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Mapping the seafloor in the deep ocean is currently performed using sonar systems on surface vessels (low-resolution maps) or undersea vessels (high-resolution maps). Surface-based mapping can cover a much wider search area and is not burdened by the complex logistics required for deploying undersea vessels. However, practical size constraints for a towbody or hull-mounted sonar array result in limits in beamforming and imaging resolution. For cost-effective high-resolution mapping of the deep ocean floor from the surface, a mobile wide-aperture sparse array with subarrays distributed across multiple autonomous surface vessels (ASVs) has been designed. Such a system could enable a surface-based sensor to cover a wide area while achieving high-resolution bathymetry, with resolution cells on the order of 1 m2 at a 6 km depth. For coherent 3D imaging, such a system must dynamically track the precise relative position of each boat’s sonar subarray through ocean-induced motions, estimate water column and bottom reflection properties, and mitigate interference from the array sidelobes. Sea testing of this core sparse acoustic array technology has been conducted, and planning is underway for relative navigation testing with ASVs capable of hosting an acoustic subarray.

We report a deep learning method to predict high-resolution stress fields from material microstructures, using a novel class of progressive attention-based transformer diffusion models. We train the model with a small dataset of pairs of input microstructures and resulting atomic-level Von Mises stress fields obtained from molecular dynamics (MD) simulations, and show excellent capacity to accurately predict results. We conduct a series of computational experiments to explore generalizability of the model and show that while the model was trained on a small dataset that featured samples of multiple cracks, the model can accurately predict distinct fracture scenarios such as single cracks, or crack-like defects with very different shapes. A comparison with MD simulations provides excellent comparison to the ground truth results in all cases. The results indicate that exciting opportunities that lie ahead in using progressive transformer diffusion models in the physical sciences, to produce high-fidelity and high-resolution field images. Graphical abstract

Covariant Lyapunov vectors or CLVs span the expanding and contracting directions of perturbations along trajectories in a chaotic dynamical system. Due to efficient algorithms to compute them that only utilize trajectory information, they have been widely applied across scientific disciplines, principally for sensitivity analysis and predictions under uncertainty. In this paper, we develop a numerical method to compute the directional derivatives of the first CLV along its own direction; the norm of this derivative is also the curvature of one-dimensional unstable manifolds. Similar to the computation of CLVs, the present method for their derivatives is iterative and analogously uses the second-order derivative of the chaotic map along trajectories, in addition to the Jacobian. We validate the new method on a super-contracting Smale–Williams Solenoid attractor. We also demonstrate the algorithm on several other examples including smoothly perturbed Arnold Cat maps, and the Lorenz’63 attractor, obtaining visualizations of the curvature of each attractor. Furthermore, we reveal a fundamental connection of the derivation of the CLV self-derivative computation with an efficient computation of linear response of chaotic systems.

3D spider webs exhibit highly intricate fiber architectures and owe their outstanding performance to a hierarchical organization that spans orders of magnitude in length scale from the molecular silk protein, to micrometer-sized fibers, and up to cm-scale web. Similarly, but in a completely different physical manifestation, music has a hierarchical structure composed of elementary sine wave building blocks that can be combined with other waveforms to create complex timbres, which are then arranged within larger-scale musical compositions. Although apparently different, spider webs and music have many similarities, as we point out in this work. Here, we propose an intuitive and interactive way to explore and visualize a 3D Cyrtophora citricola spider web geometry that has been digitally modeled with micron-scale details from full-scale laboratory experiments. We use model-based sonification to translate the web architecture into sound, allowing for aural perception and interpretation of its essential topological features. We implement this sonification using Unity3D and Max/MSP to create an interactive spider web environment in which a user travels through a virtual spider web. Each silk fiber in their field of view is sonified using different sine waves. Together, the sonified fibers create new and more complex timbres that reflects the architecture of 3D spider webs. These concepts are implemented into a spider web-based instrument for live performances, art installations and data exploration. It provides an unprecedented and creative way to immerse the composer, audience and user in an immersive multimedia experience generated by the complexity of a 3D spider web.

We propose a differential geometric approach for building families of low-rank covariance matrices, via interpolation on low-rank matrix manifolds. In contrast with standard parametric covariance classes, these families offer significant flexibility for problem-specific tailoring via the choice of “anchor” matrices for interpolation, for instance over a grid of relevant conditions describing the underlying stochastic process. The interpolation is computationally tractable in high dimensions, as it only involves manipulations of low-rank matrix factors. We also consider the problem of covariance identification, i.e., selecting the most representative member of the covariance family given a data set. In this setting, standard procedures such as maximum likelihood estimation are nontrivial because the covariance family is rank-deficient; we resolve this issue by casting the identification problem as distance minimization. We demonstrate the utility of these differential geometric families for interpolation and identification in a practical application: wind field covariance approximation for unmanned aerial vehicle navigation.

