(4ax) Deterministic Optimization of Hybrid Models for Advanced Manufacturing Systems

My primary area of research, optimization, has a ubiquitous presence across scientific and technical fields, and particularly within the Process System Engineering (PSE) subdomain of Chemical Engineering. One significant challenge in optimization lies in addressing problem formulations that exhibit nonconvexity, that may be introduced from even the simplest process models, such as mixing. When integer-valued decisions variables are also included, this leads to the mixed-integer nonlinear programming (MINLP) formulation of many common design problems.

Problems that are expressed as MINLPs are fundamental to many technical and business critical tasks, which motivates my interest in this area. Within the PSE community, plant planning and scheduling, process synthesis and control, process intensification, fault-detection, and parameter estimation are all key problems that may all be approached using MINLP formulations. Within the broader scientific community, notable application areas range from aerospace and finance to biomedical engineering. Deterministic approaches to solving these NP-hard problems use variations of classic branch-and-bound algorithms. Many applications may benefit from the rigorous identification of globally optimal solutions either by reducing costs associated with suboptimal configurations or by avoiding potential spurious results.

My interests lie in the development of algorithms used to solve MINLPs relevant to both the PSE and the broader technical community. I am particularly motivated by worst-case design applications and the formal verification of safety-critical systems through the solution of semi-infinite programs (SIPs). In investigating this area, I have made several theoretical contributions relevant to addressing particularly complex and challenging MINLPs and SIPs that involve embedded dynamical systems, the presence of complex simulations, and/or novel surrogate model architectures. In practice, these theoretical advances must be coupled with readily available and performant software implementations to provide efficient solution methods. To this end, I have remained actively engaged with the Julia programming language community by developing and releasing open-source optimization software. More recently, I’ve begun to apply these novel contributions to Industry 4.0 critical problems such as process-aware job shop planning and scheduling formulations.

In the immediate future, I believe that the further exploration of process system optimization involving novel machine learning (ML) architectures will represent a promising area of study that I seek to participate in. I expect this to be particularly true as the broad applicability of ML methods and remarkable success of the ResNet architecture has led to the emergence of a plethora of novel architectures that the broader chemical engineering community has yet to explore (let alone the PSE community). In particular, emerging deep equilibrium models and neural networks have drawn attention for the potential in classical, as well as physics-informed machine learning tasks. However, the use of these models in processes systems applications is particularly challenging as the formulations break common factorable assumptions needed for deterministic optimization that underlie many design tasks. A combination of emerging approaches in global dynamic optimization with implicit relaxation methods will be required to address this emerging class of surrogate models; a combination of methods that I believe my graduate preparation leaves me well-positioned to address.

On a longer timescale, I’m interested in developing PSE approaches tailored to smaller job shops and specialty product manufacturing. It is generally acceptable that digital twin modeling efforts will rely on a combination of mechanistic and data-driven hybrid models to achieve this task. Advances in hybrid modeling approaches related to this area will be critical in providing Industry 4.0 tools needed for smaller and more flexible operations. In particular, the design of robust manufacturing systems (and supply chains) relating to specialized products are a key consideration, both at the plant level and in the broader societal interests, as evidence throughout this past year. As such, the ability to incorporate both sustainability-based design objectives with adequate system robustness can be expected to remain a key design challenge in the foreseeable future. I look forward to continuing to address these complex and challenging classes of problems as I have done throughout my career.

Teaching Interests

I firmly center my identity as an instructor around experiential learning, mentoring, and active learning approaches. This commitment stems from my years in industry where I took on the responsibility of mentoring junior engineers, in which capacity I coordinated projects for and provided direct supervision to groups of MIT Practice School students gaining work experience at Corning, Inc. In my graduate education, I have served as a teaching assistant for a variety of undergraduate courses including “Chemical Engineering Laboratory” (Columbia, CHEN 3810), “Process Controls & Dynamics” (UCONN, CHEG 4147), “Chemical Engineering Analysis” (UCONN, CHEG 3145), and a graduate level course “Uncertainty Analysis, Robust Design, and Optimization” (UCONN, SE 5102).

