Data-driven learning is generalized to consider history-dependent multi-fidelity data, while quantifying epistemic uncertainty and disentangling it from data noise (aleatoric uncertainty). This generalization is hierarchical and adapts to different learning scenarios: from training the simplest single-fidelity deterministic neural networks up to the proposed multi-fidelity variance estimation Bayesian recurrent neural networks. The proposed methodology is demonstrated by applying it to different data-driven constitutive modeling scenarios for history-dependent plasticity of elastoplastic biphasic materials that include multiple fidelities with and without aleatoric uncertainty (noise). The method accurately predicts the response and quantifies model error while also discovering the noise distribution (when present). The versatility and generality of the proposed method open opportunities for future real-world applications in diverse scientific and engineering domains; especially, the most challenging cases involving design and analysis under uncertainty.

Additive manufacturing methods together with topology optimization have enabled the creation of multiscale structures with controlled spatially-varying material microstructure. However, topology optimization or inverse design of such structures in the presence of nonlinearities remains a challenge due to the expense of computational homogenization methods and the complexity of differentiably parameterizing the microstructural response. A solution to this challenge lies in machine learning techniques that offer efficient, differentiable mappings between the material response and its microstructural descriptors. This work presents a framework for designing multiscale heterogeneous structures with spatially varying microstructures by merging a homogenization-based topology optimization strategy with a consistent machine learning approach grounded in hyperelasticity theory. We leverage neural architectures that adhere to critical physical principles such as polyconvexity, objectivity, material symmetry, and thermodynamic consistency to supply the framework with a reliable constitutive model that is dependent on material microstructural descriptors. Our findings highlight the potential of integrating consistent machine learning models with density-based topology optimization for enhancing design optimization of heterogeneous hyperelastic structures under finite deformations.

Neural networks (NNs) hold great promise for advancing inverse design via topology optimization (TO), yet misconceptions about their application persist. This article focuses on neural topology optimization (neural TO), which leverages NNs to reparameterize the decision space and reshape the optimization landscape. While the method is still in its infancy, our analysis tools reveal critical insights into the NNs’ impact on the optimization process. We demonstrate that the choice of NN architecture significantly influences the objective landscape and the optimizer’s path to an optimum. Notably, NNs introduce non-convexities even in otherwise convex landscapes, potentially delaying convergence in convex problems but enhancing exploration for non-convex problems. This analysis lays the groundwork for future advancements by highlighting: (1) the potential of neural TO for non-convex problems and dedicated GPU hardware (the “good”), (2) the limitations in smooth landscapes (the “bad”), and (3) the complex challenge of selecting optimal NN architectures and hyperparameters for superior performance (the “ugly”).

In the pursuit of designing safer and more efficient energy-absorbing structures, engineers must tackle the challenge of improving crush performance while balancing multiple conflicting objectives, such as maximising energy absorption and minimising peak impact forces. Accurately simulating real-world conditions necessitates the use of complex material models to replicate the non-linear behaviour of materials under impact, which comes at a significant computational cost. This study addresses these challenges by introducing a multi-objective Bayesian optimisation framework specifically developed to optimise spinodoid structures for crush energy absorption. Spinodoid structures, characterised by their scalable, non-periodic topologies and efficient stress distribution, offer a promising direction for advanced structural design. However, optimising design parameters to enhance crush performance is far from straightforward, particularly under realistic conditions. Conventional optimisation methods, although effective, often require a large number of costly simulations to identify suitable solutions, making the process both time-consuming and resource intensive. In this context, multi-objective Bayesian optimisation provides a clear advantage by intelligently navigating the design space, learning from each evaluation to reduce the number of simulations required, and efficiently addressing the complexities of non-linear material behaviour. By integrating finite element analysis with Bayesian optimisation, the framework developed in this study tackles the dual challenge of improving energy absorption and reducing peak force, particularly in scenarios where plastic deformation plays a critical role. Leveraging scalarisation and hypervolume-based techniques, the framework effectively identifies Pareto-optimal solutions that balance these conflicting objectives while accounting for the complexities of plastic material behaviour. Importantly, the approach also prevents problematic densification, ensuring structural integrity during impact. The results not only demonstrate the framework's ability to outperform the NSGA-II algorithm but also highlight its potential for wider applications in structural and material optimisation. The framework's adaptability to various design requirements underscores its capability to address complex, multi-objective optimisation challenges associated with real-world conditions.

Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that fulfill a PDE at the boundary and within the domain of interest can be challenging and non-unique due to the complexity of the loss landscape that needs to be traversed. Although a variety of multi-task learning and transfer learning approaches have been proposed to overcome these issues, no incremental training procedure has been proposed for PINNs. As demonstrated herein, by developing incremental PINNs (iPINNs) we can effectively mitigate such training challenges and learn multiple tasks (equations) sequentially without additional parameters for new tasks. Interestingly, we show that this also improves performance for every equation in the sequence. Our approach learns multiple PDEs starting from the simplest one by creating its own subnetwork for each PDE and allowing each subnetwork to overlap with previously learned subnetworks. We demonstrate that previous subnetworks are a good initialization for a new equation if PDEs share similarities. We also show that iPINNs achieve lower prediction error than regular PINNs for two different scenarios: (1) learning a family of equations (e.g., 1-D convection PDE); and (2) learning PDEs resulting from a combination of processes (e.g., 1-D reaction–diffusion PDE). The ability to learn all problems with a single network together with learning more complex PDEs with better generalization than regular PINNs will open new avenues in this field.

High-aspect-ratio mechanical resonators are pivotal in precision sensing, from macroscopic gravitational wave detectors to nanoscale acoustics. However, fabrication challenges and high computational costs have limited the length-to-thickness ratio of these devices, leaving a largely unexplored regime in nano-engineering. We present nanomechanical resonators that extend centimeters in length yet retain nanometer thickness. We explore this expanded design space using an optimization approach which judiciously employs fast millimeter-scale simulations to steer the more computationally intensive centimeter-scale design optimization. By employing delicate nanofabrication techniques, our approach ensures high-yield realization, experimentally confirming room-temperature quality factors close to theoretical predictions. The synergy between nanofabrication, design optimization guided by machine learning, and precision engineering opens a solid-state path to room-temperature quality factors approaching 10 billion at kilohertz mechanical frequencies – comparable to the performance of leading cryogenic resonators and levitated nanospheres, even under significantly less stringent temperature and vacuum conditions.

We introduce a new continual (or lifelong) learning algorithm called LDA-CP &S that performs segmentation tasks without undergoing catastrophic forgetting. The method is applied to two different surface defect segmentation problems that are learned incrementally, i.e., providing data about one type of defect at a time, while still being capable of predicting every defect that was seen previously. Our method creates a defect-related subnetwork for each defect type via iterative pruning and trains a classifier based on linear discriminant analysis (LDA). At the inference stage, we first predict the defect type with LDA and then predict the surface defects using the selected subnetwork. We compare our method with other continual learning methods showing a significant improvement – mean Intersection over Union better by a factor of two when compared to existing methods on both datasets. Importantly, our approach shows comparable results with joint training when all the training data (all defects) are seen simultaneously.

Current deep neural networks (DNNs) are overparameterized and use most of their neuronal connections during inference for each task. The human brain, however, developed specialized regions for different tasks and performs inference with a small fraction of its neuronal connections. We propose an iterative pruning strategy introducing a simple importance-score metric that deactivates unimportant connections, tackling overparameterization in DNNs and modulating the firing patterns. The aim is to find the smallest number of connections that is still capable of solving a given task with comparable accuracy, i.e. a simpler subnetwork. We achieve comparable performance for LeNet architectures on MNIST, and significantly higher parameter compression than state-of-the-art algorithms for VGG and ResNet architectures on CIFAR-10/100 and Tiny-ImageNet. Our approach also performs well for the two different optimizers considered—Adam and SGD. The algorithm is not designed to minimize FLOPs when considering current hardware and software implementations, although it performs reasonably when compared to the state of the art.

The human brain is capable of learning tasks sequentially mostly without forgetting. However, deep neural networks (DNNs) suffer from catastrophic forgetting when learning one task after another. We address this challenge considering a class-incremental learning scenario where the DNN sees test data without knowing the task from which this data originates. During training, Continual Prune-and-Select (CP&S) finds a subnetwork within the DNN that is responsible for solving a given task. Then, during inference, CP&S selects the correct subnetwork to make predictions for that task. A new task is learned by training available neuronal connections of the DNN (previously untrained) to create a new subnetwork by pruning, which can include previously trained connections belonging to other subnetwork(s) because it does not update shared connections. This enables to eliminate catastrophic forgetting by creating specialized regions in the DNN that do not conflict with each other while still allowing knowledge transfer across them. The CP&S strategy is implemented with different subnetwork selection strategies, revealing superior performance to state-of-the-art continual learning methods tested on various datasets (CIFAR-100, CUB-200-2011, ImageNet-100 and ImageNet-1000). In particular, CP&S is capable of sequentially learning 10 tasks from ImageNet-1000 keeping an accuracy around 94% with negligible forgetting, a first-of-its-kind result in class-incremental learning. To the best of the authors’ knowledge, this represents an improvement in accuracy above 10% when compared to the best alternative method.

