Structural vibrations are a source of unwanted noise in engineering systems like cars, trains or airplanes. Minimizing these vibrations is crucial for improving passenger comfort. This work presents a novel design optimization approach based on guided flow matching for reducing vibrations by placing beadings (indentations) in plate-like structures. Our method integrates a generative flow matching model and a surrogate model trained to predict structural vibrations. During the generation process, the flow matching model pushes towards manufacturability while the surrogate model pushes to low-vibration solutions. The flow matching model and its training data implicitly define the design space, enabling a broader exploration of potential solutions as no optimization of manually-defined design parameters is required. We apply our method to a range of differentiable optimization objectives, including direct optimization of specific eigenfrequencies through careful construction of the objective function. Results demonstrate that our method generates diverse and manufacturable plate designs with reduced structural vibrations compared to designs from random search, a criterion-based design heuristic and genetic optimization. The code and data are available from https://github.com/ecker-lab/Optimizing_Vibrating_Plates.

Accurate and efficient fluid flow models are essential for applications relating to many physical phenomena including geophysical, aerodynamic, and biological systems. While these flows may exhibit rich and multiscale dynamics, in many cases underlying low-rank structures exist which describe the bulk of the motion. These structures tend to be spatially large and temporally slow, and may contain most of the energy in a given flow. The extraction and parsimonious representation of these low-rank dynamics from high-dimensional data is a key challenge. Inspired by the success of physics-informed machine learning methods, we propose a spectrally-informed approach to extract low-rank models of fluid flows by leveraging known spectral properties in the learning process. We incorporate this knowledge by imposing regularizations on the learned dynamics, which bias the training process towards learning low-frequency structures with corresponding higher power. We demonstrate the effectiveness of this method to improve prediction and produce learned models which better match the underlying spectral properties of prototypical fluid flows.

In this work we aim to mimic the human ability to acquire the intuition to estimate the performance of a design from visual inspection and experience alone. We study the ability of convolutional neural networks to predict static and dynamic properties of cantilever beams directly from their raw cross-section images. Using pixels as the only input, the resulting models learn to predict beam properties such as volume maximum deflection and eigenfrequencies with 4.54% and 1.43% Mean Average Percentage Error (MAPE) respectively, compared to the Finite Element Analysis (FEA) approach. Training these models doesn't require prior knowledge of theory or relevant geometric properties, but rather relies solely on simulated or empirical data, thereby making predictions based on "experience" as opposed to theoretical knowledge. Since this approach is over 1000 times faster than FEA, it can be adopted to create surrogate models that could speed up the preliminary optimization studies where numerous consecutive evaluations of similar geometries are required. We suggest that this modeling approach would aid in addressing challenging optimization problems involving complex structures and physical phenomena for which theoretical models are unavailable.

The computer screen shows a height map of the 1716 'Messiah' Stradivari violin, taken from a 3D scan (left); and an X-ray of the ribs of the 1718 'San Lorenzo' Stradivari (right) The following extract is from The Strad's September 2021 issue feature'Violin Making and AI: Intelligent Design'. To read it in full, click here to subscribe and login. The idea that the shape and thickness of a violin's top and back plates can affect its sound is nothing new. Antonio Stradivari was undoubtedly aware of it 300 years ago, and the science behind it was scrutinised and written up at length by Carleen Hutchins in the 1950s. Since then, the phenomenon of violin'modes' and resonances has been investigated by both violin makers and academics; indeed, for many luthiers, one of the first steps in making a new instrument will be to examine its'tap tones', or speed of sound along the plates.

Optimizing the reliability and the robustness of a design is important but often unaffordable due to high sample requirements. Surrogate models based on statistical and machine learning methods are used to increase the sample efficiency. However, for higher dimensional or multi-modal systems, surrogate models may also require a large amount of samples to achieve good results. We propose a sequential sampling strategy for the surrogate based solution of multi-objective reliability based robust design optimization problems. Proposed local Latin hypercube refinement (LoLHR) strategy is model-agnostic and can be combined with any surrogate model because there is no free lunch but possibly a budget one. The proposed method is compared to stationary sampling as well as other proposed strategies from the literature. Gaussian process and support vector regression are both used as surrogate models. Empirical evidence is presented, showing that LoLHR achieves on average better results compared to other surrogate based strategies on the tested examples.

Of all the characteristics of a violin, those that concern its shape are probably the most important ones, as the violin maker has complete control over them. Contemporary violin making, however, is still based more on tradition than understanding, and a definitive scientific study of the specific relations that exist between shape and vibrational properties is yet to come and sorely missed. In this article, using standard statistical learning tools, we show that the modal frequencies of violin tops can, in fact, be predicted from geometric parameters, and that artificial intelligence can be successfully applied to traditional violin making. We also study how modal frequencies vary with the thicknesses of the plate (a process often referred to as {\em plate tuning}) and discuss the complexity of this dependency. Finally, we propose a predictive tool for plate tuning, which takes into account material and geometric parameters.