Katherine Piper

Katherine Piper

3rd Year PhD Student in Computational Mechanics

Talks and presentations

(Upcoming) Constraint-Driven Diffusion Maps for Automatic Reduced-Space Learning

February 24, 2027

Conference Presentation, SIAM Computational Science and Engineering, 2027, Pittsburgh, PA, USA

The Diffusion Maps (DMaps) algorithm is a manifold discovery technique that provides latent space coordinates for reduced-order models (ROMs) via spectral decomposition of a local kernel graph Laplacian which approximates the continuous Laplace-Beltrami operator. However, this method suffers from challenges inherent to kernel methods and harmonic analysis. First, success depends heavily on tuning the kernel width parameter. Second, the algorithm frequently discovers duplicate higher-frequency modes before uncovering coordinates that span new dimensions, meaning Laplacian spectral properties do not reliably indicate the data's intrinsic dimensionality. These issues are further exacerbated in real-world datasets that are highly nonlinear, noisy, sparse, or have varying point densities.

Multiscale Architectured Wick Geometries in Additively Manufactured Loop Heat Pipes

October 06, 2026

Conference Presentation, Materials Science and Technology, Pittsburgh, PA, USA

Recent advances in additive manufacturing have enabled high-volume, low-cost production of multiscale architectured porous wicks for loop heat pipes. Wicks developed through additive manufacturing, however, have low permeability, limiting thermal performance. We develop a physics-informed design approach for additively manufactured loop heat pipe wicks, aiming to maximize the rate of surface evaporation, compensating for other shortcomings in the additive manufacturing process. Using our multiscale architectured porous wicks, we find a 50% improvement in thermal performance over other state-of-the-art designs. Additionally, we demonstrate a 2-week design-manufacturing-test lead time and less than 3% performance variation across several manufactured samples. In addition to our design methodology and process, we present the motivation for low-cost manufacturing of loop heat pipes and future avenues for development in multiscale porous architectured materials.

Constructing Surrogate Models with Constraints for Additive Manufacturing.

October 05, 2026

Conference Presentation, Materials Science and Technology, Pittsburgh, PA, USA

Machine learning models for additive manufacturing often result in unreliable predictions which violate physical or manufacturing constraints and require significant post-hoc correction. In this talk, we present an alternate approach to machine learning to strictly enforce constraints while avoiding pitfalls of traditional neural-network-based methods. We develop Newton-type methods for engineering scale problems, addressing the need for reliable constrained optimization in additive manufacturing. By discretizing the optimization statement as a quadratic program and solving a second-order KKT system via interior point (barrier) methods, we enforce constraints by construction rather than through penalization. Our methods are structure-preserving, enforcing any underlying governing laws, geometric constraints, or other application-dependent requirements. We demonstrate this approach on a range of test problems and identify further applications for these methods to find reliable, constraint-satisfying predictions in additive manufacturing

Fracture in Ductile Functionally Graded Materials.

October 06, 2024

Conference Presentation, Materials Science and Technology, Pittsburgh, PA, USA

Functionally graded materials promise idealized properties including controlled thermal expansion ratios, more efficient cooling paths, and optimized structural properties. However, unknown metal phases formed within the gradient region when manufacturing FGMs have a wide range of properties which limit the accuracy of numerical methods. Existing studies on fracture in gradient materials avoid metals due to these complex phase transformations within the gradient region. In this study, we use experimental techniques to aid in developing an accurate phase field simulation of fracture mechanics in a gradient alloy between C300 and Invar36. We have developed a methodology for measuring mechanical properties within a gradient alloy and implementing these properties into a state-of-the-art phase field model for fracture. Additionally, we identify critical compositions and metal phases which would lead to variance in fracture propagation.