A critical issue that affects engineers trying to assess the structural integrity of various infrastructures, such as metal rods or acoustic ducts, is the challenge of detecting internal fractures (defects). Traditionally, engineers depend on audible and visual aids to identify these fractures, as they do not physically dissect the object in question into multiple pieces to check for inconsistencies. This research introduces ideas towards the development of a robust strategy to image such defects using only a small set of minimal, non-invasive measurements. Assuming a one dimensional model (e.g. longitudinal waves in long and thin rods/acoustic ducts or transverse vibrations of strings), we make use of the continuous one-dimensional wave equation to model these physical phenomena and then employ specialized mathematical analysis tools (the Laplace transform and optimization) to introduce our defect imaging ideas. In particular, we will focus on the case of a long bar which is homogeneous throughout except in a small area where a defect in its Young's modulus is present. We will first demonstrate how the problem is equivalent to a spring-mass vibrational system, and then show how our imaging strategy makes use of the Laplace domain analytic map between the characteristics of the respective defect and the measurement data. More explicitly, we will utilize MATLAB (a platform for numerical computations) to collect synthetic data (computational alternative to real world measurements) for several scenarios with one defect of arbitrary location and stiffness. Subsequently, we will use this data along with our analytically developed map (between defect characteristics and measurements) to construct a residual function which, once optimized, will reveal the location and magnitude of the stiffness defect.

We introduce PROD (Palpative Reconstruction of Deformables), a novel method for reconstructing the shape and mechanical properties of deformable objects using elastostatic signed distance functions (SDFs). Unlike traditional approaches that rely on purely geometric or visual data, PROD integrates palpative interaction -- measured through force-controlled surface probing -- to estimate both the static and dynamic response of soft materials. We model the deformation of an object as an elastostatic process and derive a governing Poisson equation for estimating its SDF from a sparse set of pose and force measurements. By incorporating steady-state elastodynamic assumptions, we show that the undeformed SDF can be recovered from deformed observations with provable convergence. Our approach also enables the estimation of material stiffness by analyzing displacement responses to varying force inputs. We demonstrate the robustness of PROD in handling pose errors, non-normal force application, and curvature errors in simulated soft body interactions. These capabilities make PROD a powerful tool for reconstructing deformable objects in applications ranging from robotic manipulation to medical imaging and haptic feedback systems.

We revisit a classical assumption for analyzing stochastic gradient algorithms where the squared norm of the stochastic subgradient (or the variance for smooth problems) is allowed to grow as fast as the squared norm of the optimization variable. We contextualize this assumption in view of its inception in the 1960s, its seemingly independent appearance in the recent literature, its relationship to weakest-known variance assumptions for analyzing stochastic gradient algorithms, and its relevance in deterministic problems for non-Lipschitz nonsmooth convex optimization. We build on and extend a connection recently made between this assumption and the Halpern iteration. For convex nonsmooth, and potentially stochastic, optimization, we analyze horizon-free, anytime algorithms with last-iterate rates. For problems beyond simple constrained optimization, such as convex problems with functional constraints or regularized convex-concave min-max problems, we obtain rates for optimality measures that do not require boundedness of the feasible set.

In this study, we propose Explainable Multimodal Machine Learning (EMML), which integrates the analysis of diverse data types (multimodal data) using factor analysis for feature extraction with Explainable AI (XAI), for carbon nanotube (CNT) fibers prepared from aqueous dispersions. This method is a powerful approach to elucidate the mechanisms governing material properties, where multi-stage fabrication conditions and multiscale structures have complex influences. Thus, in our case, this approach helps us understand how different processing steps and structures at various scales impact the final properties of CNT fibers. The analysis targeted structures ranging from the nanoscale to the macroscale, including aggregation size distributions of CNT dispersions and the effective length of CNTs. Furthermore, because some types of data were difficult to interpret using standard methods, challenging-to-interpret distribution data were analyzed using Negative Matrix Factorization (NMF) for extracting key features that determine the outcome. Contribution analysis with SHapley Additive exPlanations (SHAP) demonstrated that small, uniformly distributed aggregates are crucial for improving fracture strength, while CNTs with long effective lengths are significant factors for enhancing electrical conductivity. The analysis also identified thresholds and trends for these key factors to assist in defining the conditions needed to optimize CNT fiber properties. EMML is not limited to CNT fibers but can be applied to the design of other materials derived from nanomaterials, making it a useful tool for developing a wide range of advanced materials. This approach provides a foundation for advancing data-driven materials research.

In this section, we review closely related literature on decentralized optimization, communicationefficient algorithms, and communication compression. Decentralized optimization Decentralized optimization, which is a special class of linearly constrained (consensus constraint) optimization problems, has been studied for a long time [3, 9]. Many centralized algorithms can be intuitively converted into decentralized counterparts by using gossip averaging [14, 53], which mixes parameters from neighboring clients to enforce consensus. However, direct applications of gossip averaging often lead to either slow convergence or high error floors [34], and many fixes have been proposed in response [44, 56, 38, 7, 35]. Among them, gradient tracking [38, 7, 35], which applies the idea of dynamic average consensus [59] to global gradient estimation, provides a systematic approach to reduce the variance and has been successfully applied to decentralize many algorithms with faster rates of convergence. Communication-efficient algorithms While decentralized optimization is a classical topic, the focus on communication efficiency is relatively new due to the advances in large-scale machine learning.

