Sumários

Final Implementation Troubleshooting and Report Preparation

27 Maio 2026, 13:30 • Rafael Neto Henriques

This session served as the final practical-laboratory class before the evaluation phase. Dedicated to concluding the project work, hands-on assistance was provided to help students troubleshoot and resolve any last-minute computational or coding issues within their MATLAB or Python models. Alongside finalizing the algorithms, the class focused heavily on the communication of their findings. Final suggestions and targeted feedback were given regarding the organization, structuring, and formatting of the project reports, ensuring that all groups were fully prepared to clearly articulate their mathematical methodologies and physiological interpretations for their final submissions.

Non-Parametric Model Identification and Model Validation

27 Maio 2026, 10:00 • Rafael Neto Henriques

The first part of the session focused on the signal estimation problem within input/output data models, specifically exploring the mathematical process of deconvolution. The inherent challenges of deconvolution were discussed, highlighting that it is often an ill-posed and ill-conditioned problem, especially when discretized into a matrix formalism and influenced by measurement errors. To mitigate these issues, regularization methods were introduced to achieve an optimal balance between data fit and solution smoothness by minimizing a penalized least squares cost function.

The second half of the class shifted to the comprehensive framework of model validation. It was emphasized that a valid model must successfully fulfill its intended practical purpose and be well-founded during its conceptual design, such as ensuring compatibility with feasible steady states. The multidimensional criteria for validating a model as a whole were then outlined. The lecture concluded by establishing rules for good modeling practice. These rules cautioned against the "garbage paradigm" and emphasized that a robust model must be falsifiable and subject to continuous critical evaluation by its creator.

Final Implementation Troubleshooting and Report Preparation

27 Maio 2026, 08:30 • Rafael Neto Henriques

Advanced Parameter Estimation, Model Selection, and Optimal Design

26 Maio 2026, 11:00 • Rafael Neto Henriques

This theoretical class concluded the material on parametric model estimation by moving beyond standard regression techniques. The session began with a brief synthesis of how parameter estimation directly supports a posteriori identification, parameter sensitivity analysis, and residual evaluation. The practical challenge of testing for model order when choosing between competing mathematical models of varying complexities was then addressed. The principle of parsimony was introduced, explaining how the Akaike Information Criterion (AIC) and Schwartz Criterion (SC) are used to penalize overfitting and evaluate the overall predictive plausibility of a model.

The focus then shifted to more advanced, robust estimation methods. Maximum Likelihood Estimation (MLE) was introduced as a necessary alternative to standard least squares when experimental data is corrupted by non-Gaussian noise. Building on probabilistic approaches, Bayesian Estimation and the Maximum A Posteriori (MAP) framework were also explained, demonstrating how integrating a priori probability distributions can refine parameter precision.

In the final segment of the class, the mathematical fundamentals of Optimal Experimental Design were covered. It was demonstrated how to systematically determine the most efficient experimental acquisition settings by computing and maximizing the determinant of the Fisher Information Matrix.

Project discussion

26 Maio 2026, 08:30 • Alexandre da Rocha Freire de Andrade

Project discussion