Abstract:Process Flow Diagrams (PFDs) and Process and Instrumentation Diagrams (PIDs) are critical tools for industrial process design, control, and safety. However, the generation of precise and regulation-compliant diagrams remains a significant challenge, particularly in scaling breakthroughs from material discovery to industrial production in an era of automation and digitalization. This paper introduces an autonomous agentic framework to address these challenges through a twostage approach involving knowledge acquisition and generation. The framework integrates specialized sub-agents for retrieving and synthesizing multimodal data from publicly available online sources and constructs ontological knowledge graphs using a Graph Retrieval-Augmented Generation (Graph RAG) paradigm. These capabilities enable the automation of diagram generation and open-domain question answering (ODQA) tasks with high contextual accuracy. Extensive empirical experiments demonstrate the frameworks ability to deliver regulation-compliant diagrams with minimal expert intervention, highlighting its practical utility for industrial applications.
Abstract:Digital Twin technology creates virtual replicas of physical objects, processes, or systems by replicating their properties, data, and behaviors. This advanced technology offers a range of intelligent functionalities, such as modeling, simulation, and data-driven decision-making, that facilitate design optimization, performance estimation, and monitoring operations. Forecasting plays a pivotal role in Digital Twin technology, as it enables the prediction of future outcomes, supports informed decision-making, minimizes risks, driving improvements in efficiency, productivity, and cost reduction. Recently, Digital Twin technology has leveraged Graph forecasting techniques in large-scale complex sensor networks to enable accurate forecasting and simulation of diverse scenarios, fostering proactive and data-driven decision making. However, existing Graph forecasting techniques lack scalability for many real-world applications. They have limited ability to adapt to non-stationary environments, retain past knowledge, lack a mechanism to capture the higher order spatio-temporal dynamics, and estimate uncertainty in model predictions. To surmount the challenges, we introduce a hybrid architecture that enhances the hypergraph representation learning backbone by incorporating fast adaptation to new patterns and memory-based retrieval of past knowledge. This balance aims to improve the slowly-learned backbone and achieve better performance in adapting to recent changes. In addition, it models the time-varying uncertainty of multi-horizon forecasts, providing estimates of prediction uncertainty. Our forecasting architecture has been validated through ablation studies and has demonstrated promising results across multiple benchmark datasets, surpassing state-ofthe-art forecasting methods by a significant margin.
Abstract:Accurately predicting the behavior of complex dynamical systems, characterized by high-dimensional multivariate time series(MTS) in interconnected sensor networks, is crucial for informed decision-making in various applications to minimize risk. While graph forecasting networks(GFNs) are ideal for forecasting MTS data that exhibit spatio-temporal dependencies, prior works rely solely on the domain-specific knowledge of time-series variables inter-relationships to model the nonlinear dynamics, neglecting inherent relational structural dependencies among the variables within the MTS data. In contrast, contemporary works infer relational structures from MTS data but neglect domain-specific knowledge. The proposed hybrid architecture addresses these limitations by combining both domain-specific knowledge and implicit knowledge of the relational structure underlying the MTS data using Knowledge-Based Compositional Generalization. The hybrid architecture shows promising results on multiple benchmark datasets, outperforming state-of-the-art forecasting methods. Additionally, the architecture models the time varying uncertainty of multi-horizon forecasts.
Abstract:Forecasting the behaviour of complex dynamical systems such as interconnected sensor networks characterized by high-dimensional multivariate time series(MTS) is of paramount importance for making informed decisions and planning for the future in a broad spectrum of applications. Graph forecasting networks(GFNs) are well-suited for forecasting MTS data that exhibit spatio-temporal dependencies. However, most prior works of GFN-based methods on MTS forecasting rely on domain-expertise to model the nonlinear dynamics of the system, but neglect the potential to leverage the inherent relational-structural dependencies among time series variables underlying MTS data. On the other hand, contemporary works attempt to infer the relational structure of the complex dependencies between the variables and simultaneously learn the nonlinear dynamics of the interconnected system but neglect the possibility of incorporating domain-specific prior knowledge to improve forecast accuracy. To this end, we propose a hybrid architecture that combines explicit prior knowledge with implicit knowledge of the relational structure within the MTS data. It jointly learns intra-series temporal dependencies and inter-series spatial dependencies by encoding time-conditioned structural spatio-temporal inductive biases to provide more accurate and reliable forecasts. It also models the time-varying uncertainty of the multi-horizon forecasts to support decision-making by providing estimates of prediction uncertainty. The proposed architecture has shown promising results on multiple benchmark datasets and outperforms state-of-the-art forecasting methods by a significant margin. We report and discuss the ablation studies to validate our forecasting architecture.
Abstract:Microrobotics is an attractive area of research as small-scale robots have the potential to improve the precision and dexterity offered by minimally invasive surgeries. One example of such a tool is a pair of micro-surgical scissors that was developed for cutting of tumors or cancerous tissues present deep inside the body such as in the brain. This task is often deemed difficult or impossible with conventional robotic tools due to their size and dexterity. The scissors are designed with two magnets placed a specific distance apart to maximize deflection and generate cutting forces. However, remote actuation and size requirements of the micro-surgical scissors limits the force that can be generated to puncture the tissue. To address the limitation of small output forces, we use an evolutionary algorithm to further optimize the performance of the scissors. In this study, the design of the previously developed untethered micro-surgical scissors has been modified and their performance is enhanced by determining the optimal position of the magnets as well as the direction of each magnetic moment. The developed algorithm is successfully applied to a 4-magnet configuration which results in increased net torque. This improvement in net torque is directly translated into higher cutting forces. The new configuration generates a cutting force of 58 mN from 80 generations of the evolutionary algorithm which is a 1.65 times improvement from the original design. Furthermore, the developed algorithm has the advantage that it can be deployed with minor modifications to other microrobotic tools and systems, opening up new possibilities for various medical procedures and applications.
