Research — Hyeonbin Moon

Mechanics has long provided the mathematical language for describing how materials and structures behave under load, heat, and deformation. Computational simulation, particularly the finite element method, turned these governing equations into predictive engineering tools. More recently, machine learning has introduced a new capability: learning directly from data, often without an explicit physical model.

Each of these developments builds on the one before it — mechanics supplies simulation with its governing equations, and simulation supplies data-driven methods with a benchmark for physical validity. Purely data-driven approaches, however, tend to treat mechanics and simulation only as sources of training data rather than as structural priors for the model itself. This becomes a real limitation when engineering data is sparse, noisy, or indirect relative to the complexity of the systems it describes.

My research addresses this limitation by embedding governing equations and numerical structure directly into the learning framework, rather than relying on data alone. This intrusive, physics-informed approach — grounded in mechanics and numerical analysis — produces models that remain physically consistent and trustworthy even when data is severely limited.

Long-term, my aim is to close the gap between simulation and the real world, in both predictive accuracy and trustworthiness. A prediction without a quantified degree of trust is of limited use for real engineering decisions. I work toward a research direction in which physics-informed modeling and uncertainty quantification are treated as inseparable, enabling real-time, physically consistent digital twins that can be deployed with confidence in high-stakes engineering systems.

Current Focus

I'm currently focusing on the following:

Mechanics-Based Material & Structural Modeling

Finite element modeling and constitutive theory form the physical basis for describing how materials and structures respond to mechanical, thermal, and coupled multiphysics loading. This work defines the governing equations, boundary conditions, and numerical discretization that any downstream model must remain consistent with. It plays the role of a foundation layer: every learning-based method further down this list inherits its physical validity from the accuracy of this mechanics description. Without it, data-driven components would have no structure to be grounded in, and predictions would reduce to pattern-matching with no guarantee of physical plausibility.

Physics-Informed Machine Learning

Governing equations and numerical structure are embedded directly into neural network training — through physics-informed neural networks and differentiable simulation — rather than learned solely from data. This method serves as the bridge between the mechanics foundation above and practical prediction: it allows a model to be trained on far less data than a purely data-driven counterpart would require, because the physics itself constrains the space of admissible solutions. This is essential in engineering settings where high-fidelity experiments or simulations are expensive to generate, and where extrapolating safely beyond observed conditions matters more than fitting them well.

Reduced-Order Modeling for Real-Time Simulation

Intrusive and stochastic reduced-order models compress high-fidelity simulations into low-dimensional representations that run orders of magnitude faster, while preserving the underlying physical structure of the full-order model. This addresses a practical bottleneck: physically accurate simulations are often too computationally expensive to run in real time, which makes them unusable for applications requiring immediate feedback, such as monitoring or control. Reduced-order modeling exists precisely to resolve this tension between fidelity and speed, making real-time deployment possible without discarding the physics that makes predictions trustworthy.

Uncertainty Quantification for Trustworthy Prediction

A prediction alone is not enough to support a real engineering decision — it must come with a quantified degree of confidence attached to it. This work focuses on developing frameworks that estimate that confidence directly from the model, so that a result is not just a number but a statement of how much that number can be trusted. This role is what converts a model's output into information that can support a decision. It is indispensable in applications such as structural health monitoring and digital twins, where the cost of an overconfident wrong prediction can be severe, and where knowing when a model should not be trusted is as important as the prediction itself.