Algorithmic Differentiation Mission Planning and Control

• Applicant: Professor Dr. Uwe Naumann
• Subject Area: Computer Architecture, Embedded and Massively Parallel Systems ; Methods in Artificial Intelligence and Machine Learning ; Software Engineering and Programming Languages
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 551025029

This project aims to optimize differentiable programs or, more precisely, the corresponding differentiated programs. The latter have been playing a significant role in simulation and optimization of phenomena in science and engineering for many decades. Similarly, more recent progress in algorithms for artificial intelligence and machine learning rely on the efficient computation of derivatives of objective functions given as differentiable programs. The vast majority of established methods for calibration of parameterized numerical simulations as well as, analogously, for efficient training of models for effective inference in the context of practically relevant applications require at least first derivatives (gradients, resp. Jacobians). Hence, this project sets its focus on first-order algorithmic differentiation. The central research question becomes the following: How to model, optimize, and implement first derivative code for modular differentiable programs, such that feasible and theoretically (near-)optimal solutions of the Jacobian Accumulation problem yield (near-)optimal run time in practice? Formal methods for the approximate solution of the inherent combinatorial optimization problems shall be developed / evolved. The focus is on transferability of theoretical reductions in computational cost to real-world scenarios. Thus, we expect to make a significant contribution to the sustained use of derivative-based numerical methods in computational science, engineering and finance as well as in scientific machine learning.

• DFG Programme: Research Grants