This contribution focuses on the parameter identification of hysteresis model from measurements by employing automatic differentiation and neural networks. We first introduce the thermodynamically consistent energy based hysteresis model and the parameters which are to be identified. Then we demonstrate how the model can benefit from automatic differentiation. A main step is the parametrization of the hysteresis model based on distribution functions, which makes it possible to treat the identification process as an unconstrained optimization problem. Next, the hysteresis model is sampled, and the generated datasets are used to train neural networks to predict the hysteresis parameters. An important point here is the data generation part. Care needs to be taken so that the generated dataset covers a large space of possible solutions from which the network can learn. The described methods are tested and verified on synthetic as well as measurement data.

This talk presents a data-driven variational method that embeds high-fidelity measured data in the surrogate or deficient models via variationally derived loss functions to enhance the modeling capability of physics-based models. Key idea is the hierarchical mathematical structure of the multiscale method which is exploited to derive residual based closure terms that are comprised of the first-principles theory and sensor-based measurements. Since closure terms represent errors in the system, embedding data through these terms in the variational formulation leads to discrepancy-informed closure models that inject computation-based intelligence in the modeling framework. The resulting method is driven not only by boundary and initial conditions, but also by measurements that are taken at only a few observation points in the target system. Specifically, the data-embedding term behaves like residual-based least-squares loss functions, thus retaining variational consistency. The structure of the loss function is analyzed in the context of variational correction to the modeled response wherein loss function penalizes the difference in the modeled response from the measured data that represents the local behavior of the system. Formulation is applied to time dependent problems and the effect of the variationally embedded loss function on transient response of the system is analyzed under a variety of loading conditions. Specifically, the damped solution and correct energy time histories are recovered by including known data in the undamped situation. The enhanced stability and accuracy of the DDV method is manifested via reconstructed displacement and velocity fields that yield time histories of strain and kinetic energies that match the target systems. The proposed DDV method also serves as a procedure for restoring the eigenvalues and eigenvectors of a deficient dynamical system when known data is taken into consideration. Method is applied to smooth as well as non-smooth model problems and mathematical attributes of the formulation are investigated.

Recent studies have indicated that intracranial aneurysm rupture is influenced by various factors, including clinical, morphological, and hemodynamic characteristics identified through Computational Fluid Dynamics (CFD) analysis. Based on these insights, there have been endeavors to develop machine learning models capable of predicting aneurysm rupture. Additionally, it has been observed that the risk of rupture increases with the growth of intracranial aneurysms. However, there has been limited research on machine learning models predicting aneurysm rupture while simultaneously considering aneurysm growth in addition to conventional parameters including hemodynamics. In this study, we aim to develop a machine learning model for predicting aneurysm rupture by introducing the temporal change rate in aneurysm size as a new morphological feature, and to evaluate its impact on prediction accuracy. Out of 533 intracranial aneurysms smaller than 10 mm analyzed through CFD (21 ruptured during observation, 512 unruptured), 357 cases were randomly assigned as Training Data and 176 as Test Data. The analysis included 43 features, covering clinical, hemodynamic, and morphological factors, specifically focusing on the temporal change rate in aneurysm length, width, and neck diameter. Two prediction models were developed: Model A, which considered the temporal change rate, and Model B, which excludes it. These models were applied to the Test Data, and their sensitivity and specificity were calculated and compared. Model A exhibited a sensitivity of 89.8% and a specificity of 74.0%, while Model B demonstrated values of 62.2% and 62.3%, respectively. Additionally, in Model A, the temporal change rate in aneurysm length emerged as the most influential morphological factor, alongside significant hemodynamic factors such as the maximum oscillatory shear index (OSI). Both morphological and hemodynamic factors, including the temporal change rate, significantly influenced the prediction of rupture risk for intracranial aneurysms, resulting in improved prediction accuracy.

The nonlinear governing equation of mass-spring-damper dynamics usually consists of a known linear structure and an undetermined complicated component. This work proposes two physics-informed methods to model the unknown component by either a Koopman-guided auto-encoder or a topology-aware graph. Both frameworks show competitive performance for dynamic forecasting under new control inputs in multiple synthetic and experimental case studies, outperforming deep learning and physics-informed benchmarks. A time-series anomaly detection technique based on Jensen-Shannon distance is also proposed. Furthermore, the interpretable graph model can diagnose local system anomalies.

The identification of useful observables that jointly and uniquely characterize their collective behavior is a pressing challenge in data-driven scientific discovery and inference. One such set of observables is clearly the coupled field variables constrained by prevalent conservation laws. This is, however, too much knolwegde to be informed by scant information gleaned from sparse data. Furthermore, reasonable arguments can be made that such an exhaustive characterization, while sufficient, may not be necessary for informing physically-grounded predictions of natural phenomena. The quest for necessary observables and their achievable performance is motivated by the surge of interest in machine learning and digital twins. In this talk I will describe recent efforts in my research group to design data mining and data interpretation paradigms geared towards discovering necessary observables and assessing their mathematical and statistical behavior.

In modern turbofan engines, notably those with an Ultra High Bypass Ratio (UHBR), fan noise significantly contributes to overall noise levels, characterized by both broadband and tonal noise components. Acoustic liners, designed to mitigate these components, are crucial for effective noise absorption. To ensure their effectiveness, it is imperative to study these liners under various flight conditions. This paper addresses the attenuation of low-frequency tonal noise using adapted acoustic liners. The design of liners needed for targeting low frequencies must have particular geometries and cannot be based on standard geometry acoustic liners. This means that there is a need to optimize these liners on the basis of high-fidelity simulations. However, simulations can be computationally expensive and not always feasible. The challenge lies in developing a model that encompasses both known and unknown variability in operating conditions to ensure robustness against uncertainties. Generating an extensive database through exhaustive exploration of design parameters via high-fidelity simulations is not practical. Thus, a robust statistical metamodel is developed to model a parameterized aeroacoustic liner impedance as a function of frequency and main control parameters using a small dataset from computationally expensive aeroacoustic simulations, requiring the use of an adapted learning algorithm that is chosen as Probabilistic Learning on Manifolds (PLoM). Furthermore, a statistical Artificial Neural Network (ANN)-based metamodel is introduced as another representation, offering greater versatility. It includes a prior conditional probability model for the PCA- based statistical reduced representation of the frequency-sampled vector of log-resistance and reactance. This model imposes statistical constraints, presenting challenges for training the ANN-based model using classical optimization methods. An alternative approach involves constructing a second large dataset using conditional statistics estimated with learned realizations from PLoM.