We investigate the formal synthesis of global polynomial Lyapunov functions for polynomial vector fields. We establish that a sign-definite polynomial must satisfy specific algebraic constraints, which we leverage to develop a set of straightforward symbolic reduction rules. These rules can be recursively applied to symbolically simplify the Lyapunov candidate, enabling more efficient and robust discovery of Lyapunov functions via optimization or satisfiability modulo theories (SMT) solving. In many cases, without such simplification, finding a valid Lyapunov function is often infeasible. When strict Lyapunov functions are unavailable, we design synthesis procedures for finding weak Lyapunov functions to verify global asymptotic stability using LaSalle's invariance principle. Finally, we encode instability conditions for Lyapunov functions and develop SMT procedures to disprove global asymptotic stability. Through a series of examples, we demonstrate that the proposed symbolic reduction, LaSalle-type conditions, and instability tests allow us to efficiently solve many cases that would otherwise be challenging.
This paper introduces a generative model designed for multimodal control over text-to-image foundation generative AI models such as Stable Diffusion, specifically tailored for engineering design synthesis. Our model proposes parametric, image, and text control modalities to enhance design precision and diversity. Firstly, it handles both partial and complete parametric inputs using a diffusion model that acts as a design autocomplete co-pilot, coupled with a parametric encoder to process the information. Secondly, the model utilizes assembly graphs to systematically assemble input component images, which are then processed through a component encoder to capture essential visual data. Thirdly, textual descriptions are integrated via CLIP encoding, ensuring a comprehensive interpretation of design intent. These diverse inputs are synthesized through a multimodal fusion technique, creating a joint embedding that acts as the input to a module inspired by ControlNet. This integration allows the model to apply robust multimodal control to foundation models, facilitating the generation of complex and precise engineering designs. This approach broadens the capabilities of AI-driven design tools and demonstrates significant advancements in precise control based on diverse data modalities for enhanced design generation.
Research in the field of Materials Science and Engineering focuses on the design, synthesis, properties, and performance of materials. An important class of materials that is widely investigated are crystalline materials, including metals and semiconductors. Crystalline material typically contains a distinct type of defect called "dislocation". This defect significantly affects various material properties, including strength, fracture toughness, and ductility. Researchers have devoted a significant effort in recent years to understanding dislocation behavior through experimental characterization techniques and simulations, e.g., dislocation dynamics simulations. This paper presents how data from dislocation dynamics simulations can be modeled using semantic web technologies through annotating data with ontologies. We extend the already existing Dislocation Ontology by adding missing concepts and aligning it with two other domain-related ontologies (i.e., the Elementary Multi-perspective Material Ontology and the Materials Design Ontology) allowing for representing the dislocation simulation data efficiently. Moreover, we show a real-world use case by representing the discrete dislocation dynamics data as a knowledge graph (DisLocKG) that illustrates the relationship between them. We also developed a SPARQL endpoint that brings extensive flexibility to query DisLocKG.
Generative adversarial networks (GAN) have recently been used for a design synthesis of mechanical shapes. A GAN sometimes outputs physically unreasonable shapes. For example, when a GAN model is trained to output airfoil shapes that indicate required aerodynamic performance, significant errors occur in the performance values. This is because the GAN model only considers data but does not consider the aerodynamic equations that lie under the data. This paper proposes the physics-guided training of the GAN model to guide the model to learn physical validity. Physical validity is computed using general-purpose software located outside the neural network model. Such general-purpose software cannot be used in physics-informed neural network frameworks, because physical equations must be implemented inside the neural network models. Additionally, a limitation of generative models is that the output data are similar to the training data and cannot generate completely new shapes. However, because the proposed model is guided by a physical model and does not use a training dataset, it can generate completely new shapes. Numerical experiments show that the proposed model drastically improves the accuracy. Moreover, the output shapes differ from those of the training dataset but still satisfy the physical validity, overcoming the limitations of existing GAN models.