Abstract:The rapid growth of data from edge devices has catalyzed the performance of machine learning algorithms. However, the data generated resides at client devices thus there are majorly two challenge faced by traditional machine learning paradigms - centralization of data for training and secondly for most the generated data the class labels are missing and there is very poor incentives to clients to manually label their data owing to high cost and lack of expertise. To overcome these issues, there have been initial attempts to handle unlabelled data in a privacy preserving distributed manner using unsupervised federated data clustering. The goal is partition the data available on clients into $k$ partitions (called clusters) without actual exchange of data. Most of the existing algorithms are highly dependent on data distribution patterns across clients or are computationally expensive. Furthermore, due to presence of skewed nature of data across clients in most of practical scenarios existing models might result in clients suffering high clustering cost making them reluctant to participate in federated process. To this, we are first to introduce the idea of personalization in federated clustering. The goal is achieve balance between achieving lower clustering cost and at same time achieving uniform cost across clients. We propose p-FClus that addresses these goal in a single round of communication between server and clients. We validate the efficacy of p-FClus against variety of federated datasets showcasing it's data independence nature, applicability to any finite $\ell$-norm, while simultaneously achieving lower cost and variance.
Abstract:In recent years, there has been a surge of interest in proving discretization bounds for diffusion models. These works show that for essentially any data distribution, one can approximately sample in polynomial time given a sufficiently accurate estimate of its score functions at different noise levels. In this work, we propose a new discretization scheme for diffusion models inspired by Shen and Lee's randomized midpoint method for log-concave sampling~\cite{ShenL19}. We prove that this approach achieves the best known dimension dependence for sampling from arbitrary smooth distributions in total variation distance ($\widetilde O(d^{5/12})$ compared to $\widetilde O(\sqrt{d})$ from prior work). We also show that our algorithm can be parallelized to run in only $\widetilde O(\log^2 d)$ parallel rounds, constituting the first provable guarantees for parallel sampling with diffusion models. As a byproduct of our methods, for the well-studied problem of log-concave sampling in total variation distance, we give an algorithm and simple analysis achieving dimension dependence $\widetilde O(d^{5/12})$ compared to $\widetilde O(\sqrt{d})$ from prior work.
Abstract:Diffusion models are a remarkably effective way of learning and sampling from a distribution $p(x)$. In posterior sampling, one is also given a measurement model $p(y \mid x)$ and a measurement $y$, and would like to sample from $p(x \mid y)$. Posterior sampling is useful for tasks such as inpainting, super-resolution, and MRI reconstruction, so a number of recent works have given algorithms to heuristically approximate it; but none are known to converge to the correct distribution in polynomial time. In this paper we show that posterior sampling is \emph{computationally intractable}: under the most basic assumption in cryptography -- that one-way functions exist -- there are instances for which \emph{every} algorithm takes superpolynomial time, even though \emph{unconditional} sampling is provably fast. We also show that the exponential-time rejection sampling algorithm is essentially optimal under the stronger plausible assumption that there are one-way functions that take exponential time to invert.
Abstract:Score-based diffusion models have become the most popular approach to deep generative modeling of images, largely due to their empirical performance and reliability. Recently, a number of theoretical works \citep{chen2022, Chen2022ImprovedAO, Chenetal23flowode, benton2023linear} have shown that diffusion models can efficiently sample, assuming $L^2$-accurate score estimates. The score-matching objective naturally approximates the true score in $L^2$, but the sample complexity of existing bounds depends \emph{polynomially} on the data radius and desired Wasserstein accuracy. By contrast, the time complexity of sampling is only logarithmic in these parameters. We show that estimating the score in $L^2$ \emph{requires} this polynomial dependence, but that a number of samples that scales polylogarithmically in the Wasserstein accuracy actually do suffice for sampling. We show that with a polylogarithmic number of samples, the ERM of the score-matching objective is $L^2$ accurate on all but a probability $\delta$ fraction of the true distribution, and that this weaker guarantee is sufficient for efficient sampling.
Abstract:The mean of an unknown variance-$\sigma^2$ distribution $f$ can be estimated from $n$ samples with variance $\frac{\sigma^2}{n}$ and nearly corresponding subgaussian rate. When $f$ is known up to translation, this can be improved asymptotically to $\frac{1}{n\mathcal I}$, where $\mathcal I$ is the Fisher information of the distribution. Such an improvement is not possible for general unknown $f$, but [Stone, 1975] showed that this asymptotic convergence $\textit{is}$ possible if $f$ is $\textit{symmetric}$ about its mean. Stone's bound is asymptotic, however: the $n$ required for convergence depends in an unspecified way on the distribution $f$ and failure probability $\delta$. In this paper we give finite-sample guarantees for symmetric mean estimation in terms of Fisher information. For every $f, n, \delta$ with $n > \log \frac{1}{\delta}$, we get convergence close to a subgaussian with variance $\frac{1}{n \mathcal I_r}$, where $\mathcal I_r$ is the $r$-$\textit{smoothed}$ Fisher information with smoothing radius $r$ that decays polynomially in $n$. Such a bound essentially matches the finite-sample guarantees in the known-$f$ setting.