C. Nataraj

Zihan Liu, Prashant N. Kambali, C. Nataraj

Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing operational conditions, unknown interactions, excitations, and parametric drift. While data-based models can capture the current state of complex systems, they face significant challenges, including excessive data dependence, limited generalizability to changing conditions, and inability to predict parametric dependence. This has led to combining physics and data in modeling, termed physics-infused machine learning, often using numerical simulations from physics-based models. This paper introduces a novel approach that departs from standard techniques by uncovering information from nonlinear dynamical modeling and embedding it in data-based models. The goal is to create a hybrid adaptive modeling framework that integrates data-based modeling with newly measured data and analytical nonlinear dynamical models for enhanced accuracy, parametric dependence, and improved generalizability. By explicitly incorporating nonlinear dynamic phenomena through perturbation methods, the predictive capabilities are more realistic and insightful compared to knowledge obtained from brute-force numerical simulations. In particular, perturbation methods are utilized to derive asymptotic solutions which are parameterized to generate frequency responses. Frequency responses provide comprehensive insights into dynamics and nonlinearity which are quantified and extracted as high-quality features. A machine-learning model, trained by these features, tracks parameter variations and updates the mismatched model. The results demonstrate that this adaptive modeling method outperforms numerical gray box models in prediction accuracy and computational efficiency.

Lucas Steinmetz, Shivam Maheshwari, Garik Kazanjian et al.

Traumatic brain injury (TBI) presents a significant public health challenge, often resulting in mortality or lasting disability. Predicting outcomes such as mortality and Functional Status Scale (FSS) scores can enhance treatment strategies and inform clinical decision-making. This study applies supervised machine learning (ML) methods to predict mortality and FSS scores using a real-world dataset of 300 pediatric TBI patients from the University of Colorado School of Medicine. The dataset captures clinical features, including demographics, injury mechanisms, and hospitalization outcomes. Eighteen ML models were evaluated for mortality prediction, and thirteen models were assessed for FSS score prediction. Performance was measured using accuracy, ROC AUC, F1-score, and mean squared error. Logistic regression and Extra Trees models achieved high precision in mortality prediction, while linear regression demonstrated the best FSS score prediction. Feature selection reduced 103 clinical variables to the most relevant, enhancing model efficiency and interpretability. This research highlights the role of ML models in identifying high-risk patients and supporting personalized interventions, demonstrating the potential of data-driven analytics to improve TBI care and integrate into clinical workflows.

Mauro J. Sanchirico, Xun Jiao, C. Nataraj

Polynomial expansions are important in the analysis of neural network nonlinearities. They have been applied thereto addressing well-known difficulties in verification, explainability, and security. Existing approaches span classical Taylor and Chebyshev methods, asymptotics, and many numerical approaches. We find that while these individually have useful properties such as exact error formulas, adjustable domain, and robustness to undefined derivatives, there are no approaches that provide a consistent method yielding an expansion with all these properties. To address this, we develop an analytically modified integral transform expansion (AMITE), a novel expansion via integral transforms modified using derived criteria for convergence. We show the general expansion and then demonstrate application for two popular activation functions, hyperbolic tangent and rectified linear units. Compared with existing expansions (i.e., Chebyshev, Taylor, and numerical) employed to this end, AMITE is the first to provide six previously mutually exclusive desired expansion properties such as exact formulas for the coefficients and exact expansion errors (Table II). We demonstrate the effectiveness of AMITE in two case studies. First, a multivariate polynomial form is efficiently extracted from a single hidden layer black-box Multi-Layer Perceptron (MLP) to facilitate equivalence testing from noisy stimulus-response pairs. Second, a variety of Feed-Forward Neural Network (FFNN) architectures having between 3 and 7 layers are range bounded using Taylor models improved by the AMITE polynomials and error formulas. AMITE presents a new dimension of expansion methods suitable for analysis/approximation of nonlinearities in neural networks, opening new directions and opportunities for the theoretical analysis and systematic testing of neural networks.