Machine discovery of partial differential equations from spatiotemporal data: A sparse Bayesian learning framework.

This study presents a general framework, namely, Sparse Spatiotemporal System Discovery (S3d), for discovering dynamical models given by Partial Differential Equations (PDEs) from spatiotemporal data. S3d is built on the recent development of sparse Bayesian learning, which enforces sparsity in the estimated PDEs. This approach enables a balance between model complexity and fitting error with theoretical guarantees. The proposed framework integrates Bayesian inference and a sparse priori distribution with the sparse regression method. It also introduces a principled iterative re-weighted algorithm to select dominant features in PDEs and solve for the sparse coefficients. We have demonstrated the discovery of the complex Ginzburg-Landau equation from a traveling-wave convection experiment, as well as several other PDEs, including the important cases of Navier-Stokes and sine-Gordon equations, from simulated data.

Development and Validation of a Prognostic Risk Score System for COVID-19 Inpatients: A Multi-Center Retrospective Study in China.

Coronavirus disease 2019 (COVID-19) has become a worldwide pandemic. Hospitalized patients of COVID-19 suffer from a high mortality rate, motivating the development of convenient and practical methods that allow clinicians to promptly identify high-risk patients. Here, we have developed a risk score using clinical data from 1479 inpatients admitted to Tongji Hospital, Wuhan, China (development cohort) and externally validated with data from two other centers: 141 inpatients from Jinyintan Hospital, Wuhan, China (validation cohort 1) and 432 inpatients from The Third People's Hospital of Shenzhen, Shenzhen, China (validation cohort 2). The risk score is based on three biomarkers that are readily available in routine blood samples and can easily be translated into a probability of death. The risk score can predict the mortality of individual patients more than 12 d in advance with more than 90% accuracy across all cohorts. Moreover, the Kaplan-Meier score shows that patients can be clearly differentiated upon admission as low, intermediate, or high risk, with an area under the curve (AUC) score of 0.9551. In summary, a simple risk score has been validated to predict death in patients infected with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2); it has also been validated in independent cohorts.

Data driven discovery of cyber physical systems.

Cyber-physical systems embed software into the physical world. They appear in a wide range of applications such as smart grids, robotics, and intelligent manufacturing. Cyber-physical systems have proved resistant to modeling due to their intrinsic complexity arising from the combination of physical and cyber components and the interaction between them. This study proposes a general framework for discovering cyber-physical systems directly from data. The framework involves the identification of physical systems as well as the inference of transition logics. It has been applied successfully to a number of real-world examples. The novel framework seeks to understand the underlying mechanism of cyber-physical systems as well as make predictions concerning their state trajectories based on the discovered models. Such information has been proven essential for the assessment of the performance of cyber-physical systems; it can potentially help debug in the implementation procedure and guide the redesign to achieve the required performance.