3D graphene assemblies are proposed as solutions to meet the goal toward efficient utilization of 2D graphene sheets, showing excellent performances in applications such as mechanical support, energy storage, and electrochemical catalysis. However, given the diversity and complexity of possible graphene 3D structures, there does not yet exist a systematic approach that can generate target 3D shapes and also, evaluate their performance. Here high-throughput data generation is combined with artificial intelligence approaches to realize rapid structure formation and property quantification of 3D graphene foams with mathematically controlled topologies, driven by molecular dynamics simulations. More than 4000 different foam structures are created, which feature diverse topologies that contain potential pathways for small molecules and auxetic structures with negative Poisson's ratio. Empowered by machine learning (ML) algorithms including graph neural networks, not only global properties such as elastic moduli, but also local behaviors such as atomic stress can be predicted and optimized based on their atomic structure, bypassing expensive atomistic simulations. The key findings of the research reported in this paper include a high-throughput virtual framework of generating diverse 3D graphene assemblies with mechanical performances quantification, and highly efficient methods of evaluating physical properties based on ML.

We describe a method to generate 3D architected materials based on mathematically parameterized human readable word input, offering a direct materialization of language. Our method uses a combination of a vector quantized generative adversarial network and contrastive language-image pre-training neural networks to generate images, which are translated into 3D architectures that are then 3D printed using fused deposition modeling into materials with varying rigidity. The novel materials are further analyzed in a metallic realization as an aluminum-based nano-architecture, using molecular dynamics modeling and thereby providing mechanistic insights into the physical behavior of the material under extreme compressive loading. This work offers a novel way to design, understand, and manufacture 3D architected materials designed from mathematically parameterized language input. Our work features, at its core, a generally applicable algorithm that transforms any 2D image data into hierarchical fully tileable, periodic architected materials. This method can have broader applications beyond language-based materials design and can render other avenues for the analysis and manufacturing of architected materials, including microstructure gradients through parametric modeling. As an emerging field, language-based design approaches can have a profound impact on end-to-end design environments and drive a new understanding of physical phenomena that intersect directly with human language and creativity. It may also be used to exploit information mined from diverse and complex databases and data sources.

Deep learning holds great promise for applications in materials science, including the discovery of physical laws and materials design.

In the first two years of the COVID-19 pandemic, members of Boston Emergency Medical Services, the City of Boston’s municipal ambulance service, had 7,689 encounters with confirmed-positive Boston residents. As COVID-19 virus strains continue to infect residents in Boston and across the country, understanding the correlation between population positivity, EMS encounters, and hospitalizations can inform healthcare response. This study examines urban virus-surveillance indicators that can serve as an early warning of the volume of Emergency Medical Services (EMS) encounters with COVID-19 positive patients and subsequently how EMS encounters with confirmed COVID-19 patients can serve as an early indicator of future hospital-demand surges. With daily data from Boston EMS and three other public agencies, we evaluate the relationship between five indicators and confirmed Boston EMS COVID-19 encounters by estimating separate Auto Regressive Integrated Moving Average models and cross-correlating their residuals. This study finds a significant and positive correlation between new COVID-19 cases citywide and EMS encounters 6 days later (p < 0.01), as well as between confirmed EMS encounters with COVID-19 patients and the number of intensive care unit beds occupied 7- and 18 -days later (p < 0.01). This study provides city health leadership needed clarity on the specific ordering and associated time lag in which infections in the population increase, EMS members encounter positive patients, and hospitals deliver care.

Parametric derivatives of statistics are highly desired quantities in prediction, design optimization and uncertainty quantification. In the presence of chaos, the rigorous computation of these quantities is certainly possible, but mathematically complicated and computationally expensive. Based on Ruelle’s formalism, this paper shows that the sophisticated linear response algorithm can be dramatically simplified in higher-dimensional systems featuring statistical homogeneity in the physical space. We argue that the contribution of the SRB (Sinai–Ruelle–Bowen) measure gradient, which is an integral yet the most cumbersome part of the full algorithm, is negligible if the objective function is appropriately aligned with unstable manifolds. This abstract condition could potentially be satisfied by a vast family of real-world chaotic systems, regardless of the physical meaning and mathematical form of the objective function and perturbed parameter. We demonstrate several numerical examples that support these conclusions and that present the use and performance of a simplified linear response algorithm. In the numerical experiments, we consider physical models described by differential equations, including Lorenz 96 and Kuramoto–Sivashinsky.