As a dedicated instructor in the final stage (Fall 2020, grad) of completing a certificate in graduate instruction through UCONN’s Center for Excellence in Teaching and Learning (CETL), I have taken advantage of the immense opportunities to make the engineering classroom a more engaging, and inclusive space for students with different backgrounds and skillsets. I was invited to design and facilitate a graduate seminar (UCONN, GRAD 6000) through UCONN’S CETL on implementing constructive modes of groupwork in the classroom setting, with a particular focus on inclusive and equitable practices. I have developed supplemental digital course materials for “Chemical Engineering Analysis” funded by grants provided by CACHE and UCONN’s CETL that have been positively received by students. This work allowed for increased scaffolding of coding-related content, reducing student frustration while allowing students to engage with rich technical challenges that have drawn so many of them to the field.

As a consequence of both my professional experience and my graduate training, I’m well-suited to provide instruction on a range of undergraduate and graduate topics, particularly in the areas of optimization, process control, data analytics, and numerical methods. Moreover, I would also be comfortable providing undergraduate instruction in areas relating to process and product design, transport phenomena, and chemical reaction engineering. There are two courses I’d be particularly passionate about developing, namely:

• Undergraduate Transport Phenomena: As a foundation of modern chemical engineering, the ability to thoroughly contextualize transport phenomena. I hope to develop a top-down approach to this course which centers around deconstructing modern literature examples with modern tools though the use of heavily scaffolded assignments.
• Hybrid Process Modeling: Modular approaches to development that focus on familiarizing students with model formulation, sensitivity and robustness, model verification, optimization, and optimal experimental design approaches. Special attention would be paid to considerations made when applying a mixture of first-principles and data-driven process models to real-world situations.

As today’s chemical engineers have increasingly focused on product design applications, I believe re-centering these courses in top-down skills-oriented fashion will provide practitioners both the skills and flexibility to excel in an Industry 4.0 future. Moreover, as someone with a broad technical background and expertise spanning mathematical biology, coatings, material science, and process design, I believe I could readily adapt this content to fit with multidisciplinary specialties of the individual institution.

Presentations at the Current AIChE Annual Meeting

[A] Approaches to Improve Bilinear Relaxations in Reduced-Space. Matthew Wilhelm, Matthew Stuber. Advances in global optimization

[B] EAGO.jl: Next Generation Global & Robust Optimization in Julia, Revisited. Matthew Wilhelm, Robert Gottlieb, Matthew Stuber. Software Tools and Implementations for Process Systems Engineering

[C] Robust Optimization with Hybrid First-Principles Data-Driven Models. Chenyu Wang, Matthew Wilhelm, Matthew Stuber. Foundations of Systems and Process Operations.

Select Patents and Publications

[1] Huang, Tian, Jin, Yuhui, Wilhelm, Matthew E. Articles having vias with geometry attributes and methods for fabricating the same Patent Application No. US 20180342450A1. November, 2018. (Granted)

[2] Jin, Yuhui and Wilhelm, Matthew E. Glass-based substrate with vias and process of forming the same. Patent Application No. US 20170103249 A1. April, 2017 (Granted)

[3] M.E. Wilhelm and M.D. Stuber. “EAGO.jl: Easy Advanced Global Optimization in Julia” Optimization Methods and Software (2020).

[4] M Wilhelm, A. Le, M Stuber. “Global Optimization of Stiff Dynamical Systems” AIChE Journal, Futures Issue, 65 (12): e16836 (2019)

[5] Martin, H. et al. “Dexamethasone Increases Cisplatin-Loaded Nanocarrier Delivery and Efficacy in Metastatic Breast Cancer by Normalizing the Tumor Microenvironment.” ACS Nano, 13(6): 6396-6408 (2019).

[6] Hale, W.T., Wilhelm, M.E., et al. “Semi-Infinite Programming for Global Guarantees of Robust Fault Detection and Isolation in Safety-Critical Systems.” Computers & Chemical Engineering, 126, 218-230 (2019).

[7] Yang Y.L., Sun C, Wilhelm M.E., Fox L.J., Zhu J, Kaufman L.J. (2011) Influence of chondroitin sulfate and hyaluronic acid on structure, mechanical properties, and glioma invasion of collagen I gels. Biomaterials. 32(31):7932-40.

[8] M. Wilhelm, M. Chhetri, J. Rychtář, O. Rueppell (2011) A Game Theoretical Analysis of the Mating Sign Behavior in the Honey Bee. Bulletin of Mathematical Biology. 73(3):626-638.

A complete list of publications may be found using the link below:

https://scholar.google.com/citations?user=sr4baQ0AAAAJ&hl=en