UC Berkeley

Data from physics simulation is utilized in data assimilation and reduced order model.

First of all, data assimilation technique for additive manufacturing (AM) processes is developed. Physics simulation data of the AM process is enhanced by fusing it with measured data using Kalman filter. It enables better monitoring of AM processes in real-time, which is essential for on-line control of system parameters to produce high-quality parts. Furthermore, this combined system outputs uncertainty measurements on the state estimation that can be used as guide for sensor positioning control, resulting in the closed-loop feedback control system.

Secondly, a fast and accurate physics-informed neural network reduced order model (ROM), namely nonlinear manifold ROM is developed. The high-fidelity simulation data is used to train the neural network model to learn the solution space representation. The novel ROM can better approximate high-fidelity model solutions with a smaller latent space dimension than the traditional linear subspace ROMs. To the best of author’s knowledge, this ROM is the first kind of the neural network ROM that utilizes the existing numerical discretization of the full order model and achieves a noticeable speed-up without losing much accuracy at the same time. The speed-up of the method was enabled by choosing a sparse shallow neural network as the nonlinear manifold and applying efficient hyper-reduction computation. Its performance is demonstrated in two numerical examples which are 1D inviscid Burgers' equation and 2D viscous Burgers' equation with high Reynolds number.

Finally, a space-time ROM for linear dynamical systems is introduced. The space-time ROM accelerates solution processes considerably with high accuracy. This ROM is based on data-driven linear subspace solution representation where the high-fidelity simulation data is used to build a space-time basis. The Galerkin and least-squares Petrov-Galerkin projection space-time ROMs are formulated and their performances are demonstrated using 2D linear diffusion equation and 2D linear convection-diffusion equation. The sample Python code is presented for educational purpose. It is worth introducing the linear subspace-based space-time ROM because the linear dynamical systems are being extensively used. For example, there are electric circuit analysis, signal processing, and semi-discretized partial differential equations.