Multilevel domain decomposition-based architectures for physics-informed neural networks

Physics-informed neural networks (PINNs) are a popular and powerful approach for solving problems involving differential equations, yet they often struggle to solve problems with high frequency and/or multi-scale solutions. Finite basis physics-informed neural networks (FBPINNs) improve the performance of PINNs in this regime by combining them with an overlapping domain decomposition approach. In this paper, the FBPINN approach is extended by adding multiple levels of domain decompositions to their solution ansatz, inspired by classical multilevel Schwarz domain decomposition methods (DDMs). Furthermore, analogous to typical tests for classical DDMs, strong and weak scaling studies designed for measuring how the accuracy of PINNs and FBPINNs behaves with respect to computational effort and solution complexity are carried out. Our numerical results show that the proposed multilevel FBPINNs consistently and significantly outperform PINNs across a range of problems with high frequency and multi-scale solutions. Furthermore, as expected in classical DDMs, we show that multilevel FBPINNs improve the scalability of FBPINNs to large numbers of subdomains by aiding global communication between subdomains.Comment: 25 pages, 9 figure

Active topolectrical circuits

The transfer of topological concepts from the quantum world to classical mechanical and electronic systems has opened fundamentally new approaches to protected information transmission and wave guidance. A particularly promising technology are recently discovered topolectrical circuits that achieve robust electric signal transduction by mimicking edge currents in quantum Hall systems. In parallel, modern active matter research has shown how autonomous units driven by internal energy reservoirs can spontaneously self-organize into collective coherent dynamics. Here, we unify key ideas from these two previously disparate fields to develop design principles for active topolectrical circuits (ATCs) that can self-excite topologically protected global signal patterns. Realizing autonomous active units through nonlinear Chua diode circuits, we theoretically predict and experimentally confirm the emergence of self-organized protected edge oscillations in one- and two-dimensional ATCs. The close agreement between theory, simulations and experiments implies that nonlinear ATCs provide a robust and versatile platform for developing high-dimensional autonomous electrical circuits with topologically protected functionalities.Comment: 10 pages, 4 figures, includes supplementary material. This version adds 2D experiment

Next-Generation Microshutter Arrays for Large-Format Imaging and Spectroscopy

A next-generation microshutter array, LArge Microshutter Array (LAMA), was developed as a multi-object field selector. LAMA consists of small-scaled microshutter arrays that can be combined to form large-scale microshutter array mosaics. Microshutter actuation is accomplished via electrostatic attraction between the shutter and a counter electrode, and 2D addressing can be accomplished by applying an electrostatic potential between a row of shutters and a column, orthogonal to the row, of counter electrodes. Microelectromechanical system (MEMS) technology is used to fabricate the microshutter arrays. The main feature of the microshutter device is to use a set of standard surface micromachining processes for device fabrication. Electrostatic actuation is used to eliminate the need for macromechanical magnet actuating components. A simplified electrostatic actuation with no macro components (e.g. moving magnets) required for actuation and latching of the shutters will make the microshutter arrays robust and less prone to mechanical failure. Smaller-size individual arrays will help to increase the yield and thus reduce the cost and improve robustness of the fabrication process. Reducing the size of the individual shutter array to about one square inch and building the large-scale mosaics by tiling these smaller-size arrays would further help to reduce the cost of the device due to the higher yield of smaller devices. The LAMA development is based on prior experience acquired while developing microshutter arrays for the James Webb Space Telescope (JWST), but it will have different features. The LAMA modular design permits large-format mosaicking to cover a field of view at least 50 times larger than JWST MSA. The LAMA electrostatic, instead of magnetic, actuation enables operation cycles at least 100 times faster and a mass significantly smaller compared to JWST MSA. Also, standard surface micromachining technology will simplify the fabrication process, increasing yield and reducing cost

