Adrián J. Lew

Designing high-performance parts increasingly requires not just choosing a shape, but also tailoring what material goes where inside that shape. Additive manufacturing technologies are making such spatial control of material properties more and more feasible, opening the door to designs that were once impossible. Yet the palette of materials typically available to designers is limited and fixed, while the full range of conceivable materials is vast—and often uncertain. This raises a fundamental challenge: how do we optimize a part’s material distribution when many of the materials that might be ideal do not yet exist, or their feasibility is unknown? In this talk, we frame material properties themselves as design variables, co-optimizing their spatial distribution together with the part’s performance objectives. The key difficulty is constraining this search to materials that are actually possible. We address this through a feasibility function that quantifies the likelihood that a given combination of material properties can be realized, enabling designers to balance ambition against risk. This strategy makes it possible to explore ambitious design spaces—such as graded or hybrid materials—while still grounding the results in manufacturable reality. We illustrate the approach through examples in mechanical and thermal design, showing how feasibilityguided optimization produces new insights into “what material to place where.”

We introduce copresheaf topological neural networks (CTNNs), a powerful unifying framework that encapsulates a wide spectrum of deep learning architectures, designed to operate on structured data, including images, point clouds, graphs, meshes, and topological manifolds. While deep learning has profoundly impacted domains ranging from digital assistants to autonomous systems, the principled design of neural architectures tailored to specific tasks and data types remains one of the field's most persistent open challenges. CTNNs address this gap by formulating model design in the language of copresheaves, a concept from algebraic topology that generalizes most practical deep learning models in use today. This abstract yet constructive formulation yields a rich design space from which theoretically sound and practically effective solutions can be derived to tackle core challenges in representation learning, such as long-range dependencies, oversmoothing, heterophily, and non-Euclidean domains. Our empirical results on structured data benchmarks demonstrate that CTNNs consistently outperform conventional baselines, particularly in tasks requiring hierarchical or localized sensitivity. These results establish CTNNs as a principled multi-scale foundation for the next generation of deep learning architectures.

ABSTRACT The computation of damping rates of an oscillating fluid with a free surface in which viscosity is small and surface tension high is numerically challenging. A typical application requiring such computation is drop‐on‐demand (DoD) microfluidic devices that eject liquid metal droplets, where accurate knowledge of the damping rates for the least‐damped oscillation modes following droplet ejection is paramount for assessing jetting stability at higher jetting frequencies, as ejection from a nonquiescent meniscus can result in deviations from nominal droplet properties. Computational fluid dynamics (CFD) simulations often struggle to accurately predict meniscus damping unless very fine discretizations are adopted, so calculations are slow and computationally expensive. The faster alternative we adopt here is to compute the damping rate directly from the eigenvalues of the linearized problem. The presence of a surface tension term in Stokes or sloshing problems requires approximation of the meniscus displacements as well, which introduces additional complexity in their numerical solution. In this paper, we consider the combined effects of viscosity and surface tension, approximate the meniscus displacements, and construct a finite element method to compute the fluid's oscillation modes. We prove that if the finite element spaces satisfy a typical inf‐sup condition, and the space of the meniscus displacements is a subset of the set of normal traces of the space of velocities, then the method is free of spurious modes with zero or positive damping rates. To construct numerical examples, we implement the method with Taylor‐Hood elements for the velocity and pressure fields, and with continuous piecewise quadratic elements for the displacement of the meniscus. We verify the numerical convergence of the method by reproducing the solution to an analytical benchmark problem and two more complex examples with axisymmetric geometry. Remarkably, the spatial shape and temporal evolution (angular frequency and damping rate) of the set of least‐damped oscillation modes are obtained in a matter of minutes, compared to days for a CFD simulation. The method's ability to quickly generate accurate estimates of fluid oscillation damping rates makes it suitable for integration into design loops for prototyping microfluidic nozzles.

The widespread application of metal additive manufacturing (AM) is limited by the ability to control the complex interactions between the energy source and the feedstock material. Here, we develop a generalizable process to introduce nanoscale grooves to the surface of metal powders which increases the powder absorptivity by up to 70% during laser powder bed fusion. Absorptivity enhancements in copper, copper-silver, and tungsten enable energy-efficient manufacturing, with printing of pure copper at relative densities up to 92% using laser energy densities as low as 83 joules per cubic millimeter. Simulations show that the enhanced powder absorptivity results from plasmon-enabled light concentration in nanoscale grooves combined with multiple scattering events. The approach taken here demonstrates a general method to enhance the absorptivity and printability of reflective and refractory metal powders by changing the surface morphology of the feedstock without altering its composition.

The widespread application of metal additive manufacturing (AM) is limited by the ability to control the complex interactions between the energy source and the feedstock material. Here we develop a generalizable process to introduce nanoscale grooves to the surface of metal powders which increases the powder absorptivity by up to 70% during laser powder bed fusion. Absorptivity enhancements in copper, copper-silver, and tungsten enables energy efficient manufacturing, with printing of pure copper at relative densities up to 92% using laser energy densities as low as 82 J/mm^3. Simulations show the enhanced powder absorptivity results from plasmon-enabled light concentration in nanoscale grooves combined with multiple scattering events. The approach taken here demonstrates a general method to enhance the absorptivity and printability of reflective and refractory metal powders by changing the surface morphology of the feedstock without altering its composition.

Abstract Laser Powder Bed Fusion (LPBF) is a form of metal additive manufacturing in which a laser traces a path on a metal powder bed to heat powder particles and progressively melt and/or fuse them together to form a part. Outcomes of LPBF are functions of the metal's temperature history and are strongly affected by the path traced by the laser. Using temperature field optimization for LPBF as a motivating application, we focus on a class of combinatorial problems where admissible control policies are a permutation of a set of control actions. We abstract this class of problems as an optimal control problem with the objective of identifying an admissible control policy that minimizes a cost function of a dynamical system's state. While, in principle, the effect of the control actions on the cost function can last an infinitely long time, we will consider systems in which the effects of these control actions can be considered to last short (finite) periods of time. In this paper, we formalize this class of combinatorial problems as a Traveling Salesperson Problem with History and prove its equivalence to an Equality Generalized Traveling Salesperson Problem (E‐GTSP), enabling the use of well‐developed E‐GTSP solvers. We demonstrate this equivalence by computing the solutions obtained using an E‐GTSP solver for an LPBF‐inspired application.

In this work, we present and prove results underlying a method which uses functionals derived from the interaction integral to approximate the stress intensity factors along a three-dimensional crack front. We first prove that the functionals possess a pair of important properties. The functionals are well-defined and continuous for square-integrable tensor fields, such as the gradient of a finite element solution. Furthermore, the stress intensity factors are representatives of such functionals in a space of functions over the crack front. Our second result is an error estimate for the numerical stress intensity factors computed via our method. The latter property of the functionals provides a recipe for numerical stress intensity factors; we apply the functionals to the gradient of a finite element approximation for a specific set of crack front variations, and we calculate the stress intensity factors by inverting the mass matrix for those variations.