Tungsten-copper (W-Cu) compounds are widely utilized in various industrial fields due to their exceptional mechanical properties. In this study, we have developed a neural-network-based deep potential (DP) model that covers a wide range of temperatures, ranging from 0 to 3,000 K, and pressures, varying from 0 to 10 GPa. This study presents a model trained using density functional theory data for full concentration CuxW100-x compounds. Through this model, we systematically investigate the structural and mechanical properties of W-Cu alloys and have the following findings. First, the bulk modulus (B) and Young's modulus (E) of W-Cu alloys exhibit a linear decline as the Cu content increases, indicating a softening trend in the CuxW100-x compounds as the Cu concentration rises. Second, a higher Cu content results in higher critical strain and lower critical stress for these compounds. A brittle-to-ductile transition in the deformation mode predicted is predicted at around 37.5 at. % Cu content. Third, tensile loading tests in the W-Cu gradient structure reveal that Cu-poor region serves as a barrier, hindering shear band propagation while promoting new shear band formation in the Cu-rich region. The above results from the DP model are anticipated to aid in exploring the physical mechanisms underlying the complex phenomena of W-Cu systems and contribute to the advancement of methodologies for materials simulation.

Following the first part of our project, this paper comprehensively studies two types of extragradient-based methods: anchored extragradient and Nesterov's accelerated extragradient for solving [non]linear inclusions (and, in particular, equations), primarily under the Lipschitz continuity and the co-hypomonotonicity assumptions. We unify and generalize a class of anchored extragradient methods for monotone inclusions to a wider range of schemes encompassing existing algorithms as special cases. We establish $\mathcal{O}(1/k)$ last-iterate convergence rates on the residual norm of the underlying mapping for this general framework and then specialize it to obtain convergence guarantees for specific instances, where $k$ denotes the iteration counter. We extend our approach to a class of anchored Tseng's forward-backward-forward splitting methods to obtain a broader class of algorithms for solving co-hypomonotone inclusions. Again, we analyze $\mathcal{O}(1/k)$ last-iterate convergence rates for this general scheme and specialize it to obtain convergence results for existing and new variants. We generalize and unify Nesterov's accelerated extra-gradient method to a new class of algorithms that covers existing schemes as special instances while generating new variants. For these schemes, we can prove $\mathcal{O}(1/k)$ last-iterate convergence rates for the residual norm under co-hypomonotonicity, covering a class of nonmonotone problems. We propose another novel class of Nesterov's accelerated extragradient methods to solve inclusions. Interestingly, these algorithms achieve both $\mathcal{O}(1/k)$ and $o(1/k)$ last-iterate convergence rates, and also the convergence of iterate sequences under co-hypomonotonicity and Lipschitz continuity. Finally, we provide a set of numerical experiments encompassing different scenarios to validate our algorithms and theoretical guarantees.

Touch is a crucial sensing modality that provides rich information about object properties and interactions with the physical environment. Humans and robots both benefit from using touch to perceive and interact with the surrounding environment (Johansson and Flanagan, 2009; Li et al., 2020; Calandra et al., 2017). However, no existing systems provide rich, multi-modal digital touch-sensing capabilities through a hemispherical compliant embodiment. Here, we describe several conceptual and technological innovations to improve the digitization of touch. These advances are embodied in an artificial finger-shaped sensor with advanced sensing capabilities. Significantly, this fingertip contains high-resolution sensors (~8.3 million taxels) that respond to omnidirectional touch, capture multi-modal signals, and use on-device artificial intelligence to process the data in real time. Evaluations show that the artificial fingertip can resolve spatial features as small as 7 um, sense normal and shear forces with a resolution of 1.01 mN and 1.27 mN, respectively, perceive vibrations up to 10 kHz, sense heat, and even sense odor. Furthermore, it embeds an on-device AI neural network accelerator that acts as a peripheral nervous system on a robot and mimics the reflex arc found in humans. These results demonstrate the possibility of digitizing touch with superhuman performance. The implications are profound, and we anticipate potential applications in robotics (industrial, medical, agricultural, and consumer-level), virtual reality and telepresence, prosthetics, and e-commerce. Toward digitizing touch at scale, we open-source a modular platform to facilitate future research on the nature of touch.

This work leverages laser vibrometry and the weak form of the sparse identification of nonlinear dynamics (WSINDy) for partial differential equations to learn macroscale governing equations from full-field experimental data. In the experiments, two beam-like specimens, one aluminum and one IDOX/Estane composite, are subjected to shear wave excitation in the low frequency regime and the response is measured in the form of particle velocity on the specimen surface. The WSINDy for PDEs algorithm is applied to the resulting spatio-temporal data to discover the effective dynamics of the specimens from a family of potential PDEs. The discovered PDE is of the recognizable Euler-Bernoulli beam model form, from which the Young's modulus for the two materials are estimated. An ensemble version of the WSINDy algorithm is also used which results in information about the uncertainty in the PDE coefficients and Young's moduli. The discovered PDEs are also simulated with a finite element code to compare against the experimental data with reasonable accuracy. Using full-field experimental data and WSINDy together is a powerful non-destructive approach for learning unknown governing equations and gaining insights about mechanical systems in the dynamic regime.