While linear systems have been useful in solving problems across different fields, the need for improved performance and efficiency has prompted them to operate in nonlinear modes. As a result, nonlinear models are now essential for the design and control of these systems. However, identifying a nonlinear system is more complicated than identifying a linear one. Therefore, modeling and identifying nonlinear systems are crucial for the design, manufacturing, and testing of complex systems. This study presents using advanced nonlinear methods based on deep learning for system identification. Two deep neural network models, LSTM autoencoder and Normalizing Flows, are explored for their potential to extract temporal features from time series data and relate them to system parameters, respectively. The presented framework offers a nonlinear approach to system identification, enabling it to handle complex systems. As case studies, we consider Duffing and Lorenz systems, as well as fluid flows such as flows over a cylinder and the 2-D lid-driven cavity problem. The results indicate that the presented framework is capable of capturing features and effectively relating them to system parameters, satisfying the identification requirements of nonlinear systems.

Conventional physics-based modeling techniques involve high effort, e.g., time and expert knowledge, while data-driven methods often lack interpretability, structure, and sometimes reliability. To mitigate this, we present a data-driven system identification framework that derives models in the port-Hamiltonian (pH) formulation. This formulation is suitable for multi-physical systems while guaranteeing the useful system theoretical properties of passivity and stability. Our framework combines linear and nonlinear reduction with structured, physics-motivated system identification. In this process, high-dimensional state data obtained from possibly nonlinear systems serves as input for an autoencoder, which then performs two tasks: (i) nonlinearly transforming and (ii) reducing this data onto a low-dimensional latent space. In this space, a linear pH system, that satisfies the pH properties per construction, is parameterized by the weights of a neural network. The mathematical requirements are met by defining the pH matrices through Cholesky factorizations. The neural networks that define the coordinate transformation and the pH system are identified in a joint optimization process to match the dynamics observed in the data while defining a linear pH system in the latent space. The learned, low-dimensional pH system can describe even nonlinear systems and is rapidly computable due to its small size. The method is exemplified by a parametric mass-spring-damper and a nonlinear pendulum example, as well as the high-dimensional model of a disc brake with linear thermoelastic behavior.

Port-Hamiltonian systems (pHS) allow for a structure-preserving modeling of dynamical systems. Coupling pHS via linear relations between input and output defines an overall pHS, which is structure preserving. However, in multiphysics applications, some subsystems do not allow for a physical pHS description, as (a) this is not available or (b) too expensive. Here, data-driven approaches can be used to deliver a pHS for such subsystems, which can then be coupled to the other subsystems in a structure-preserving way. In this work, we derive a data-driven identification approach for port-Hamiltonian differential algebraic equation (DAE) systems. The approach uses input and state space data to estimate nonlinear effort functions of pH-DAEs. As underlying technique, we us (multi-task) Gaussian processes. This work thereby extends over the current state of the art, in which only port-Hamiltonian ordinary differential equation systems could be identified via Gaussian processes. We apply this approach successfully to two applications from network design and constrained multibody system dynamics, based on pH-DAE system of index one and three, respectively.

The post-acute sequelae of SARS-CoV-2 infection (PASC) refers to a broad spectrum of symptoms and signs that are persistent, exacerbated or newly incident in the period after acute SARS-CoV-2 infection. Most studies have examined these conditions individually without providing evidence on co-occurring conditions. In this study, we leveraged the electronic health record data of two large cohorts, INSIGHT and OneFlorida+, from the national Patient-Centered Clinical Research Network. We created a development cohort from INSIGHT and a validation cohort from OneFlorida+ including 20,881 and 13,724 patients, respectively, who were SARS-CoV-2 infected, and we investigated their newly incident diagnoses 30–180 days after a documented SARS-CoV-2 infection. Through machine learning analysis of over 137 symptoms and conditions, we identified four reproducible PASC subphenotypes, dominated by cardiac and renal (including 33.75% and 25.43% of the patients in the development and validation cohorts); respiratory, sleep and anxiety (32.75% and 38.48%); musculoskeletal and nervous system (23.37% and 23.35%); and digestive and respiratory system (10.14% and 12.74%) sequelae. These subphenotypes were associated with distinct patient demographics, underlying conditions before SARS-CoV-2 infection and acute infection phase severity. Our study provides insights into the heterogeneity of PASC and may inform stratified decision-making in the management of PASC conditions. Machine learning applied to electronic health records in two US cohorts from the RECOVER initiative identified four Long-COVID subphenotypes that differ in the involvement of organ systems, previous SARS-CoV-2 infection severity and underlying conditions.