This combined computational–experimental work describes with atomistic resolution the interfacial interaction between the silk and hydroxyapatite and the potential implications for the development of osteoinductive silk biomaterials.

We present a computational framework based on graph neural networks (GNNs) to predict the natural frequencies of proteins from primary amino acid sequences and contact/distance maps.

We introduce a novel geometry-informed irreversible perturbation that accelerates convergence of the Langevin algorithm for Bayesian computation. It is well documented that there exist perturbations to the Langevin dynamics that preserve its invariant measure while accelerating its convergence. Irreversible perturbations and reversible perturbations (such as Riemannian manifold Langevin dynamics (RMLD)) have separately been shown to improve the performance of Langevin samplers. We consider these two perturbations simultaneously by presenting a novel form of irreversible perturbation for RMLD that is informed by the underlying geometry. Through numerical examples, we show that this new irreversible perturbation can improve estimation performance over irreversible perturbations that do not take the geometry into account. Moreover we demonstrate that irreversible perturbations generally can be implemented in conjunction with the stochastic gradient version of the Langevin algorithm. Lastly, while continuous-time irreversible perturbations cannot impair the performance of a Langevin estimator, the situation can sometimes be more complicated when discretization is considered. To this end, we describe a discrete-time example in which irreversibility increases both the bias and variance of the resulting estimator.

This work uses nanomechanics and nanodynamics to bridge the gap between structure and function of coronavirus, reporting a predictive model that associates vibrational patterns of the virus spike protein with infectiousness and lethality.

This review revisits the state of the art of research efforts on the design of mechanical materials using machine learning.

Telepresence-enabled exploration of deep sea environments has developed over the past 30 years, providing access to archaeologists, scientists, and the general public to sites otherwise inaccessible due to depth. Pioneered through the inception of the JASON Project in the late 1980 s, telepresence missions have expanded to two dedicated ships of exploration, NOAA Ship Okeanos Explorer and exploration vessel Nautilus, and has been implemented on a series of opportunistic missions on other vessels. This paper chronicles the history of the use of telepresence for the exploration of shipwrecks in deep water as well as how this capability has allowed the public to engage with such missions. Broadening the scope of who can explore the deep sea, telepresence has also expanded what is observed and documented in the deep, which speaks to humanity’s use of the maritime world and an archaeology of discard through our material disposed of into the deep sea.

Manufactured parts are meticulously engineered to perform well with respect to several conflicting metrics, like weight, stress, and cost. The best achievable trade-offs reside on the Pareto front , which can be discovered via performance-driven optimization. The objectives that define this Pareto front often incorporate assumptions about the context in which a part will be used, including loading conditions, environmental influences, material properties, or regions that must be preserved to interface with a surrounding assembly. Existing multi-objective optimization tools are only equipped to study one context at a time, so engineers must run independent optimizations for each context of interest. However, engineered parts frequently appear in many contexts: wind turbines must perform well in many wind speeds, and a bracket might be optimized several times with its bolt-holes fixed in different locations on each run. In this paper, we formulate a framework for variable-context multi-objective optimization. We introduce the Pareto gamut , which captures Pareto fronts over a range of contexts. We develop a global/local optimization algorithm to discover the Pareto gamut directly, rather than discovering a single fixed-context "slice" at a time. To validate our method, we adapt existing multi-objective optimization benchmarks to contextual scenarios. We also demonstrate the practical utility of Pareto gamut exploration for several engineering design problems.

© 2019 Association for Computing Machinery. Image tracing is a foundational component of the workflow in graphic design, engineering, and computer animation, linking hand-drawn concept images to collections of smooth curves needed for geometry processing and editing. Even for clean line drawings, modern algorithms often fail to faithfully vectorize junctions, or points at which curves meet; this produces vector drawings with incorrect connectivity. This subtle issue undermines the practical application of vectorization tools and accounts for hesitance among artists and engineers to use automatic vectorization software. To address this issue, we propose a novel image vectorization method based on state-of-the-art mathematical algorithms for frame field processing. Our algorithm is tailored specifically to disambiguate junctions without sacrificing quality.

Virtual labs allow researchers to design high-throughput and macro-level experiments that are not feasible in traditional in-person physical lab settings. Despite the increasing popularity of online research, researchers still face many technical and logistical barriers when designing and deploying virtual lab experiments. While several platforms exist to facilitate the development of virtual lab experiments, they typically present researchers with a stark trade-off between usability and functionality. We introduce Empirica: a modular virtual lab that offers a solution to the usability–functionality trade-off by employing a “flexible defaults” design strategy. This strategy enables us to maintain complete “build anything” flexibility while offering a development platform that is accessible to novice programmers. Empirica’s architecture is designed to allow for parameterizable experimental designs, reusable protocols, and rapid development. These features will increase the accessibility of virtual lab experiments, remove barriers to innovation in experiment design, and enable rapid progress in the understanding of human behavior.