For decades, mechanical resonators with high sensitivity have been realized using thin-film materials under high tensile loads. Although there are remarkable strides in achieving low-dissipation mechanical sensors by utilizing high tensile stress, the performance of even the best strategy is limited by the tensile fracture strength of the resonator materials. In this study, a wafer-scale amorphous thin film is uncovered, which has the highest ultimate tensile strength ever measured for a nanostructured amorphous material. This silicon carbide (SiC) material exhibits an ultimate tensile strength of over 10 GPa, reaching the regime reserved for strong crystalline materials and approaching levels experimentally shown in graphene nanoribbons. Amorphous SiC strings with high aspect ratios are fabricated, with mechanical modes exceeding quality factors 10⁸ at room temperature, the highest value achieves among SiC resonators. These performances are demonstrated faithfully after characterizing the mechanical properties of the thin film using the resonance behaviors of free-standing resonators. This robust thin-film material has significant potential for applications in nanomechanical sensors, solar cells, biological applications, space exploration, and other areas requiring strength and stability in dynamic environments. The findings of this study open up new possibilities for the use of amorphous thin-film materials in high-performance applications.

Data-driven modeling in mechanics is evolving rapidly based on recent machine learning advances, especially on artificial neural networks. As the field matures, new data and models created by different groups become available, opening possibilities for cooperative modeling. However, artificial neural networks suffer from catastrophic forgetting, i.e. they forget how to perform an old task when trained on a new one. This hinders cooperation because adapting an existing model for a new task affects the performance on a previous task trained by someone else. The authors developed a continual learning method that addresses this issue, applying it here for the first time to solid mechanics. In particular, the method is applied to recurrent neural networks to predict history-dependent plasticity behavior, although it can be used on any other architecture (feedforward, convolutional, etc.) and to predict other phenomena. This work intends to spawn future developments on continual learning that will foster cooperative strategies among the mechanics community to solve increasingly challenging problems. We show that the chosen continual learning strategy can sequentially learn several constitutive laws without forgetting them, using less data to achieve the same error as standard (non-cooperative) training of one law per model.

This article introduces adaptivity in Clustering-based Reduced Order Models (ACROMs). The strategy is demonstrated for a particular CROM called Self-Consistent Clustering Analysis (SCA), extending it into the Adaptive Self-Consistent Clustering Analysis (ASCA) method. This is shown to improve predictions of Representative Volume Elements (RVEs) of materials exhibiting history-dependent localization phenomena such as plasticity, damage and fracture. The overall approach is composed of three main building blocks: target clusters selection criterion, adaptive cluster analysis, and computation of cluster interaction tensors. In addition, an adaptive clustering solution rewinding procedure and a dynamic adaptivity split factor strategy are suggested to further enhance the adaptive process. The ASCA method is shown to perform better than its static counterpart when capturing the multi-scale elasto-plastic behavior of a particle–matrix composite and predicting the associated fracture and toughness. The proposed adaptivity strategy can be followed in other CROMs to extend them into ACROMs, opening new avenues to explore adaptivity in this context.

Stiffness in compliant mechanisms can be dramatically altered and even eliminated entirely by using static balancing. This requires elastic energy to be inserted before operation, which is most often done with an additional device or preloading assembly. Adding such devices contrasts starkly with primary motivations for using compliant mechanisms, such as part count reduction, increased precision, and miniaturization. However, statically balanced compliant mechanisms with a fully monolithic architecture are scarce. In this article, we introduce two novel statically balanced compliant mechanisms with linear and rotary kinematics that do not require preloading assembly, enabling miniaturization. Static balance is achieved by the principle of opposing constant force and extended to a rotational device by using opposing constant torque mechanisms for the first time. A constant force mechanism based on existing work is used and inspired a novel constant torque mechanism. A single-piece device is obtained by monolithically integrating a bistable switch for preloading, which allows static balance to be turned on and off. The linear device reduces stiffness by 98.5% over 10 mm, has significantly reduced device complexity and has doubled relative range of motion from 3.3% to 6.6% compared to the state of the art. The rotary device reduces stiffness by 90.5% over 0.35 rad.