Programmable Aperture with MEMS Microshutter Arrays

A microshutter array (MSA) has been developed for use as an aperture array for multi-object selections in James Webb Space Telescope (JWST) technology. Light shields, molybdenum nitride (MoN) coating on shutters, and aluminum/aluminum oxide coatings on interior walls are put on each shutter for light leak prevention, and to enhance optical contrast. Individual shutters are patterned with a torsion flexure that permits shutters to open 90 deg. with a minimized mechanical stress concentration. The shutters are actuated magnetically, latched, and addressed electrostatically. Also, micromechanical features are tailored onto individual shutters to prevent stiction. An individual shutter consists of a torsion hinge, a shutter blade, a front electrode that is coated on the shutter blade, a backside electrode that is coated on the interior walls, and a magnetic cobalt-iron coating. The magnetic coating is patterned into stripes on microshutters so that shutters can respond to an external magnetic field for the magnetic actuation. A set of column electrodes is placed on top of shutters, and a set of row electrodes on sidewalls is underneath the shutters so that they can be electrostatically latched open. A linear permanent magnet is aligned with the shutter rows and is positioned above a flipped upside-down array, and sweeps across the array in a direction parallel to shutter columns. As the magnet sweeps across the array, sequential rows of shutters are rotated from their natural horizontal orientation to a vertical open position, where they approach vertical electrodes on the sidewalls. When the electrodes are biased with a sufficient electrostatic force to overcome the mechanical restoring force of torsion bars, shutters remain latched to vertical electrodes in their open state. When the bias is removed, or is insufficient, the shutters return to their horizontal, closed positions. To release a shutter, both the electrode on the shutter and the one on the back wall where the shutter sits are grounded. The shutters with one or both ungrounded electrodes are held open. Sub-micron bumps underneath light shields and silicon ribs on back walls are the two features to prevent stiction. These features ensure that the microshutter array functions properly in mechanical motions. The MSA technology can be used primarily in multi-object imaging and spectroscopy, photomask generation, light switches, and in the stepper equipment used to make integrated circuits and MEMS (microelectromechanical systems) devices

Developing an Accessible 3D Printing Pipeline

Digital technology provides an opportunity for people with disabilities to be involved in artistic activities, such as virtual sculpting whose output can be fabricated using 3D printing. Existing accessible solutions, however, present mainly a set of separate tools rather than a whole cohesive production pipeline which takes into an account the specific needs of the user group. Challenges include accessible user interfaces for all pipeline steps, suitable shape modelling operations, ”3D Print” button and model data formats that require no post-processing or clean-up operations for the Direct Fabrication step. In this paper we discuss an accessible pipeline which includes 3D modelling and 3D printing, providing an example of a 3D modelling system with developed special-purpose applications allowing children with complex disabilities to participate in sculpting activities through accessible interfaces such as eye-gaze control

Virtual sculpting and 3D printing for young people with disabilities

In this paper, we present the SHIVA project which was designed to provide virtual sculpting tools for young people with complex disabilities, to allow them to engage with artistic and creative activities that they might otherwise never be able to access. Modern 3D printing then allows us to physically build their creations. To achieve this, we combined our expertise in education, accessible technology, user interfaces and geometric modelling. We built a generic accessible graphical user interface (GUI) and a suitable geometric modelling system and used these to produce two prototype modelling exercises. These tools were deployed in a school for students with complex disabilities and are now being used for a variety of educational and developmental purposes. In this paper, we present the project's motivations, approach and implementation details together with initial results, including 3D printed objects designed by young people who have disabilties

Improving the Visible and Infrared Contrast Ratio of Microshutter Arrays

Three device improvements have been developed that dramatically enhance the contrast ratio of microshutters. The goal of a microshutter is to allow as much light through as possible when the shutters are in the open configuration, and preventing any light from passing through when they are in the closed position. The ratio of the transmitted light that is blocked is defined here as the contrast ratio. Three major components contribute to the improved performance of these microshutters: 1. The precise implementation of light shields, which protect the gap around the shutters so no light can leak through. It has been ascertained that without the light shield there would be a gap on the order of 1 percent of the shutter area, limiting the contrast to a maximum of 100. 2. The precise coating of the interior wall of each microshutter was improved with an insulator and metal using an angle deposition technique. The coating prevents any infrared light that finds an entrance on the surface of the microshutter cell from being emitted from a sidewall. Since silicon is in effect transparent to any light with a wavelength longer than .1 micrometer, these coatings are essential to blocking any stray signals when the shutters are closed. 3. A thin film of molybdenum nitride (MoN) was integrated onto the surface of the microshutter blade. This film provides the majority of light blockage over the microshutter and also ensures that the shutter can be operated over a wide temperature range by maintaining its flatness. These improvements were motivated by the requirements dictated by the James Webb Space Telescope NIRSpec instrument. The science goals of the NIRSpec require observing some of the very faintest objects in a given field of view that also may contain some very bright objects. To observe the faint objects, the light from the bright objects - which could be thousands of times brighter - must be completely blocked. If a closed microshutter is even slightly transmissive, a very bright object will still transmit a small signal, which can be larger than a signal from a very faint object transmitted through an open shutter. Since this situation can completely corrupt the results, it was necessary that the closed shutters be able to attenuate light by at least a factor of 2,000. There currently exist four flight-quality microshutter arrays that have been fully or are currently undergoing testing and the results support that the three improvements described above have successfully led to contrast levels greater than 50,000 in over 99 percent of the microshutters at an operating temperature of 35 K. Applications for these high-contrast microshutters are in the photomask generation and stepper equipment used to make integrated circuits and microelectromechanical (MEMS) devices. Since microshutters are a reconfigurable optical element, their versatility in these industries provides an improvement over printed masks and fixed projection alignment systems