© 2020 Owner/Author. Field-guided parameterization methods have proven effective for quad meshing of surfaces; these methods compute smooth cross fields to guide the meshing process and then integrate the fields to construct a discrete mesh. A key challenge in extending these methods to three dimensions, however, is representation of field values. Whereas cross fields can be represented by tangent vector fields that form a linear space, the 3D analog - an octahedral frame field - takes values in a nonlinear manifold. In this work, we describe the space of octahedral frames in the language of differential and algebraic geometry. With this understanding, we develop geometry-aware tools for optimization of octahedral fields, namely geodesic stepping and exact projection via semidefinite relaxation. Our algebraic approach not only provides an elegant and mathematically sound description of the space of octahedral frames but also suggests a generalization to frames whose three axes scale independently, better capturing the singular behavior we expect to see in volumetric frame fields. These new odeco frames, so called as they are represented by orthogonally decomposable tensors, also admit a semidefinite program-based projection operator. Our description of the spaces of octahedral and odeco frames suggests computing frame fields via manifold-based optimization algorithms; we show that these algorithms efficiently produce high-quality fields while maintaining stability and smoothness.

Understanding fracture is critical to the design of resilient nanomaterials. Molecular dynamics offers a way to study fracture at an atomistic level, but is computationally expensive with limitations of scalability. In this work, we build upon machine-learning approaches for predicting nanoscopic fracture mechanisms including crack instabilities and branching as a function of crystal orientation. We focus on a particular technologically relevant material system, graphene, and apply a deep learning method to the study of such nanomaterials and explore the parameter space necessary for calibrating machine-learning predictions to meaningful results. Our results validate the ability of deep learning methods to quantitatively capture graphene fracture behavior, including its fractal dimension as a function of crystal orientation, and provide promise toward the wider application of deep learning to materials design, opening the potential for other 2D materials., NSF (Grant 1122374), Office of Naval Research (Grants N000141612333 and N000141912375), AFOSR-MURI (Contract FA9550-15-1-0514), Army Research Office (Contract W911NF1920098), NIH (Grant U01-EB014976)

© 2020 The Authors. Published by Elsevier Ltd on behalf of The Chinese Society of Theoretical and Applied Mechanics Sensitivity analysis in chaotic dynamical systems is a challenging task from a computational point of view. In this work, we present a numerical investigation of a novel approach, known as the space-split sensitivity or S3 algorithm. The S3 algorithm is an ergodic-averaging method to differentiate statistics in ergodic, chaotic systems, rigorously based on the theory of hyperbolic dynamics. We illustrate S3 on one-dimensional chaotic maps, revealing its computational advantage over naïve finite difference computations of the same statistical response. In addition, we provide an intuitive explanation of the key components of the S3 algorithm, including the density gradient function.

Transformer neural networks have become widely used in a variety of AI applications, enabling significant advances in Natural Language Processing (NLP) and computer vision. Here we demonstrate the use of transformer neural networks in the de novo design of architected materials using a unique approach based on text input that enables the design to be directed by descriptive text, such as “a regular lattice of steel”. Since transformer neural nets enable the conversion of data from distinct forms into one another, including text into images, such methods have the potential to be used as a natural-language-driven tool to develop complex materials designs. In this study we use the Contrastive Language-Image Pre-Training (CLIP) and VQGAN neural networks in an iterative process to generate images that reflect text prompt driven materials designs. We then use the resulting images to generate three-dimensional models that can be realized using additive manufacturing, resulting in physical samples of these text-based materials. We present several such word-to-matter examples, and analyze 3D printed material specimen through associated additional finite element analysis, especially focused on mechanical properties including mechanism design. As an emerging new field, such language-based design approaches can have profound impact, including the use of transformer neural nets to generate machine code for 3D printing, optimization of processing conditions, and other end-to-end design environments that intersect directly with human language.

© 2019 Copyright held by the owner/author(s). Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can sometimes be computed between nearly isometric meshes, the more general case of meshes with diverse geometries remains challenging. We propose a novel approach for direct map computation between triangle meshes without mapping to an intermediate domain, which optimizes for the harmonicity and reversibility of the forward and backward maps. Our method is general both in the information it can receive as input, e.g., point landmarks, a dense map, or a functional map, and in the diversity of the geometries to which it can be applied. We demonstrate that our maps exhibit lower conformal distortion than the state of the art, while succeeding in correctly mapping key features of the input shapes.