Harsh Vardhan

Harsh Vardhan, David Hyde, Umesh Timalsina et al.

Physics simulations like computational fluid dynamics (CFD) are a computational bottleneck in computer-aided design (CAD) optimization processes. To overcome this bottleneck, one requires either an optimization framework that is highly sample-efficient, or a fast data-driven proxy (surrogate model) for long-running simulations. Both approaches have benefits and limitations. Bayesian optimization is often used for sample efficiency, but it solves one specific problem and struggles with transferability; alternatively, surrogate models can offer fast and often more generalizable solutions for CFD problems, but gathering data for and training such models can be computationally demanding. In this work, we leverage recent advances in optimization and artificial intelligence (AI) to explore both of these potential approaches, in the context of designing an optimal unmanned underwater vehicle (UUV) hull. Our study finds that the Bayesian Optimization-Lower Condition Bound (BO-LCB) algorithm is the most sample-efficient optimization framework and has the best convergence behavior of those considered. Subsequently, we show that our DNN-based surrogate model predicts drag force on test data in tight agreement with CFD simulations, with a mean absolute percentage error (MAPE) of 1.85%. Combining these results, we demonstrate a two-orders-of-magnitude speedup (with comparable accuracy) for the design optimization process when the surrogate model is used. To our knowledge, this is the first study applying Bayesian optimization and DNN-based surrogate modeling to the problem of UUV design optimization, and we share our developments as open-source software.

Harsh Vardhan, Janos Sztipanovits

Designing an inexpensive approximate surrogate model that captures the salient features of an expensive high-fidelity behavior is a prevalent approach in design optimization. In recent times, Deep Learning (DL) models are being used as a promising surrogate computational model for engineering problems. However, the main challenge in creating a DL-based surrogate is to simulate/label a large number of design points, which is time-consuming for computationally costly and/or high-dimensional engineering problems. In the present work, we propose a novel sampling technique by combining the active learning (AL) method with DL. We call this method $ε$-weighted hybrid query strategy ($ε$-HQS) , which focuses on the evaluation of the surrogate at each learning iteration and provides an estimate of the failure probability of the surrogate in the Design Space. By reusing already collected training and test data, the learned failure probability guides the next iteration's sampling process to the region of the high probability of failure. During the empirical evaluation, better accuracy of the surrogate was observed in comparison to other methods of sample selection. We empirically evaluated this method in two different engineering design domains, finite element based static stress analysis of submarine pressure vessel(computationally costly process) and second submarine propeller design( high dimensional problem). https://github.com/vardhah/epsilon_weighted_Hybrid_Query_Strategy

Xiaofan Yu, Ludmila Cherkasova, Harsh Vardhan et al.

Federated Learning (FL) has gained increasing interest in recent years as a distributed on-device learning paradigm. However, multiple challenges remain to be addressed for deploying FL in real-world Internet-of-Things (IoT) networks with hierarchies. Although existing works have proposed various approaches to account data heterogeneity, system heterogeneity, unexpected stragglers and scalibility, none of them provides a systematic solution to address all of the challenges in a hierarchical and unreliable IoT network. In this paper, we propose an asynchronous and hierarchical framework (Async-HFL) for performing FL in a common three-tier IoT network architecture. In response to the largely varied delays, Async-HFL employs asynchronous aggregations at both the gateway and the cloud levels thus avoids long waiting time. To fully unleash the potential of Async-HFL in converging speed under system heterogeneities and stragglers, we design device selection at the gateway level and device-gateway association at the cloud level. Device selection chooses edge devices to trigger local training in real-time while device-gateway association determines the network topology periodically after several cloud epochs, both satisfying bandwidth limitation. We evaluate Async-HFL's convergence speedup using large-scale simulations based on ns-3 and a network topology from NYCMesh. Our results show that Async-HFL converges 1.08-1.31x faster in wall-clock time and saves up to 21.6% total communication cost compared to state-of-the-art asynchronous FL algorithms (with client selection). We further validate Async-HFL on a physical deployment and observe robust convergence under unexpected stragglers.

