Saksham Kiroriwal

Saksham Kiroriwal, Julius Pfrommer, Jürgen Beyerer

Bayesian optimization (BO) is a powerful method for optimizing black-box manufacturing processes, but its performance is often limited when dealing with high-dimensional multi-stage systems, where we can observe intermediate outputs. Standard BO models the process as a black box and ignores the intermediate observations and the underlying process structure. Partially Observable Gaussian Process Networks (POGPN) model the process as a Directed Acyclic Graph (DAG). However, using intermediate observations is challenging when the observations are high-dimensional state-space time series. Process-expert knowledge can be used to extract low-dimensional latent features from the high-dimensional state-space data. We propose POGPN-JPSS, a framework that combines POGPN with Joint Parameter and State-Space (JPSS) modeling to use intermediate extracted information. We demonstrate the effectiveness of POGPN-JPSS on a challenging, high-dimensional simulation of a multi-stage bioethanol production process. Our results show that POGPN-JPSS significantly outperforms state-of-the-art methods by achieving the desired performance threshold twice as fast and with greater reliability. The fast optimization directly translates to substantial savings in time and resources. This highlights the importance of combining expert knowledge with structured probabilistic models for rapid process maturation.

Saksham Kiroriwal, Julius Pfrommer, Jürgen Beyerer

To reduce the curse of dimensionality for Gaussian processes (GP), they can be decomposed into a Gaussian Process Network (GPN) of coupled subprocesses with lower dimensionality. In some cases, intermediate observations are available within the GPN. However, intermediate observations are often indirect, noisy, and incomplete in most real-world systems. This work introduces the Partially Observable Gaussian Process Network (POGPN) to model real-world process networks. We model a joint distribution of latent functions of subprocesses and make inferences using observations from all subprocesses. POGPN incorporates observation lenses (observation likelihoods) into the well-established inference method of deep Gaussian processes. We also introduce two training methods for POPGN to make inferences on the whole network using node observations. The application to benchmark problems demonstrates how incorporating partial observations during training and inference can improve the predictive performance of the overall network, offering a promising outlook for its practical application.