A sustainable AI framework for nonlinear regression problems in Engineering Mechanics

• Applicant: Professor Dr.-Ing. Marcus Stoffel
• Subject Area: Mechanics ; Applied Mechanics, Statics and Dynamics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 550613313

The present proposal aims to introduce a spiking neural network (SNN) framework for neuromorphic computing with applications to numerical simulations of load-carrying engineering structures. The framework will include data-driven and physics-informed variants and will be verified on neuromorphic chips acting as co-processors next to classical CPU/GPU chips. In recent years, spiking neural networks have been introduced in science as the third generation of artificial neural networks, leading to tremendous energy savings on neuromorphic processors. This sustainable effect is due to the sparse nature of signal processing in between spiking neurons, leading to much fewer scalar multiplications as in second-generation networks. The spiking neuron’s efficiency is even more pronounced by their inherently recurrent nature being useful for recursive function approximations and path-dependencies, e.g., for inelastic material behaviour. For these reasons, a regression framework for SNNs is proposed to explore the high potential of neuromorphic computations and to apply them to physical applications. However, besides many classification studies with SNNs in the literature, nonlinear neuromorphic regression analysis represents a gap in research. Hence, a general SNN approach for function approximation is developed which can be applied to complex signal processing taking surrogate gradients due to the discontinuous spike representation into account. Furthermore, interfaces between real physical and binary spiking values are necessary. Following this intention, a hybrid approach composed of second and third-generation topologies is introduced along with a study about encoding/decoding strategies. In the present proposal, hybrid topologies are applied to Finite Element algorithms to solve boundary value problems of dynamically loaded structures undergoing inelastic deformations. So-called intelligent Finite Elements are developed with SNNs in the Gaussian points, yielding in this way two innovations. Firstly, a nonlinear regression framework with SNNs is established; secondly, a physics-informed approach with SNNs is introduced; both approaches are new in literature and, further, both strategies are implemented in FEM codes and applied to structural deformations. A power profiling for energy saving and accelerated FE simulations in comparison to classical FEM is demonstrated.

• DFG Programme: Research Grants