Harsh Vardhan, Peter Volgyesi, Will Hedgecock et al.

Automatic underwater vehicle hull Design optimization is a complex engineering process for generating a UUV hull with optimized properties on a given requirement. First, it involves the integration of involved computationally complex engineering simulation tools. Second, it needs integration of a sample efficient optimization framework with the integrated toolchain. To this end, we integrated the CAD tool called FreeCAD with CFD tool openFoam for automatic design evaluation. For optimization, we chose Bayesian optimization (BO), which is a well-known technique developed for optimizing time-consuming expensive engineering simulations and has proven to be very sample efficient in a variety of problems, including hyper-parameter tuning and experimental design. During the optimization process, we can handle infeasible design as constraints integrated into the optimization process. By integrating domain-specific toolchain with AI-based optimization, we executed the automatic design optimization of underwater vehicle hull design. For empirical evaluation, we took two different use cases of real-world underwater vehicle design to validate the execution of our tool.

C. Donoso-Oliva, I. Becker, P. Protopapas et al.

Taking inspiration from natural language embeddings, we present ASTROMER, a transformer-based model to create representations of light curves. ASTROMER was pre-trained in a self-supervised manner, requiring no human-labeled data. We used millions of R-band light sequences to adjust the ASTROMER weights. The learned representation can be easily adapted to other surveys by re-training ASTROMER on new sources. The power of ASTROMER consists of using the representation to extract light curve embeddings that can enhance the training of other models, such as classifiers or regressors. As an example, we used ASTROMER embeddings to train two neural-based classifiers that use labeled variable stars from MACHO, OGLE-III, and ATLAS. In all experiments, ASTROMER-based classifiers outperformed a baseline recurrent neural network trained on light curves directly when limited labeled data was available. Furthermore, using ASTROMER embeddings decreases computational resources needed while achieving state-of-the-art results. Finally, we provide a Python library that includes all the functionalities employed in this work. The library, main code, and pre-trained weights are available at https://github.com/astromer-science

Sarthak Kapoor, Harsh Vardhan, Umesh Timalsina et al.

High fidelity design evaluation processes such as Computational Fluid Dynamics and Finite Element Analysis are often replaced with data driven surrogates to reduce computational cost in engineering design optimization. However, building accurate surrogate models still requires a large number of expensive simulations. To address this challenge, we introduce epsilon HQS, a scalable active learning strategy that leverages a student teacher framework to train deep neural networks efficiently. Unlike Bayesian AL methods, which are computationally demanding with DNNs, epsilon HQS selectively queries informative samples to reduce labeling cost. Applied to CFD, FEA, and propeller design tasks, our method achieves higher accuracy under fixed labeling cost budgets.

Harsh Vardhan, Janos Sztipanovits

Most machine learning-based regressors extract information from data collected via past observations of limited length to make predictions in the future. Consequently, when input to these trained models is data with significantly different statistical properties from data used for training, there is no guarantee of accurate prediction. Consequently, using these models on out-of-distribution input data may result in a completely different predicted outcome from the desired one, which is not only erroneous but can also be hazardous in some cases. Successful deployment of these machine learning models in any system requires a detection system, which should be able to distinguish between out-of-distribution and in-distribution data (i.e. similar to training data). In this paper, we introduce a novel approach for this detection process using a Reduced Robust Random Cut Forest (RRRCF) data structure, which can be used on both small and large data sets. Similar to the Robust Random Cut Forest (RRCF), RRRCF is a structured, but a reduced representation of the training data sub-space in form of cut trees. Empirical results of this method on both low and high-dimensional data showed that inference about data being in/out of training distribution can be made efficiently and the model is easy to train with no difficult hyper-parameter tuning. The paper discusses two different use-cases for testing and validating results.