From ultrasensitive detectors of fundamental forces to quantum networks and sensors, mechanical resonators are enabling next-generation technologies to operate in room-temperature environments. Currently, silicon nitride nanoresonators stand as a leading microchip platform in these advances by allowing for mechanical resonators whose motion is remarkably isolated from ambient thermal noise. However, to date, human intuition has remained the driving force behind design processes. Here, inspired by nature and guided by machine learning, a spiderweb nanomechanical resonator is developed that exhibits vibration modes, which are isolated from ambient thermal environments via a novel “torsional soft-clamping” mechanism discovered by the data-driven optimization algorithm. This bioinspired resonator is then fabricated, experimentally confirming a new paradigm in mechanics with quality factors above 1 billion in room-temperature environments. In contrast to other state-of-the-art resonators, this milestone is achieved with a compact design that does not require sub-micrometer lithographic features or complex phononic bandgaps, making it significantly easier and cheaper to manufacture at large scales. These results demonstrate the ability of machine learning to work in tandem with human intuition to augment creative possibilities and uncover new strategies in computing and nanotechnology.

We introduce two essential building blocks with binary stiffness for mechanical digital machines. The large scale fully compliant mechanisms have rectilinear and rotational kinematics and use a new V-shaped negative stiffness structure to create two extreme states of stiffness by static balancing. The use of a mechanical bistable switch allows us to toggle between near-zero-stiffness and high-stiffness states, effectively turning off and on stiffness. A stiffness reduction of 98.8% and 99.9% is achieved for linear and rotary motion over a range of 13.3% (20mm) and 0.4rad (23∘) respectively. Stiffness states can be reversibly changed by toggling the mechanical switch, or irreversibly by actuating the main stage. These binary stiffness mechanisms could set the stage for a new type of mechanical logic, adaptive and programmable metamaterials and other types of digital mechanical devices. Practical mechanical digital machines and materials require miniaturized and easily micro-manufactured components. We have therefore carefully considered scalability by integrating all required structures into a planar and monolithic architecture. This allows miniaturization and fabrication with conventional surface-micro-machining and additive manufacturing such as photolithography, two-photon lithography and fused deposition modeling.

This work represents the first step towards the application of machine learning techniques in the prediction of statistical design allowables of composite laminates. Building on data generated analytically, four machine algorithms (XGBoost, Random Forests, Gaussian Processes and Artificial Neural Networks) are used to predict the notched strength of composite laminates and their statistical distribution, associated to the uncertainty related to the material properties and geometrical features. This work focuses not only on the so-called Legacy Quad Laminates (0°/90°/±45°), typically used in the design of composite aerostructures, but also on the newer concept of double-double (or double-angle ply) laminates. Very good representations of the design space, translating in low generalization relative errors of around ±10%, and very accurate representations of the distributions of notched strengths around single design points and corresponding B-basis allowables are obtained. All machine learning algorithms, with the exception of the Random Forests, show very good performances, with Gaussian Processes outperforming the others for very small number of data points while Artificial Neural Networks have better performance for larger training sets. This work serves as basis for the prediction of first-ply failure, ultimate strength and failure mode of composite specimens based on non-linear finite element simulations, providing further reduction of the computational time required to virtually obtain the design allowables for composite laminates.

Gaussian processes are well-established Bayesian machine learning algorithms with significant merits, despite a strong limitation: lack of scalability. Clever solutions address this issue by inducing sparsity through low-rank approximations, often based on the Nystrom method. Here, we propose a different method to achieve better scalability and higher accuracy using quantum computing, outperforming classical Bayesian neural networks for large datasets significantly. Unlike other approaches to quantum machine learning, the computationally expensive linear algebra operations are not just replaced with their quantum counterparts. Instead, we start from a recent study that proposed a quantum circuit for implementing quantum Gaussian processes and then we use quantum phase estimation to induce a low-rank approximation analogous to that in classical sparse Gaussian processes. We provide evidence through numerical tests, mathematical error bound estimation, and complexity analysis that the method can address the “curse of dimensionality,” where each additional input parameter no longer leads to an exponential growth of the computational cost. This is also demonstrated by applying the algorithm in a practical setting and using it in the data-driven design of a recently proposed metamaterial. The algorithm, however, requires significant quantum computing hardware improvements before quantum advantage can be achieved.