Research

Multiple mathematical models are often available for engineering processes, differing in scale (e.g., models of materials vs the processes they are used in) or in rigor (e.g., models for process design vs for control). We study methods to link inherently related models for optimal decision making, often by embedding reduced-order “surrogate” models in larger optimisation problems.

Ongoing themes include (1) optimisation methods for machine learning surrogates, (2) deriving new reduced-order mdoels, and (3) applications in process and energy systems. Finally, these research strands coincide with (4) generic advancements in optimisation and software:

1. Optimisation of Trained Machine Learning Models

Many applications embed trained machine learning (ML) models in optimisation problems. For example, ML models can be used as surrogates for functions that are otherwise difficult to represent, such as acquisition functions for black-box optimisation. On the other hand, optimisation can be used to investigate extreme behaviour (e.g., adversarial inputs) of a trained model. Our research here studies optimisation formulations for trained ML models, with a goal of improving performance and scalability.

Representative publications:

• Thebelt, A., Tsay, C., Lee, R. M., Sudermann-Merx, N., Walz, D., Shafei, B., & Misener, R. (2022). Tree ensemble kernels for Bayesian optimization with known constraints over mixed-feature spaces. NeurIPS arXiv
• Tsay, C., Kronqvist, J., Thebelt, A., & Misener, R. (2021). Partition-based formulations for mixed-integer optimization of trained ReLU neural networks. NeurIPS. link arXiv
• Tsay, C. (2021). Sobolev trained neural network surrogate models for optimization. Comput. Chem. Eng. link preprint

2. Reduced-Order Models for Scheduling and Control

Solving optimisation problems efficiently is often essential when making recurring decisions in scheduling and control. Therefore, a model must be carefully chosen by considering trade-offs between computational tractability and accurate representation of the underlying process. This often involves using approximations, such as via model reduction. Our research here studies methods (primarily data-driven) for deriving reduced-order models and for model dimensionality reduction.

Representative publications:

• Cronjaeger, C., Pattison, R.C., & Tsay, C. (2022). Tensor-based autoencoder models for hyperspectral produce data. Comput.-Aided Chem. Eng. link
• Tsay, C., & Baldea, M. (2020). Integrating production scheduling and process control using latent variable dynamic models. Control Eng. Pract. link arXiv
• Tsay, C., Kumar, A., Flores Cerrillo, J., & Baldea, M. (2019). Optimal demand response scheduling of an industrial air separation unit using data-driven dynamic models. Comput. Chem. Eng. link

3. Modelling and Optimisation of Energy Systems

Mathematical modelling and optimisation can guide the design of new engineering systems by simultaneously considering intricate trade-offs among decision variables. Nevertheless, modelling real-world processes often requires nonlinear and/or discrete relationships, making optimisation challenging. With a focus on applications in process and energy systems, we study how improvements at the modelling and optimisation levels can expedite solutions and expand the level of detail captured during optimisation.

Representative publications:

• Thebelt, A., Tsay, C., Lee, R.M., Sudermann-Merx, N., Walz, D., Tranter, T., & Misener, R. (2022). Multi-objective constrained optimization for energy applications via tree ensembles. Appl. Energy. link arXiv
• Tsay, C., Pattison, R.C., Zhang, Y., Rochelle, G.T., & Baldea, M. (2019). Rate-based modeling and economic optimization of next-generation amine-based carbon capture plants. Appl. Energy. link preprint
• Tsay, C., Pattison, R.C., & Baldea, M. (2017). A pseudo-transient optimization framework for periodic processes: Pressure swing adsorption and simulated moving bed chromatography. AIChE J. link preprint

4. Computational Optimisation and Software

We continually seek generic advancements in methods and software for computational optimisation that may arise during research in the above themes. Moreover, we aim to develop open-source and user-friendly implementations for researchers and practitioners.

Representative publications:

• Folch, J.P., Zhang, S., Lee, R.M., Shafei, B., Walz, D., Tsay, C., van der Wilk, M. & Misener, R. (2022). SnAKe: Bayesian Optimization with Pathwise Exploration. NeurIPS arXiv
• Ceccon, F., Jalving, J., Haddad, J., Thebelt, A., Tsay, C., Laird, C.D., & Misener, R. (2022). OMLT: Optimization & Machine Learning Toolkit. JMLR arXiv
• Kronqvist J., Misener, R., Tsay, C. (2021). Between steps: Intermediate relaxations between big-M and convex hull formulations. CPAIOR link arXiv