effect of milorganite, a commercially available organic soil amendment, on soil nutrients, plant growth, and yield has been investigated. However, its effect on soil hydraulic properties remains less understood. Therefore, this study aimed to investigate the effect of milorganite amendment on soil evaporation, moisture retention, hydraulic conductivity, and electrical conductivity of a Krome soil. A column experiment was conducted with two milorganite application rates (15 and 30% v/v) and a non-amended control soil. The results revealed that milorganite reduced evaporation rates and the length of Stage I of the evaporation process compared with the control. Moreover, milorganite increased moisture retention at saturation and permanent wilting point while decreasing soil hydraulic conductivity. In addition, milorganite increased soil electrical conductivity. Overall, milorganite resulted in increased soil moisture retention; however, moisture in the soil may not be readily available for plants due to increased soil salinity.