Physics-Informed Data-Driven Simulation

The simulation of complex multi-physical processes as additive manufacturing is extremely demanding and time-consuming using conventional numerical methods. Therefore, in engineering often only simplified  analytical or empirical models are used. Thanks to advances in machine learning, reliable empirical approaches can increasingly be obtained from big data. However, the generation of big data in additive manufacturing requires complex and expensive sensor technology. In the presence of high speed and large thermal gradients it is sometimes simply not possible to reliably generate certain data, even with the best sensor technology at hand.

It has already been shown that neural networks can also be trained without big data, only on the basis of initial and boundary conditions which are available anyways. This has led to an accurate and stable mesh free method, the Neural Particle Method. However, this method is not intelligent, i.e. the training only replaces the solution of a system of equations as it is necessary e.g. within Finite Elements. Predictions for the future beyond the trained time step cannot be made.

In the course of this project it will be investigated to what extent simulation with neural networks on the one hand and data-based empirical modeling on the other hand can be combined in a symbiotic manner. The ultimate goal is the generation of reliable models for complex dynamical systems known as digital twins.