In the rapidly advancing field of multi-modal machine learning (MMML), the convergence of multiple data modalities has the potential to reshape various applications. This paper presents a comprehensive overview of the current state, advancements, and challenges of MMML within the sphere of engineering design. The review begins with a deep dive into five fundamental concepts of MMML:multi-modal information representation, fusion, alignment, translation, and co-learning. Following this, we explore the cutting-edge applications of MMML, placing a particular emphasis on tasks pertinent to engineering design, such as cross-modal synthesis, multi-modal prediction, and cross-modal information retrieval. Through this comprehensive overview, we highlight the inherent challenges in adopting MMML in engineering design, and proffer potential directions for future research. To spur on the continued evolution of MMML in engineering design, we advocate for concentrated efforts to construct extensive multi-modal design datasets, develop effective data-driven MMML techniques tailored to design applications, and enhance the scalability and interpretability of MMML models. MMML models, as the next generation of intelligent design tools, hold a promising future to impact how products are designed.
Accurate estimation of the states of a nonlinear dynamical system is crucial for their design, synthesis, and analysis. Particle filters are estimators constructed by simulating trajectories from a sampling distribution and averaging them based on their importance weight. For particle filters to be computationally tractable, it must be feasible to simulate the trajectories by drawing from the sampling distribution. Simultaneously, these trajectories need to reflect the reality of the nonlinear dynamical system so that the resulting estimators are accurate. Thus, the crux of particle filters lies in designing sampling distributions that are both easy to sample from and lead to accurate estimators. In this work, we propose to learn the sampling distributions. We put forward four methods for learning sampling distributions from observed measurements. Three of the methods are parametric methods in which we learn the mean and covariance matrix of a multivariate Gaussian distribution; each methods exploits a different aspect of the data (generic, time structure, graph structure). The fourth method is a nonparametric alternative in which we directly learn a transform of a uniform random variable. All four methods are trained in an unsupervised manner by maximizing the likelihood that the states may have produced the observed measurements. Our computational experiments demonstrate that learned sampling distributions exhibit better performance than designed, minimum-degeneracy sampling distributions.
Machine learning has recently gained traction as a way to overcome the slow accelerator generation and implementation process on an FPGA. It can be used to build performance and resource usage models that enable fast early-stage design space exploration. First, training requires large amounts of data (features extracted from design synthesis and implementation tools), which is cost-inefficient because of the time-consuming accelerator design and implementation process. Second, a model trained for a specific environment cannot predict performance or resource usage for a new, unknown environment. In a cloud system, renting a platform for data collection to build an ML model can significantly increase the total-cost-ownership (TCO) of a system. Third, ML-based models trained using a limited number of samples are prone to overfitting. To overcome these limitations, we propose LEAPER, a transfer learning-based approach for prediction of performance and resource usage in FPGA-based systems. The key idea of LEAPER is to transfer an ML-based performance and resource usage model trained for a low-end edge environment to a new, high-end cloud environment to provide fast and accurate predictions for accelerator implementation. Experimental results show that LEAPER (1) provides, on average across six workloads and five FPGAs, 85% accuracy when we use our transferred model for prediction in a cloud environment with 5-shot learning and (2) reduces design-space exploration time for accelerator implementation on an FPGA by 10x, from days to only a few hours.
Structural topology optimization, which aims to find the optimal physical structure that maximizes mechanical performance, is vital in engineering design applications in aerospace, mechanical, and civil engineering. Generative adversarial networks (GANs) have recently emerged as a popular alternative to traditional iterative topology optimization methods. However, these models are often difficult to train, have limited generalizability, and due to their goal of mimicking optimal structures, neglect manufacturability and performance objectives like mechanical compliance. We propose TopoDiff - a conditional diffusion-model-based architecture to perform performance-aware and manufacturability-aware topology optimization that overcomes these issues. Our model introduces a surrogate model-based guidance strategy that actively favors structures with low compliance and good manufacturability. Our method significantly outperforms a state-of-art conditional GAN by reducing the average error on physical performance by a factor of eight and by producing eleven times fewer infeasible samples. By introducing diffusion models to topology optimization, we show that conditional diffusion models have the ability to outperform GANs in engineering design synthesis applications too. Our work also suggests a general framework for engineering optimization problems using diffusion models and external performance with constraint-aware guidance. We publicly share the data, code, and trained models here: https://decode.mit.edu/projects/topodiff/.