Harsh Vardhan, Peter Volgyesi, Janos Sztipanovits

In computer-aided engineering design, the goal of a designer is to find an optimal design on a given requirement using the numerical simulator in loop with an optimization method. In this design optimization process, a good design optimization process is one that can reduce the time from inception to design. In this work, we take a class of design problem, that is computationally cheap to evaluate but has high dimensional design space. In such cases, traditional surrogate-based optimization does not offer any benefits. In this work, we propose an alternative way to use ML model to surrogate the design process that formulates the search problem as an inverse problem and can save time by finding the optimal design or at least a good initial seed design for optimization. By using this trained surrogate model with the traditional optimization method, we can get the best of both worlds. We call this as Surrogate Assisted Optimization (SAO)- a hybrid approach by mixing ML surrogate with the traditional optimization method. Empirical evaluations of propeller design problems show that a better efficient design can be found in fewer evaluations using SAO.

Harsh Vardhan, Janos Sztipanovits

During the design process of an autonomous underwater vehicle (AUV), the pressure vessel has a critical role. The pressure vessel contains dry electronics, power sources, and other sensors that can not be flooded. A traditional design approach for a pressure vessel design involves running multiple Finite Element Analysis (FEA) based simulations and optimizing the design to find the best suitable design which meets the requirement. Running these FEAs are computationally very costly for any optimization process and it becomes difficult to run even hundreds of evaluation. In such a case, a better approach is the surrogate design with the goal of replacing FEA-based prediction with some learning-based regressor. Once the surrogate is trained for a class of problem, then the learned response surface can be used to analyze the stress effect without running the FEA for that class of problem. The challenge of creating a surrogate for a class of problems is data generation. Since the process is computationally costly, it is not possible to densely sample the design space and the learning response surface on sparse data set becomes difficult. During experimentation, we observed that a Deep Learning-based surrogate outperforms other regression models on such sparse data. In the present work, we are utilizing the Deep Learning-based model to replace the costly finite element analysis-based simulation process. By creating the surrogate we speed up the prediction on the other design much faster than direct Finite element Analysis. We also compared our DL-based surrogate with other classical Machine Learning (ML) based regression models( random forest and Gradient Boost regressor). We observed on the sparser data, the DL-based surrogate performs much better than other regression models.

Heng Zhu, Harsh Vardhan, Arya Mazumdar

In distributed training of machine learning models, gradient descent with local iterative steps is a very popular method, variants of which are commonly known as Local-SGD or the Federated Averaging (FedAvg). In this method, gradient steps based on local datasets are taken independently in distributed compute nodes to update the local models, which are then aggregated intermittently. Although the existing convergence analysis suggests that with heterogeneous data, FedAvg encounters quick performance degradation as the number of local steps increases, it is shown to work quite well in practice, especially in the distributed training of large language models. In this work we try to explain this good performance from a viewpoint of implicit bias in Local Gradient Descent (Local-GD) with a large number of local steps. In overparameterized regime, the gradient descent at each compute node would lead the model to a specific direction locally. We characterize the dynamics of the aggregated global model and compare it to the centralized model trained with all of the data in one place. In particular, we analyze the implicit bias of gradient descent on linear models, for both regression and classification tasks. Our analysis shows that the aggregated global model converges exactly to the centralized model for regression tasks, and converges (in direction) to the same feasible set as centralized model for classification tasks. We further propose a Modified Local-GD with a refined aggregation and theoretically show it converges to the centralized model in direction for linear classification. We empirically verified our theoretical findings in linear models and also conducted experiments on distributed fine-tuning of pretrained neural networks to further apply our theory.

Harsh Vardhan, Sebastian U. Stich

Non-convex optimization problems are ubiquitous in machine learning, especially in Deep Learning. While such complex problems can often be successfully optimized in practice by using stochastic gradient descent (SGD), theoretical analysis cannot adequately explain this success. In particular, the standard analyses do not show global convergence of SGD on non-convex functions, and instead show convergence to stationary points (which can also be local minima or saddle points). We identify a broad class of nonconvex functions for which we can show that perturbed SGD (gradient descent perturbed by stochastic noise -- covering SGD as a special case) converges to a global minimum (or a neighborhood thereof), in contrast to gradient descent without noise that can get stuck in local minima far from a global solution. For example, on non-convex functions that are relatively close to a convex-like (strongly convex or PL) function we show that SGD can converge linearly to a global optimum.