Haamid Reehaan Peer Mohamed Jameel

University of Freiburg

Monday, July 13, 2026, 11:00 - 12:00

Building 102 - SR 02-012

Neural Differential-Algebraic Equations (NDAEs) sit at the intersection of scientific machine learning and process systems engineering, providing hybrid models for physical systems in which some dynamics are unknown and must be learned from data. Training these models with conventional sequential integration is computationally expensive and unable to enforce hard physical constraints during learning. This thesis proposes a simultaneous training and discretization framework for NDAEs based on Orthogonal Collocation on Finite Elements, extending recent work on the simultaneous approach to non-smooth hybrid systems. The neural network is embedded directly into the collocation constraints, transcribing the full system into a unified Nonlinear Program (NLP) that circumvents repeated numerical integration while enforcing constraints rigorously. This full-space transcription also enables the use of exact hessian information, which has been omitted in prior work. Nonsmooth activations are handled directly yielding a Mathematical Program with Complementarity Constraints (MPCC).

The framework is implemented in the CasADi ecosystem and validated on fed-batch bioreactors and non-smooth hybrid systems via the nosnoc library. Experiments confirm strict satisfaction of algebraic path constraints and exact mode-switch resolution without numerical chatter, demonstrating a robust and physically consistent methodology for learning unknown dynamics in constrained hybrid systems.