Deep Generative Machine Learning Models (DGMs) have been growing in popularity across the design community thanks to their ability to learn and mimic complex data distributions. DGMs are conventionally trained to minimize statistical divergence between the distribution over generated data and distribution over the dataset on which they are trained. While sufficient for the task of generating "realistic" fake data, this objective is typically insufficient for design synthesis tasks. Instead, design problems typically call for adherence to design requirements, such as performance targets and constraints. Advancing DGMs in engineering design requires new training objectives which promote engineering design objectives. In this paper, we present the first Deep Generative Model that simultaneously optimizes for performance, feasibility, diversity, and target achievement. We benchmark performance of the proposed method against several Deep Generative Models over eight evaluation metrics that focus on feasibility, diversity, and satisfaction of design performance targets. Methods are tested on a challenging multi-objective bicycle frame design problem with skewed, multimodal data of different datatypes. The proposed framework was found to outperform all Deep Generative Models in six of eight metrics.
Design optimization of mechanisms is a promising research area as it results in more energy-efficient machines without compromising performance. However, machine builders do not actually use the design methods described in the literature as these algorithms require too much theoretical analysis. Moreover, the design synthesis approaches in the literature predominantly utilize heuristic optimizers leading to suboptimal local minima. This research introduces a convenient optimization workflow allowing wide industrial adoption, while guaranteeing to reveal the global optimum. To guarantee that we find the global optimum, a mathematical expression of the constraints describing the feasible region of possible designs is of great importance. Therefore, kinematic analysis of the point-to-point (PTP) planar four-bar mechanism is discussed to obtain the static and dynamic constraints. Within the feasible region, objective value samples are generated through CAD multi-body software. These motion simulations determine the required torque to fulfill the movement for a certain combination of design parameters. Sparse interpolation techniques allow minimizing the required amount of samples and thus CAD simulations. Moreover, this interpolation of simulation results enables the representation of the objective in a mathematical description without in-depth analytical design analysis by the machine designer. Subsequently, the mathematical expression of the objective allows global optimizers to find a global optimal design within the feasible design space. In a case study of a coronaventilator mechanism with three design parameters (DP's), 1870 CAD motion simulations from which only 618 are used to build a model allowed to reduce the RMS torque of the mechanism by 67%.
Automated design synthesis has the potential to revolutionize the modern engineering design process and improve access to highly optimized and customized products across countless industries. Successfully adapting generative Machine Learning to design engineering may enable such automated design synthesis and is a research subject of great importance. We present a review and analysis of Deep Generative Machine Learning models in engineering design. Deep Generative Models (DGMs) typically leverage deep networks to learn from an input dataset and synthesize new designs. Recently, DGMs such as feedforward Neural Networks (NNs), Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), and certain Deep Reinforcement Learning (DRL) frameworks have shown promising results in design applications like structural optimization, materials design, and shape synthesis. The prevalence of DGMs in engineering design has skyrocketed since 2016. Anticipating continued growth, we conduct a review of recent advances to benefit researchers interested in DGMs for design. We structure our review as an exposition of the algorithms, datasets, representation methods, and applications commonly used in the current literature. In particular, we discuss key works that have introduced new techniques and methods in DGMs, successfully applied DGMs to a design-related domain, or directly supported the development of DGMs through datasets or auxiliary methods. We further identify key challenges and limitations currently seen in DGMs across design fields, such as design creativity, handling constraints and objectives, and modeling both form and functional performance simultaneously. In our discussion, we identify possible solution pathways as key areas on which to target future work.
While much of the causal inference literature has focused on addressing internal validity biases, both internal and external validity are necessary for unbiased estimates in a target population of interest. However, few generalizability approaches exist for estimating causal quantities in a target population when the target population is not well-represented by a randomized study but is reflected when additionally incorporating observational data. To generalize to a target population represented by a union of these data, we propose a class of novel conditional cross-design synthesis estimators that combine randomized and observational data, while addressing their respective biases. The estimators include outcome regression, propensity weighting, and double robust approaches. All use the covariate overlap between the randomized and observational data to remove potential unmeasured confounding bias. We apply these methods to estimate the causal effect of managed care plans on health care spending among Medicaid beneficiaries in New York City.
