Representation, Uncertainty, and Deployment:
Making the Most of Physics-Informed Machine Learning in PSE

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Integrating Physics-Informed Machine Learning and Optimal Experimental Design for Model Identification: Current Challenges and Future Opportunities

Joel A. Paulson

Department of Chemical and Biological Engineering
University of Wisconsin-Madison
USA

Abstract

Physics-informed machine learning (PIML) has emerged as a powerful framework in process systems engineering (PSE), offering a way to blend the structure of physical laws with the flexibility of data-driven models. As real-world systems increasingly deviate from idealized equations, PIML promises models that can both respect, e.g., conservation principles and adapt to imperfect data across diverse systems. Recent advances – from physics-informed neural networks to universal differential equation and symbolic regression frameworks – have made it possible to embed domain knowledge directly into training workflows as well as accelerate simulation in downstream tasks like design, optimization, estimation, and control. This talk will provide a pragmatic overview of the PIML landscape and then explore what it takes to make it dependable for decision-making in PSE and related domains. I will frame the discussion around three often-overlooked aspects that frequently determine whether a model is truly useful in practice. The first is representation: selecting or learning the right states (or features), invariants, and structures to express physics cleanly and avoid challenging or ill-posed learning problems. The second is uncertainty: ensuring model predictions include calibrated, decision-relevant confidence measures rather than ad hoc error bars. The third is deployment: building models that fit real-time computational budgets and are resilient enough to remain useful as systems evolve. Finally, I will argue that these considerations motivate the development of repeatable, modular pipelines that go beyond one-off (bespoke) architectures, and I will outline what such pipelines could look like in practice.

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Abstract

Integrating physics-informed machine learning (PIML) with optimal experimental design (OED) offers a powerful pathway for accelerating model identification in complex physical systems. PIML frameworks enable data-efficient learning by embedding governing equations and physical constraints directly into data-driven modelling architectures, while OED systematically determines the most informative experiments for reducing model uncertainty. Despite clear synergies, combining these methodologies remains challenging. Current obstacles include handling uncertainty sources that arise when assumed physics are incomplete, and developing scalable algorithms capable of operating in high-dimensional parameter and state spaces. Additionally, OED, including the application of model-based design of experiments (MBDoE) techniques, must account for uncertainty introduced by both noisy measurements and imperfect surrogate models, creating a tightly coupled inference–experimental design loop that is challenging to optimize end-to-end. Advances in uncertainty quantification, derivative-free optimization, robust MBDoE and adaptive sampling are opening new opportunities for bridging these gaps. The presentation will outline future research directions in this context, including hybrid OED–PIML pipelines to update experimental design strategies in real time, and robust online model identification approaches that can incorporate: i) automated discovery of governing equations in domains where first-principles models are only partially known, integrating intelligent model diagnostics and selection; ii) safe and robust experimental design solutions, to efficiently handle parametric uncertainty and constraints satisfaction; iii) accurate quantification of the descriptive limits of PIML models and physics-based models in the experimental design space. Together, these developments promise more reliable, data-efficient, and interpretable model identification across a wide range of applications in science and engineering, but the presentation will specifically focus on the identification of reaction process models in automated and autonomous systems for chemical synthesis.