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Invariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems, for instance, spectral submanifolds have emerged as useful…
When manufacturing parts using material extrusion additive manufacturing and anisotropic polymers, the mechanical properties of a manufactured component are strongly dependent on the print trajectory orientation. We conduct non-planar…
Fluid flow in the transonic regime finds relevance in aerospace engineering, particularly in the design of commercial air transportation vehicles. Computational fluid dynamics models of transonic flow for aerospace applications are…
Mesoscale filtering and protective layers are replete throughout the natural world. Within the body, arrays of extracellular proteins, microvilli, and cilia can act as both protective layers and mechanosensors. For example, blood flow…
Inverse design refers to the problem of optimizing the input of an objective function in order to enact a target outcome. For many real-world engineering problems, the objective function takes the form of a simulator that predicts how the…
Normalizing flows model complex probability distributions using maps obtained by composing invertible layers. Special linear layers such as masked and 1x1 convolutions play a key role in existing architectures because they increase…
Diffusion models have become a popular approach for image generation and reconstruction due to their numerous advantages. However, most diffusion-based inverse problem-solving methods only deal with 2D images, and even recently published 3D…
Urban wind flow modeling and simulation play an important role in air quality assessment and sustainable city planning. A key challenge for modeling and simulation is handling the complex geometries of the urban landscape. Low order models…
Metasurfaces are an emerging technology that may supplant many of the conventional optics found in imaging devices, displays, and precision scientific instruments. Here, we develop a method for designing optical systems composed of multiple…
Slender magnetic elements provide a versatile platform for programmable shape-morphing under remote magnetic actuation. However, a general and physically interpretable framework for the inverse design of a `magneto-elastica' under…
We present a computational framework for efficient optimization-based "inverse design" of large-area "metasurfaces" (subwavelength-patterned surfaces) for applications such as multi-wavelength and multi-angle optimizations, and…
A spreadsheet usually starts as a simple and single-user software artifact, but, as frequent as in other software systems, quickly evolves into a complex system developed by many actors. Often, different users work on different aspects of…
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…
The synthesis of a metasurface exhibiting a specific set of desired scattering properties is a time-consuming and resource-demanding process, which conventionally relies on many cycles of full-wave simulations. It requires an experienced…
Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic…
Diffusion Models (DMs) have demonstrated state-of-the-art performance in content generation without requiring adversarial training. These models are trained using a two-step process. First, a forward - diffusion - process gradually adds…
Existing curved-layer-based process planning methods for multi-axis manufacturing address collisions only indirectly and generate toolpaths in a post-processing step, leaving toolpath geometry uncontrolled during optimization. We present an…
Flexible control light field across multiple parameters is the cornerstone of versatile and miniaturized optical devices. Metasurfaces, comprising subwavelength scatterers, offer a potent platform for executing such precise manipulations.…
Interfacial fluctuations in a two-phase binary fluid mixture reveal signatures of underlying physical processes that occur within each phase and on a range of spatial and temporal scales. In this study, we investigate a model binary fluid…
An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction--diffusion process on the surface,…