Machine-learning (ML) techniques have revolutionized a host of research fields of chemical and materials science with accelerated, high-efficiency discoveries in design, synthesis, manufacturing, characterization and application of novel functional materials, especially at the nanometre scale. The reason is the time efficiency, prediction accuracy and good generalization abilities, which gradually replaces the traditional experimental or computational work. With enormous potentiality to tackle more real-world problems, ML provides a more comprehensive insight into combinations with molecules/materials under the fundamental procedures for constructing ML models, like predicting properties or functionalities from given parameters, nanoarchitecture design and generating specific models for other purposes. The key to the advances in nanomaterials discovery is how input fingerprints and output values can be linked quantitatively. Finally, some great opportunities and technical challenges are concluded in this fantastic field.
Engineering design tasks often require synthesizing new designs that meet desired performance requirements. The conventional design process, which requires iterative optimization and performance evaluation, is slow and dependent on initial designs. Past work has used conditional generative adversarial networks (cGANs) to enable direct design synthesis for given target performances. However, most existing cGANs are restricted to categorical conditions. Recent work on Continuous conditional GAN (CcGAN) tries to address this problem, but still faces two challenges: 1) it performs poorly on non-uniform performance distributions, and 2) the generated designs may not cover the entire design space. We propose a new model, named Performance Conditioned Diverse Generative Adversarial Network (PcDGAN), which introduces a singular vicinal loss combined with a Determinantal Point Processes (DPP) based loss function to enhance diversity. PcDGAN uses a new self-reinforcing score called the Lambert Log Exponential Transition Score (LLETS) for improved conditioning. Experiments on synthetic problems and a real-world airfoil design problem demonstrate that PcDGAN outperforms state-of-the-art GAN models and improves the conditioning likelihood by 69% in an airfoil generation task and up to 78% in synthetic conditional generation tasks and achieves greater design space coverage. The proposed method enables efficient design synthesis and design space exploration with applications ranging from CAD model generation to metamaterial selection.
In this paper, we present "BIKED," a dataset comprised of 4500 individually designed bicycle models sourced from hundreds of designers. We expect BIKED to enable a variety of data-driven design applications for bicycles and support the development of data-driven design methods. The dataset is comprised of a variety of design information including assembly images, component images, numerical design parameters, and class labels. In this paper, we first discuss the processing of the dataset, then highlight some prominent research questions that BIKED can help address. Of these questions, we further explore the following in detail: 1) Are there prominent gaps in the current bicycle market and design space? We explore the design space using unsupervised dimensionality reduction methods. 2) How does one identify the class of a bicycle and what factors play a key role in defining it? We address the bicycle classification task by training a multitude of classifiers using different forms of design data and identifying parameters of particular significance through permutation-based interpretability analysis. 3) How does one synthesize new bicycles using different representation methods? We consider numerous machine learning methods to generate new bicycle models as well as interpolate between and extrapolate from existing models using Variational Autoencoders. The dataset and code are available at http://decode.mit.edu/projects/biked/.
Modern machine learning techniques, such as deep neural networks, are transforming many disciplines ranging from image recognition to language understanding, by uncovering patterns in big data and making accurate predictions. They have also shown promising results for synthesizing new designs, which is crucial for creating products and enabling innovation. Generative models, including generative adversarial networks (GANs), have proven to be effective for design synthesis with applications ranging from product design to metamaterial design. These automated computational design methods can support human designers, who typically create designs by a time-consuming process of iteratively exploring ideas using experience and heuristics. However, there are still challenges remaining in automatically synthesizing `creative' designs. GAN models, however, are not capable of generating unique designs, a key to innovation and a major gap in AI-based design automation applications. This paper proposes an automated method, named CreativeGAN, for generating novel designs. It does so by identifying components that make a design unique and modifying a GAN model such that it becomes more likely to generate designs with identified unique components. The method combines state-of-art novelty detection, segmentation, novelty localization, rewriting, and generative models for creative design synthesis. Using a dataset of bicycle designs, we demonstrate that the method can create new bicycle designs with unique frames and handles, and generalize rare novelties to a broad set of designs. Our automated method requires no human intervention and demonstrates a way to rethink creative design synthesis and exploration.
Typical engineering design tasks require the effort to modify designs iteratively until they meet certain constraints, i.e., performance or attribute requirements. Past work has proposed ways to solve the inverse design problem, where desired designs are directly generated from specified requirements, thus avoid the trial and error process. Among those approaches, the conditional deep generative model shows great potential since 1) it works for complex high-dimensional designs and 2) it can generate multiple alternative designs given any condition. In this work, we propose a conditional deep generative model, Range-GAN, to achieve automatic design synthesis subject to range constraints. The proposed model addresses the sparse conditioning issue in data-driven inverse design problems by introducing a label-aware self-augmentation approach. We also propose a new uniformity loss to ensure generated designs evenly cover the given requirement range. Through a real-world example of constrained 3D shape generation, we show that the label-aware self-augmentation leads to an average improvement of 14% on the constraint satisfaction for generated 3D shapes, and the uniformity loss leads to a 125% average increase on the uniformity of generated shapes' attributes. This work laid the foundation for data-driven inverse design problems where we consider range constraints and there are sparse regions in the condition space.
Predictive materials synthesis is the primary bottleneck in realizing new functional and quantum materials. Strategies for synthesis of promising materials are currently identified by time-consuming trial and error approaches and there are no known predictive schemes to design synthesis parameters for new materials. We use reinforcement learning to predict optimal synthesis schedules, i.e. a time-sequence of reaction conditions like temperatures and reactant concentrations, for the synthesis of a prototypical quantum material, semiconducting monolayer MoS$_{2}$, using chemical vapor deposition. The predictive reinforcement leaning agent is coupled to a deep generative model to capture the crystallinity and phase-composition of synthesized MoS$_{2}$ during CVD synthesis as a function of time-dependent synthesis conditions. This model, trained on 10000 computational synthesis simulations, successfully learned threshold temperatures and chemical potentials for the onset of chemical reactions and predicted new synthesis schedules for producing well-sulfidized crystalline and phase-pure MoS$_{2}$, which were validated by computational synthesis simulations. The model can be extended to predict profiles for synthesis of complex structures including multi-phase heterostructures and can also predict long-time behavior of reacting systems, far beyond the domain of the MD simulations used to train the model, making these predictions directly relevant to experimental synthesis.
Deep generative models have proven useful for automatic design synthesis and design space exploration. However, they face three challenges when applied to engineering design: 1) generated designs lack diversity, 2) it is difficult to explicitly improve all the performance measures of generated designs, and 3) existing models generally do not generate high-performance novel designs, outside the domain of the training data. To address these challenges, we propose MO-PaDGAN, which contains a new Determinantal Point Processes based loss function for probabilistic modeling of diversity and performances. Through a real-world airfoil design example, we demonstrate that MO-PaDGAN expands the existing boundary of the design space towards high-performance regions and generates new designs with high diversity and performances exceeding training data.
Deep generative models are proven to be a useful tool for automatic design synthesis and design space exploration. When applied in engineering design, existing generative models face three challenges: 1) generated designs lack diversity and do not cover all areas of the design space, 2) it is difficult to explicitly improve the overall performance or quality of generated designs, and 3) existing models generally do not generate novel designs, outside the domain of the training data. In this paper, we simultaneously address these challenges by proposing a new Determinantal Point Processes based loss function for probabilistic modeling of diversity and quality. With this new loss function, we develop a variant of the Generative Adversarial Network, named "Performance Augmented Diverse Generative Adversarial Network" or PaDGAN, which can generate novel high-quality designs with good coverage of the design space. Using three synthetic examples and one real-world airfoil design example, we demonstrate that PaDGAN can generate diverse and high-quality designs. In comparison to a vanilla Generative Adversarial Network, on average, it generates samples with a 28% higher mean quality score with larger diversity and without the mode collapse issue. Unlike typical generative models that usually generate new designs by interpolating within the boundary of training data, we show that PaDGAN expands the design space boundary outside the training data towards high-quality regions. The proposed method is broadly applicable to many tasks including design space exploration, design optimization, and creative solution recommendation.